context stringlengths 545 71.9k | questionsrc stringlengths 16 10.2k | question stringlengths 11 563 |
|---|---|---|
what is torque ? torque is a measure of the force that can cause an object to rotate about an axis . just as force is what causes an object to accelerate in linear kinematics , torque is what causes an object to acquire angular acceleration . torque is a vector quantity . the direction of the torque vector depends on t... | what is torque ? torque is a measure of the force that can cause an object to rotate about an axis . | what is the relationship between torque and radius ? |
what is torque ? torque is a measure of the force that can cause an object to rotate about an axis . just as force is what causes an object to accelerate in linear kinematics , torque is what causes an object to acquire angular acceleration . torque is a vector quantity . the direction of the torque vector depends on t... | what is torque ? torque is a measure of the force that can cause an object to rotate about an axis . | so why is the torque applied to spin a top down to the ground ( or up in the air ) ? |
what is torque ? torque is a measure of the force that can cause an object to rotate about an axis . just as force is what causes an object to accelerate in linear kinematics , torque is what causes an object to acquire angular acceleration . torque is a vector quantity . the direction of the torque vector depends on t... | the general relationship can be non-linear and differs for different types of motor as shown in figure 5 . how can we increase or decrease torque ? it is often necessary to increase or decrease the torque produced by a motor to suit different applications . | can someone please explain why using gears will cause decrease in speed if there is an increase in torque ? |
what is torque ? torque is a measure of the force that can cause an object to rotate about an axis . just as force is what causes an object to accelerate in linear kinematics , torque is what causes an object to acquire angular acceleration . torque is a vector quantity . the direction of the torque vector depends on t... | exercise 2a : a gasoline engine producing $ 150~\mathrm { nm } $ of torque at a rotational speed of $ 300~\mathrm { rad/s } $ is used to drive a winch and lift a weight as shown in figure 6 . the winch drum has a radius of 0.25 m and is driven from the engine via a 1:50 speed reduction gear . what mass could be raised ... | for # 2a , what is speed reduction ? |
what is torque ? torque is a measure of the force that can cause an object to rotate about an axis . just as force is what causes an object to accelerate in linear kinematics , torque is what causes an object to acquire angular acceleration . torque is a vector quantity . the direction of the torque vector depends on t... | what is torque ? torque is a measure of the force that can cause an object to rotate about an axis . | and i do not understand how changing gear increases the torque ? |
what is torque ? torque is a measure of the force that can cause an object to rotate about an axis . just as force is what causes an object to accelerate in linear kinematics , torque is what causes an object to acquire angular acceleration . torque is a vector quantity . the direction of the torque vector depends on t... | here , $ \alpha $ is the angular acceleration . $ i $ is the rotational inertia , a property of a rotating system which depends on the mass distribution of the system . the larger $ i $ , the harder it is for an object to acquire angular acceleration . | when the pivot point is off-center , would you calculate the radius of an object on that system to be measured from the center of mass or the pivot point ? |
what is torque ? torque is a measure of the force that can cause an object to rotate about an axis . just as force is what causes an object to accelerate in linear kinematics , torque is what causes an object to acquire angular acceleration . torque is a vector quantity . the direction of the torque vector depends on t... | in fact , the horsepower of an engine is not typically measured directly , but calculated from measured torque and rotational speed . the relationship is : $ \begin { align } p & amp ; = \frac { \mathrm { force } \cdot \mathrm { distance } } { \mathrm { time } } \ & amp ; = \frac { \mathrm { f } \cdot 2\pi r } { t } \ ... | why , why is the distance 2 pi r ? |
what is torque ? torque is a measure of the force that can cause an object to rotate about an axis . just as force is what causes an object to accelerate in linear kinematics , torque is what causes an object to acquire angular acceleration . torque is a vector quantity . the direction of the torque vector depends on t... | if the net torque on a rotatable object is zero then it will be in rotational equilibrium and not able to acquire angular acceleration . exercise 1 : consider the wheel shown in figure 4 , acted on by two forces . what magnitude of the force $ f_2 $ will be required for the wheel to be in rotational equilibrium ? | in exercise 1 , will the answer change if we take the origin of the position vector ( 75 mm and 100 mm ) as something other than the center of the wheel ? |
what is torque ? torque is a measure of the force that can cause an object to rotate about an axis . just as force is what causes an object to accelerate in linear kinematics , torque is what causes an object to acquire angular acceleration . torque is a vector quantity . the direction of the torque vector depends on t... | the winch drum has a radius of 0.25 m and is driven from the engine via a 1:50 speed reduction gear . what mass could be raised with this setup ? ( assume the winch is in rotational equilibrium , i.e . | what is the difference between the center of mass and the center of gravity ? |
what is torque ? torque is a measure of the force that can cause an object to rotate about an axis . just as force is what causes an object to accelerate in linear kinematics , torque is what causes an object to acquire angular acceleration . torque is a vector quantity . the direction of the torque vector depends on t... | exercise 2a : a gasoline engine producing $ 150~\mathrm { nm } $ of torque at a rotational speed of $ 300~\mathrm { rad/s } $ is used to drive a winch and lift a weight as shown in figure 6 . the winch drum has a radius of 0.25 m and is driven from the engine via a 1:50 speed reduction gear . what mass could be raised ... | what exactly is a speed reduction gear in simple terms ? |
what is torque ? torque is a measure of the force that can cause an object to rotate about an axis . just as force is what causes an object to accelerate in linear kinematics , torque is what causes an object to acquire angular acceleration . torque is a vector quantity . the direction of the torque vector depends on t... | the use of adjustable gearing is necessary to obtain good performance in vehicles powered by combustion engines . these engines produce maximum torque only for a narrow range of high rotational speeds . adjustable gearing allows sufficient torque to be delivered to the wheels at any given rotational speed of the engine... | i am looking for more details as to why exactly electric motors are able to produce high torque at low speeds as compared to combustion engines ? |
what is torque ? torque is a measure of the force that can cause an object to rotate about an axis . just as force is what causes an object to accelerate in linear kinematics , torque is what causes an object to acquire angular acceleration . torque is a vector quantity . the direction of the torque vector depends on t... | adjustable gearing allows sufficient torque to be delivered to the wheels at any given rotational speed of the engine . bicycles require gearing because of the inability of humans to pedal with a cadance sufficient to achieve a useful speed when driving a wheel directly ( unless one is cycling a penny-farthing ) . adju... | why do large structures and bridges require more than just vertical and horizontal supports ? |
what is torque ? torque is a measure of the force that can cause an object to rotate about an axis . just as force is what causes an object to accelerate in linear kinematics , torque is what causes an object to acquire angular acceleration . torque is a vector quantity . the direction of the torque vector depends on t... | what is torque ? torque is a measure of the force that can cause an object to rotate about an axis . | why are diagonal supports beneficial ? |
what is torque ? torque is a measure of the force that can cause an object to rotate about an axis . just as force is what causes an object to accelerate in linear kinematics , torque is what causes an object to acquire angular acceleration . torque is a vector quantity . the direction of the torque vector depends on t... | international journal of sports physiology and performance . march 2009 ; 4 ( 1 ) :3-17 . diesel engine : mercedes 250 cdi otto cycle engine : mercedes e250 electric motor : tesla model s 85 steam locomotive : 2-8-0 `` consolidation '' locomotive at 70 % boiler capacity penny-farthing : wikimedia commons | a metallic cube of side 1.5m and of mass 3.2metric ton is on horizontal rough floor the minimum horizontal force that should be applied on the cube at a height 1.2m from the floor to turn the cube about its lower edge is ? |
what is torque ? torque is a measure of the force that can cause an object to rotate about an axis . just as force is what causes an object to accelerate in linear kinematics , torque is what causes an object to acquire angular acceleration . torque is a vector quantity . the direction of the torque vector depends on t... | what is torque ? torque is a measure of the force that can cause an object to rotate about an axis . | how are torque and the number of gears and speed related ? |
the subject of the flagellation piero della francesca ’ s flagellation of christ is proof that , sometimes , good things really do come in small packages . despite the panel ’ s size ( only 58.4 cm × 81.5 cm ) , the painting has been a mainstay in the last century in discussions of quattrocento ( fifteenth century ) pa... | above all , piero ’ s obsession with perspective ( the naturalistic recession in to space ) , is evident . in fact , the artist was the author of a treatise on perspective , entitled de perspectiva pingendi ( on the perspective of painting ) and was also known as a mathematician and geometer . who are the men in the fo... | what is a `` geometer '' if it is not the same thing as a mathematician ? |
the subject of the flagellation piero della francesca ’ s flagellation of christ is proof that , sometimes , good things really do come in small packages . despite the panel ’ s size ( only 58.4 cm × 81.5 cm ) , the painting has been a mainstay in the last century in discussions of quattrocento ( fifteenth century ) pa... | the traditional identification of these three men is that the young man in the center is oddantanio da montefeltro , ruler of urbino , flanked on either side by his advisors . all three of these men were killed in a conspiracy . in this case , it is suggested that the patron of the painting was federigo da montefeltro ... | in the seventh paragraph where christine talked about christ is being flogged by men , but was n't pontius pilate with christ and the three men asking him questions like are you the king of the jews and other things ? |
what are inclines ? slides at the park , steep driveways , and shipping truck loading ramps are all examples of inclines . inclines or inclined planes are diagonal surfaces that objects can sit on , slide up , slide down , roll up , or roll down . inclines are useful since they can reduce the amount of force required t... | they know the coefficient of static friction between their tires and the concrete driveway is $ 0.75 $ . what is the maximum angle from horizontal that the person can make their driveway and still park their car on it without slipping ? we 'll start by using newton 's second law for the parallel direction . | is the angle of incline the same as the angle pictured between the mg and mgcos ? |
what are inclines ? slides at the park , steep driveways , and shipping truck loading ramps are all examples of inclines . inclines or inclined planes are diagonal surfaces that objects can sit on , slide up , slide down , roll up , or roll down . inclines are useful since they can reduce the amount of force required t... | we 'll start by using newton 's second law for the parallel direction . $ a_\parallel=\dfrac { \sigma f_\parallel } { m } \quad \text { ( use newton 's second law for the parallel direction ) } $ $ a_\parallel=\dfrac { mg\text { sin } \theta-f_s } { m } \quad \text { ( plug in the parallel forces of gravity and static ... | like how did sine theta get on the other side without being negative ? |
what are inclines ? slides at the park , steep driveways , and shipping truck loading ramps are all examples of inclines . inclines or inclined planes are diagonal surfaces that objects can sit on , slide up , slide down , roll up , or roll down . inclines are useful since they can reduce the amount of force required t... | inclines are useful since they can reduce the amount of force required to move an object vertically . they 're considered one of the six classical simple machines . how do we use newton 's second law when dealing with inclined planes ? | also why did we do tan negative one all of a sudden ? |
what are inclines ? slides at the park , steep driveways , and shipping truck loading ramps are all examples of inclines . inclines or inclined planes are diagonal surfaces that objects can sit on , slide up , slide down , roll up , or roll down . inclines are useful since they can reduce the amount of force required t... | slides at the park , steep driveways , and shipping truck loading ramps are all examples of inclines . inclines or inclined planes are diagonal surfaces that objects can sit on , slide up , slide down , roll up , or roll down . inclines are useful since they can reduce the amount of force required to move an object ver... | why would one just sit there and the other would roll down the surface ? |
what are inclines ? slides at the park , steep driveways , and shipping truck loading ramps are all examples of inclines . inclines or inclined planes are diagonal surfaces that objects can sit on , slide up , slide down , roll up , or roll down . inclines are useful since they can reduce the amount of force required t... | in other words , for an object sitting or sliding on an incline , $ \large f_n=mg\text { cos } \theta $ what do solved examples involving inclines look like ? example 1 : snowy sliding sled a child slides down a snowy hill on a sled . the angle the hill makes with respect with horizontal is $ \theta=30^o $ and the coef... | in example 1 , is fk in the equation , mgxsin ( o ) - fk , because if you look at the diagram with respect to the box ( move your head to the right , then fk is going to the left which by convention is negative ? |
what are inclines ? slides at the park , steep driveways , and shipping truck loading ramps are all examples of inclines . inclines or inclined planes are diagonal surfaces that objects can sit on , slide up , slide down , roll up , or roll down . inclines are useful since they can reduce the amount of force required t... | what is the normal force $ f_n $ for an object on an incline ? the normal force $ f_n $ is always perpendicular to the surface exerting the force . so an inclined plane will exert a normal force perpendicular to the surface of the incline . | would the frictional force be divided by 4 ? |
what are inclines ? slides at the park , steep driveways , and shipping truck loading ramps are all examples of inclines . inclines or inclined planes are diagonal surfaces that objects can sit on , slide up , slide down , roll up , or roll down . inclines are useful since they can reduce the amount of force required t... | the angle the hill makes with respect with horizontal is $ \theta=30^o $ and the coefficient of kinetic friction between the sled and the hill is $ \mu_k=0.150 $ . the combined mass of the child and sled is $ 65.0 \text { kg } $ . what is the acceleration of the sled down the hill ? | why does n't the acceleration depend on mass ? |
what are inclines ? slides at the park , steep driveways , and shipping truck loading ramps are all examples of inclines . inclines or inclined planes are diagonal surfaces that objects can sit on , slide up , slide down , roll up , or roll down . inclines are useful since they can reduce the amount of force required t... | inclines or inclined planes are diagonal surfaces that objects can sit on , slide up , slide down , roll up , or roll down . inclines are useful since they can reduce the amount of force required to move an object vertically . they 're considered one of the six classical simple machines . | does n't the use of an incline plane also reduce the amount of work done as well ? |
what are inclines ? slides at the park , steep driveways , and shipping truck loading ramps are all examples of inclines . inclines or inclined planes are diagonal surfaces that objects can sit on , slide up , slide down , roll up , or roll down . inclines are useful since they can reduce the amount of force required t... | inclines or inclined planes are diagonal surfaces that objects can sit on , slide up , slide down , roll up , or roll down . inclines are useful since they can reduce the amount of force required to move an object vertically . they 're considered one of the six classical simple machines . | or only reduces the amount of force applied ? |
what are inclines ? slides at the park , steep driveways , and shipping truck loading ramps are all examples of inclines . inclines or inclined planes are diagonal surfaces that objects can sit on , slide up , slide down , roll up , or roll down . inclines are useful since they can reduce the amount of force required t... | we can use newton 's second law in the direction parallel to the incline to get , $ a_\parallel=\dfrac { \sigma f_\parallel } { m } \quad \text { ( use newton 's second law for the parallel direction ) } $ $ a_\parallel=\dfrac { mg\text { sin } \theta-f_k } { m } \quad \text { ( plug in the parallel forces ) } $ $ a_\p... | would n't the driveway be a case where we ca n't round up ? |
what are inclines ? slides at the park , steep driveways , and shipping truck loading ramps are all examples of inclines . inclines or inclined planes are diagonal surfaces that objects can sit on , slide up , slide down , roll up , or roll down . inclines are useful since they can reduce the amount of force required t... | what is the normal force $ f_n $ for an object on an incline ? the normal force $ f_n $ is always perpendicular to the surface exerting the force . so an inclined plane will exert a normal force perpendicular to the surface of the incline . | why do we put mass times the force of the gravitational field ( m*g ) instead of simply the force of gravity ? |
what are inclines ? slides at the park , steep driveways , and shipping truck loading ramps are all examples of inclines . inclines or inclined planes are diagonal surfaces that objects can sit on , slide up , slide down , roll up , or roll down . inclines are useful since they can reduce the amount of force required t... | they know the coefficient of static friction between their tires and the concrete driveway is $ 0.75 $ . what is the maximum angle from horizontal that the person can make their driveway and still park their car on it without slipping ? we 'll start by using newton 's second law for the parallel direction . | will in real life - a car fall from 37 degree steep driveway ? |
what are inclines ? slides at the park , steep driveways , and shipping truck loading ramps are all examples of inclines . inclines or inclined planes are diagonal surfaces that objects can sit on , slide up , slide down , roll up , or roll down . inclines are useful since they can reduce the amount of force required t... | be careful , people often mix up whether they should use $ \text { sine } $ or $ \text { cosine } $ for a given component . what is the normal force $ f_n $ for an object on an incline ? the normal force $ f_n $ is always perpendicular to the surface exerting the force . | what angle of inclination would be most efficient on a ramp , so that the speed of the object that is pushed up is constant ? |
what are inclines ? slides at the park , steep driveways , and shipping truck loading ramps are all examples of inclines . inclines or inclined planes are diagonal surfaces that objects can sit on , slide up , slide down , roll up , or roll down . inclines are useful since they can reduce the amount of force required t... | inclines are useful since they can reduce the amount of force required to move an object vertically . they 're considered one of the six classical simple machines . how do we use newton 's second law when dealing with inclined planes ? | exercise number one why two m in the numerator cancels out with one m in the denominator ? |
what are inclines ? slides at the park , steep driveways , and shipping truck loading ramps are all examples of inclines . inclines or inclined planes are diagonal surfaces that objects can sit on , slide up , slide down , roll up , or roll down . inclines are useful since they can reduce the amount of force required t... | they know the coefficient of static friction between their tires and the concrete driveway is $ 0.75 $ . what is the maximum angle from horizontal that the person can make their driveway and still park their car on it without slipping ? we 'll start by using newton 's second law for the parallel direction . | is n't the maximum angle of inclination ( so that the car does n't slip ) called the angle of repose ? |
what are inclines ? slides at the park , steep driveways , and shipping truck loading ramps are all examples of inclines . inclines or inclined planes are diagonal surfaces that objects can sit on , slide up , slide down , roll up , or roll down . inclines are useful since they can reduce the amount of force required t... | they know the coefficient of static friction between their tires and the concrete driveway is $ 0.75 $ . what is the maximum angle from horizontal that the person can make their driveway and still park their car on it without slipping ? we 'll start by using newton 's second law for the parallel direction . | in example 2 , why does n't the angle depend on the car 's mass ? |
what are inclines ? slides at the park , steep driveways , and shipping truck loading ramps are all examples of inclines . inclines or inclined planes are diagonal surfaces that objects can sit on , slide up , slide down , roll up , or roll down . inclines are useful since they can reduce the amount of force required t... | we can use newton 's second law in the direction parallel to the incline to get , $ a_\parallel=\dfrac { \sigma f_\parallel } { m } \quad \text { ( use newton 's second law for the parallel direction ) } $ $ a_\parallel=\dfrac { mg\text { sin } \theta-f_k } { m } \quad \text { ( plug in the parallel forces ) } $ $ a_\p... | how much friction is needed to stop a 50kg item traveling 50n ? |
early encounters with europeans were often recorded in african art . look closely at the top of the mask above ( and the detail below ) . do you see faces ? these represent portuguese explorers with beards and hats ( flanked by mudfish ) who visited the benin kingdom along the west coast of africa in the late 1400s . t... | early encounters with europeans were often recorded in african art . look closely at the top of the mask above ( and the detail below ) . | do you happen to know any such galleon-canoe picture ? |
the remover of obstacles the elephant-headed ganesha is renowned throughout india as the lord of beginnings , and both the placer and the remover of obstacles . it is for this reason that he is worshipped before any new venture is begun , when his benediction is essential . temporary statues are created every year for ... | temporary statues are created every year for the ganeshchaturthi festival in mumbai , and are placed in public or domestic shrines before being immersed in water at the end of the celebrations . february 3 , 2014 was the hindu festival of ganesha jayanti , ganesha ’ s birthday . the main annual ganesha festival , ganes... | why do we need to put immerse ganesha in into the water after ganesha jayanti ? |
overview in the late nineteenth century , the united states abandoned its century-long commitment to isolationism and became an imperial power . after the spanish-american war , the united states exercised significant control over cuba , annexed hawaii , and claimed guam , puerto rico , and the philippines as territori... | colonies not only provided sources of valuable raw materials ( diamonds , gold , timber , oil , rubber , and many others ) for the imperial power , their populations served as markets for the industrial products made in the home country . markets were particularly important for the united states , which had emerged as ... | what was the `` gilded age '' ? |
overview in the late nineteenth century , the united states abandoned its century-long commitment to isolationism and became an imperial power . after the spanish-american war , the united states exercised significant control over cuba , annexed hawaii , and claimed guam , puerto rico , and the philippines as territori... | the irony that a former colony , which had once rebelled against a distant government across the ocean , was now governing distant peoples was not lost on contemporary observers . others protested that imperialism would include people of `` inferior '' races in the american body politic . the anti-imperialist league , ... | why did some american citizens oppose imperialization and others supported it ? |
overview in the late nineteenth century , the united states abandoned its century-long commitment to isolationism and became an imperial power . after the spanish-american war , the united states exercised significant control over cuba , annexed hawaii , and claimed guam , puerto rico , and the philippines as territori... | overview in the late nineteenth century , the united states abandoned its century-long commitment to isolationism and became an imperial power . after the spanish-american war , the united states exercised significant control over cuba , annexed hawaii , and claimed guam , puerto rico , and the philippines as territori... | what is the puck thing ? |
overview in the late nineteenth century , the united states abandoned its century-long commitment to isolationism and became an imperial power . after the spanish-american war , the united states exercised significant control over cuba , annexed hawaii , and claimed guam , puerto rico , and the philippines as territori... | in the process , they had acquired significant influence over cuba , annexed hawaii , and claimed puerto rico , guam , and the philippines as territories . not everyone was thrilled about the united states ' new role as an imperial power . the irony that a former colony , which had once rebelled against a distant gover... | is it america taking over most of the power ? |
overview in the late nineteenth century , the united states abandoned its century-long commitment to isolationism and became an imperial power . after the spanish-american war , the united states exercised significant control over cuba , annexed hawaii , and claimed guam , puerto rico , and the philippines as territori... | was colonialism different than manifest destiny , or just a new phase of it ? should the united states have become an empire ? how long could the united states have maintained an isolationist policy towards the world ? | in the first paragraph of `` the united states becomes an empire '' , how can the spanish be crushed with such ease by the americans ? |
overview in the late nineteenth century , the united states abandoned its century-long commitment to isolationism and became an imperial power . after the spanish-american war , the united states exercised significant control over cuba , annexed hawaii , and claimed guam , puerto rico , and the philippines as territori... | convinced of the superiority of people of anglo-saxon descent , these americans saw it as the `` white man 's burden '' ( a phrase taken from a poem by the author and imperialist booster rudyard kipling ) to govern and somehow uplift the people of latin america and the pacific—whether they wanted it or not. $ ^5 $ what... | did americans really support imperialism or is it the way they wish us to believe ? |
overview in the late nineteenth century , the united states abandoned its century-long commitment to isolationism and became an imperial power . after the spanish-american war , the united states exercised significant control over cuba , annexed hawaii , and claimed guam , puerto rico , and the philippines as territori... | the united states becomes an empire these questions were still unanswered when disturbing news came from cuba , where guerrilla rebels were attempting to throw off the yoke of spanish rule . after an american warship exploded in havana harbor , the united states declared war on spain . spain was badly outmatched , and ... | so did the spanish-american war kind of cut it for the united states , making them anti-social and want to cut all ties with people so they did n't have to worry about dependence , or to depend on others sort of speak ? |
overview in the late nineteenth century , the united states abandoned its century-long commitment to isolationism and became an imperial power . after the spanish-american war , the united states exercised significant control over cuba , annexed hawaii , and claimed guam , puerto rico , and the philippines as territori... | colonies not only provided sources of valuable raw materials ( diamonds , gold , timber , oil , rubber , and many others ) for the imperial power , their populations served as markets for the industrial products made in the home country . markets were particularly important for the united states , which had emerged as ... | what was the `` gilded age '' ? |
overview in the late nineteenth century , the united states abandoned its century-long commitment to isolationism and became an imperial power . after the spanish-american war , the united states exercised significant control over cuba , annexed hawaii , and claimed guam , puerto rico , and the philippines as territori... | after an american warship exploded in havana harbor , the united states declared war on spain . spain was badly outmatched , and within six weeks the united states had triumphed in the spanish-american war . in the process , they had acquired significant influence over cuba , annexed hawaii , and claimed puerto rico , ... | what about the uss maine being a false flag to get the us into war , in addition to the fake news our press was spreading about the spanish at the time ? |
overview in the late nineteenth century , the united states abandoned its century-long commitment to isolationism and became an imperial power . after the spanish-american war , the united states exercised significant control over cuba , annexed hawaii , and claimed guam , puerto rico , and the philippines as territori... | the united states becomes an empire these questions were still unanswered when disturbing news came from cuba , where guerrilla rebels were attempting to throw off the yoke of spanish rule . after an american warship exploded in havana harbor , the united states declared war on spain . spain was badly outmatched , and ... | why is the lady from colombia pictures invalved with war ? |
overview in the late nineteenth century , the united states abandoned its century-long commitment to isolationism and became an imperial power . after the spanish-american war , the united states exercised significant control over cuba , annexed hawaii , and claimed guam , puerto rico , and the philippines as territori... | the united states becomes an empire these questions were still unanswered when disturbing news came from cuba , where guerrilla rebels were attempting to throw off the yoke of spanish rule . after an american warship exploded in havana harbor , the united states declared war on spain . spain was badly outmatched , and ... | why did the american harbor exploded ? |
the forbidden city is a large precinct of red walls and yellow glazed roof tiles located in the heart of china ’ s capital , beijing . as its name suggests , the precinct is a micro-city in its own right . measuring 961 meters in length and 753 meters in width , the forbidden city is composed of more than 90 palace com... | the establishment of the qing dynasty in 1644 did not lessen the forbidden city ’ s pivotal status , as the manchu imperial family continued to live and rule there . while no major change has been made since its completion , the precinct has undergone various renovations and minor constructions well into the twentieth-... | is it made of coral ? |
the forbidden city is a large precinct of red walls and yellow glazed roof tiles located in the heart of china ’ s capital , beijing . as its name suggests , the precinct is a micro-city in its own right . measuring 961 meters in length and 753 meters in width , the forbidden city is composed of more than 90 palace com... | such architectural and philosophical symmetry , however , fundamentally changed when the empress dowager cixi ( 1835-1908 ) renovated the palace of eternal spring ( changchungong ) and the palace of gathered elegance ( chuxiugong ) in the west part of the inner court for her fortieth and fiftieth birthday in 1874 and 1... | how does the government control the lives of the university students ? |
the forbidden city is a large precinct of red walls and yellow glazed roof tiles located in the heart of china ’ s capital , beijing . as its name suggests , the precinct is a micro-city in its own right . measuring 961 meters in length and 753 meters in width , the forbidden city is composed of more than 90 palace com... | the manchus preserved most of these structures but also added spaces for their own shamanic beliefs . the forbidden city now today , the forbidden city is still changing . as a modern museum and an historical site , the museum strikes a balance by maintaining the structures and restoring the interiors of the palace com... | was there any specific place for the emperors to live before the forbidden city was built ? |
the forbidden city is a large precinct of red walls and yellow glazed roof tiles located in the heart of china ’ s capital , beijing . as its name suggests , the precinct is a micro-city in its own right . measuring 961 meters in length and 753 meters in width , the forbidden city is composed of more than 90 palace com... | the architectural style also reflects a sense of hierarchy . each structure was designed in accordance with the treatise on architectural methods or state building standards ( yingzao fashi ) , an eleventh-century manual that specified particular designs for buildings of different ranks in chinese social structure . pu... | how are the buildings engineered ? |
floating down the usumacinta river in southeastern mexico and northwestern guatemala , various maya sites materialize out of the dense jungle , some rising above the canopy and others subsumed by a tangle of green growth . one such site is yaxchilán ( pronounced yash-chee-lan ) located in chiapas , mexico ( close to th... | the other lintels show a similar concern with rulership . lintel 2 displays bird jaguar and his son and heir , chel te ’ chan k ’ inich ( later known as shield jaguar iv ) , while another depicts bird jaguar once again dressed in royal regalia . * hieroglyphic stairway # 2 leads up to the building . | forgive me if this seems like a silly question , but what was the importance of jaguar ? |
floating down the usumacinta river in southeastern mexico and northwestern guatemala , various maya sites materialize out of the dense jungle , some rising above the canopy and others subsumed by a tangle of green growth . one such site is yaxchilán ( pronounced yash-chee-lan ) located in chiapas , mexico ( close to th... | it was most likely built by bird jaguar iv , who like his father shield jaguar ii engaged in a series of building projects and commissioned various monuments as part of his campaign to legitimate his rule . bird jaguar ascended the throne ten years after his father died , suggesting that there was perhaps a conflict ab... | how do i become a historian when i grow up ? |
overview with the invention of the cotton gin , cotton became the cash crop of the deep south , stimulating increased demand for enslaved people from the upper south to toil the land . as the disparity between plantation owners and poor white people widened in the deep south , deeply entrenched racism blurred perceived... | overview with the invention of the cotton gin , cotton became the cash crop of the deep south , stimulating increased demand for enslaved people from the upper south to toil the land . as the disparity between plantation owners and poor white people widened in the deep south , deeply entrenched racism blurred perceived... | why was cotton vital for cash crop in the deep south and important to its economy ? |
overview with the invention of the cotton gin , cotton became the cash crop of the deep south , stimulating increased demand for enslaved people from the upper south to toil the land . as the disparity between plantation owners and poor white people widened in the deep south , deeply entrenched racism blurred perceived... | enslaved people , cotton , and the steamship transformed the city from a relatively isolated corner of north america to a thriving metropolis that rivaled new york in importance . by 1850 , of the 3.2 million enslaved people in the country ’ s fifteen slave states , 1.8 million were producing cotton . by 1860 , slave l... | in the fifth paragraph , if there were 3.2 million slaves in american in 1850 , and only 1.8 million were producing cotton what were the other 1.4 million doing ? |
overview with the invention of the cotton gin , cotton became the cash crop of the deep south , stimulating increased demand for enslaved people from the upper south to toil the land . as the disparity between plantation owners and poor white people widened in the deep south , deeply entrenched racism blurred perceived... | however , cotton was a labor-intensive crop , and many plantation owners were reducing the number of people they enslaved due to high costs and low output . in 1793 , eli whitney revolutionized cotton production when he invented the cotton gin , a device that separated the seeds from raw cotton . suddenly , a process t... | when did cotton become very popular ? |
overview with the invention of the cotton gin , cotton became the cash crop of the deep south , stimulating increased demand for enslaved people from the upper south to toil the land . as the disparity between plantation owners and poor white people widened in the deep south , deeply entrenched racism blurred perceived... | however , cotton was a labor-intensive crop , and many plantation owners were reducing the number of people they enslaved due to high costs and low output . in 1793 , eli whitney revolutionized cotton production when he invented the cotton gin , a device that separated the seeds from raw cotton . suddenly , a process t... | what time period did cotton have a bigger demand ? |
overview with the invention of the cotton gin , cotton became the cash crop of the deep south , stimulating increased demand for enslaved people from the upper south to toil the land . as the disparity between plantation owners and poor white people widened in the deep south , deeply entrenched racism blurred perceived... | how so ? how did the industrial revolution affect the slave economy and vice versa ? how would you describe the relationship between the two ? | is the slave economy arguably what destroyed slave families ? |
overview with the invention of the cotton gin , cotton became the cash crop of the deep south , stimulating increased demand for enslaved people from the upper south to toil the land . as the disparity between plantation owners and poor white people widened in the deep south , deeply entrenched racism blurred perceived... | the institution of race-based slavery defused class tensions among whites because no matter how poor they were , white southerners had race in common with the mighty plantation owners . significantly , all white southerners were also bound together by the constant , prevailing fear of slave uprisings . what do you thin... | `` , why were they also bound together by constant , prevailing fear of slave uprisings ? |
overview with the invention of the cotton gin , cotton became the cash crop of the deep south , stimulating increased demand for enslaved people from the upper south to toil the land . as the disparity between plantation owners and poor white people widened in the deep south , deeply entrenched racism blurred perceived... | a demand for it already existed in the industrial textile mills in great britain , and in time , a steady stream of slave-grown american cotton would also supply northern textile mills . southern cotton , picked and processed by newly-profitable slaves , helped fuel the 19th-century industrial revolution in both the un... | what percentage of southern americans owned slaves ? |
overview with the invention of the cotton gin , cotton became the cash crop of the deep south , stimulating increased demand for enslaved people from the upper south to toil the land . as the disparity between plantation owners and poor white people widened in the deep south , deeply entrenched racism blurred perceived... | a demand for it already existed in the industrial textile mills in great britain , and in time , a steady stream of slave-grown american cotton would also supply northern textile mills . southern cotton , picked and processed by newly-profitable slaves , helped fuel the 19th-century industrial revolution in both the un... | could slaves own other slaves ? |
overview with the invention of the cotton gin , cotton became the cash crop of the deep south , stimulating increased demand for enslaved people from the upper south to toil the land . as the disparity between plantation owners and poor white people widened in the deep south , deeply entrenched racism blurred perceived... | a demand for it already existed in the industrial textile mills in great britain , and in time , a steady stream of slave-grown american cotton would also supply northern textile mills . southern cotton , picked and processed by newly-profitable slaves , helped fuel the 19th-century industrial revolution in both the un... | how did america get on to the idea to have slaves ? |
overview with the invention of the cotton gin , cotton became the cash crop of the deep south , stimulating increased demand for enslaved people from the upper south to toil the land . as the disparity between plantation owners and poor white people widened in the deep south , deeply entrenched racism blurred perceived... | however , the domestic slave trade primarily supplied the necessary labor force . as the tobacco crop dwindled , former tobacco farmers in the older states of virginia and maryland found themselves with “ surplus ” enslaved laborers whom they were obligated to feed , clothe , and shelter . some slaveholders responded t... | in the term yeomen farmers , what does the word yeomen mean ? |
overview with the invention of the cotton gin , cotton became the cash crop of the deep south , stimulating increased demand for enslaved people from the upper south to toil the land . as the disparity between plantation owners and poor white people widened in the deep south , deeply entrenched racism blurred perceived... | however , cotton was a labor-intensive crop , and many plantation owners were reducing the number of people they enslaved due to high costs and low output . in 1793 , eli whitney revolutionized cotton production when he invented the cotton gin , a device that separated the seeds from raw cotton . suddenly , a process t... | why was cotton so easy to store and transport ? |
overview with the invention of the cotton gin , cotton became the cash crop of the deep south , stimulating increased demand for enslaved people from the upper south to toil the land . as the disparity between plantation owners and poor white people widened in the deep south , deeply entrenched racism blurred perceived... | cotton is king by the mid-19th century , southern commercial centers like new orleans had become home to the greatest concentration of wealth in the united states . slavery shaped the culture and society of the south , which rested on a racial ideology of white supremacy . and importantly , many whites believed slavery... | without slavery , how would the south have managed their plantations ? |
overview with the invention of the cotton gin , cotton became the cash crop of the deep south , stimulating increased demand for enslaved people from the upper south to toil the land . as the disparity between plantation owners and poor white people widened in the deep south , deeply entrenched racism blurred perceived... | what do you think ? do you think the slave economy increased sectional tension in the antebellum period ? how so ? | do you think the slave economy increased sectional tension in the antebellum period ? |
overview with the invention of the cotton gin , cotton became the cash crop of the deep south , stimulating increased demand for enslaved people from the upper south to toil the land . as the disparity between plantation owners and poor white people widened in the deep south , deeply entrenched racism blurred perceived... | how so ? how did the industrial revolution affect the slave economy and vice versa ? how would you describe the relationship between the two ? | how did the industrial revolution affect the slave economy and vice versa ? |
overview with the invention of the cotton gin , cotton became the cash crop of the deep south , stimulating increased demand for enslaved people from the upper south to toil the land . as the disparity between plantation owners and poor white people widened in the deep south , deeply entrenched racism blurred perceived... | however , cotton was a labor-intensive crop , and many plantation owners were reducing the number of people they enslaved due to high costs and low output . in 1793 , eli whitney revolutionized cotton production when he invented the cotton gin , a device that separated the seeds from raw cotton . suddenly , a process t... | were there other valuable crops slaves harvested other than cotton ? |
overview with the invention of the cotton gin , cotton became the cash crop of the deep south , stimulating increased demand for enslaved people from the upper south to toil the land . as the disparity between plantation owners and poor white people widened in the deep south , deeply entrenched racism blurred perceived... | however , cotton was a labor-intensive crop , and many plantation owners were reducing the number of people they enslaved due to high costs and low output . in 1793 , eli whitney revolutionized cotton production when he invented the cotton gin , a device that separated the seeds from raw cotton . suddenly , a process t... | in the overveiw what is a cotton gin ? |
overview with the invention of the cotton gin , cotton became the cash crop of the deep south , stimulating increased demand for enslaved people from the upper south to toil the land . as the disparity between plantation owners and poor white people widened in the deep south , deeply entrenched racism blurred perceived... | a demand for it already existed in the industrial textile mills in great britain , and in time , a steady stream of slave-grown american cotton would also supply northern textile mills . southern cotton , picked and processed by newly-profitable slaves , helped fuel the 19th-century industrial revolution in both the un... | why did we have slaves back then ? |
why must we use xor ? does it really matter if we used and , or or xor with the one-time pad ? the answer is yes , and it ’ s extremely important to understand why . recall from the previous article that and has a 75 % chance of outputting 0 and a 25 % chance of outputting a 1 . while or has a 25 % chance of outputting... | why must we use xor ? does it really matter if we used and , or or xor with the one-time pad ? | so ... .the best for encryption would be xor , followed by and , then or ? |
why must we use xor ? does it really matter if we used and , or or xor with the one-time pad ? the answer is yes , and it ’ s extremely important to understand why . recall from the previous article that and has a 75 % chance of outputting 0 and a 25 % chance of outputting a 1 . while or has a 25 % chance of outputting... | here is a digital image of charles babbage : it contains thousands of tiny colored squares called pixels . each pixel in this image can be represented as a 24 bit sequence as shown in the previous article . let 's call this our plaintext image ( or message ) . | inverted to the images shown ? |
why must we use xor ? does it really matter if we used and , or or xor with the one-time pad ? the answer is yes , and it ’ s extremely important to understand why . recall from the previous article that and has a 75 % chance of outputting 0 and a 25 % chance of outputting a 1 . while or has a 25 % chance of outputting... | or notice most of the original message shines through . this happens anytime a random shift of 0 is applied , or when the plaintext is 1 : finally , let ’ s see what happens when we xor each bit in the image file with a stream of random bits . ( drum roll please ... ) xor where did charles go ? | what do you mean by `` this happens anytime a `` random shift '' of __ is applied ... '' ? |
why must we use xor ? does it really matter if we used and , or or xor with the one-time pad ? the answer is yes , and it ’ s extremely important to understand why . recall from the previous article that and has a 75 % chance of outputting 0 and a 25 % chance of outputting a 1 . while or has a 25 % chance of outputting... | why must we use xor ? does it really matter if we used and , or or xor with the one-time pad ? the answer is yes , and it ’ s extremely important to understand why . | if the one time pad is short , and the message is long , does n't information leak ? |
why must we use xor ? does it really matter if we used and , or or xor with the one-time pad ? the answer is yes , and it ’ s extremely important to understand why . recall from the previous article that and has a 75 % chance of outputting 0 and a 25 % chance of outputting a 1 . while or has a 25 % chance of outputting... | why must we use xor ? does it really matter if we used and , or or xor with the one-time pad ? | in short : tv static is xor ? |
why must we use xor ? does it really matter if we used and , or or xor with the one-time pad ? the answer is yes , and it ’ s extremely important to understand why . recall from the previous article that and has a 75 % chance of outputting 0 and a 25 % chance of outputting a 1 . while or has a 25 % chance of outputting... | notice that the plaintext only shines through 50 % of the time , which results in noise as each pixel is equally likely to be 0 or 1 . this image contains no information about the original image . if we didn ’ t provide the shift sequence it would be impossible for you to reverse it back to the original image . | how did you encrypt the image ? |
why must we use xor ? does it really matter if we used and , or or xor with the one-time pad ? the answer is yes , and it ’ s extremely important to understand why . recall from the previous article that and has a 75 % chance of outputting 0 and a 25 % chance of outputting a 1 . while or has a 25 % chance of outputting... | here is a digital image of charles babbage : it contains thousands of tiny colored squares called pixels . each pixel in this image can be represented as a 24 bit sequence as shown in the previous article . let 's call this our plaintext image ( or message ) . | pixel over pixel or what ? |
why must we use xor ? does it really matter if we used and , or or xor with the one-time pad ? the answer is yes , and it ’ s extremely important to understand why . recall from the previous article that and has a 75 % chance of outputting 0 and a 25 % chance of outputting a 1 . while or has a 25 % chance of outputting... | why must we use xor ? does it really matter if we used and , or or xor with the one-time pad ? | would n't it also be a better idea to use a non-commutative random binary operation ? |
why must we use xor ? does it really matter if we used and , or or xor with the one-time pad ? the answer is yes , and it ’ s extremely important to understand why . recall from the previous article that and has a 75 % chance of outputting 0 and a 25 % chance of outputting a 1 . while or has a 25 % chance of outputting... | why must we use xor ? does it really matter if we used and , or or xor with the one-time pad ? the answer is yes , and it ’ s extremely important to understand why . | why is the third picture ( the or one ) a different size ? |
why must we use xor ? does it really matter if we used and , or or xor with the one-time pad ? the answer is yes , and it ’ s extremely important to understand why . recall from the previous article that and has a 75 % chance of outputting 0 and a 25 % chance of outputting a 1 . while or has a 25 % chance of outputting... | why must we use xor ? does it really matter if we used and , or or xor with the one-time pad ? the answer is yes , and it ’ s extremely important to understand why . | what is a one-time pad ? |
why must we use xor ? does it really matter if we used and , or or xor with the one-time pad ? the answer is yes , and it ’ s extremely important to understand why . recall from the previous article that and has a 75 % chance of outputting 0 and a 25 % chance of outputting a 1 . while or has a 25 % chance of outputting... | notice that the plaintext only shines through 50 % of the time , which results in noise as each pixel is equally likely to be 0 or 1 . this image contains no information about the original image . if we didn ’ t provide the shift sequence it would be impossible for you to reverse it back to the original image . you cou... | given the pad and the final result how do you get back to the original ? |
why must we use xor ? does it really matter if we used and , or or xor with the one-time pad ? the answer is yes , and it ’ s extremely important to understand why . recall from the previous article that and has a 75 % chance of outputting 0 and a 25 % chance of outputting a 1 . while or has a 25 % chance of outputting... | why must we use xor ? does it really matter if we used and , or or xor with the one-time pad ? | what will happen if i use all three of the effects ? |
why must we use xor ? does it really matter if we used and , or or xor with the one-time pad ? the answer is yes , and it ’ s extremely important to understand why . recall from the previous article that and has a 75 % chance of outputting 0 and a 25 % chance of outputting a 1 . while or has a 25 % chance of outputting... | notice that the plaintext only shines through 50 % of the time , which results in noise as each pixel is equally likely to be 0 or 1 . this image contains no information about the original image . if we didn ’ t provide the shift sequence it would be impossible for you to reverse it back to the original image . | what is the percentage of information reserved in and and or ? |
why must we use xor ? does it really matter if we used and , or or xor with the one-time pad ? the answer is yes , and it ’ s extremely important to understand why . recall from the previous article that and has a 75 % chance of outputting 0 and a 25 % chance of outputting a 1 . while or has a 25 % chance of outputting... | notice that the plaintext only shines through 50 % of the time , which results in noise as each pixel is equally likely to be 0 or 1 . this image contains no information about the original image . if we didn ’ t provide the shift sequence it would be impossible for you to reverse it back to the original image . | is there a way to calculate the percentage of information ? |
why must we use xor ? does it really matter if we used and , or or xor with the one-time pad ? the answer is yes , and it ’ s extremely important to understand why . recall from the previous article that and has a 75 % chance of outputting 0 and a 25 % chance of outputting a 1 . while or has a 25 % chance of outputting... | if we didn ’ t provide the shift sequence it would be impossible for you to reverse it back to the original image . you could try every possible sequence , but that would result in every possible image ! how could you know it was babbage ? | so every single picture in the world is pixels ? |
why must we use xor ? does it really matter if we used and , or or xor with the one-time pad ? the answer is yes , and it ’ s extremely important to understand why . recall from the previous article that and has a 75 % chance of outputting 0 and a 25 % chance of outputting a 1 . while or has a 25 % chance of outputting... | or notice most of the original message shines through . this happens anytime a random shift of 0 is applied , or when the plaintext is 1 : finally , let ’ s see what happens when we xor each bit in the image file with a stream of random bits . ( drum roll please ... ) xor where did charles go ? | what do random shift and plaintext mean again ? |
why must we use xor ? does it really matter if we used and , or or xor with the one-time pad ? the answer is yes , and it ’ s extremely important to understand why . recall from the previous article that and has a 75 % chance of outputting 0 and a 25 % chance of outputting a 1 . while or has a 25 % chance of outputting... | why must we use xor ? does it really matter if we used and , or or xor with the one-time pad ? | out of curiosity , is there any way to calculate that ? |
why must we use xor ? does it really matter if we used and , or or xor with the one-time pad ? the answer is yes , and it ’ s extremely important to understand why . recall from the previous article that and has a 75 % chance of outputting 0 and a 25 % chance of outputting a 1 . while or has a 25 % chance of outputting... | why must we use xor ? does it really matter if we used and , or or xor with the one-time pad ? | is and spelled a n and d , or just and ? |
what you should be familiar with before taking this lesson square roots special products of binomials what you will learn in this lesson so far you have solved linear equations , which include constant terms—plain numbers—and terms with the variable raised to the first power , $ x^1=x $ . you will now learn how to solv... | but this gives us $ \sqrt { x } $ , which is not helpful . in contrast , taking the square roots of expressions like $ x^2 $ or $ ( x-2 ) ^2 $ gives us nice expressions like $ x $ or $ ( x-2 ) $ . therefore , it 's actually helpful in quadratic equations to keep things factored , because this allows us to take the squa... | when looking at the quadratic equation with the ( x- # ) ^2 what if the ^2 was next to the ( x ) in the equation ? |
what you should be familiar with before taking this lesson square roots special products of binomials what you will learn in this lesson so far you have solved linear equations , which include constant terms—plain numbers—and terms with the variable raised to the first power , $ x^1=x $ . you will now learn how to solv... | now solve a few similar equations on your own . solving $ ( x-2 ) ^2=49 $ and similar equations here is how the solution of the equation $ ( x-2 ) ^2=49 $ goes : $ \begin { align } ( x-2 ) ^2 & amp ; =49\\ \sqrt { ( x-2 ) ^2 } & amp ; =\pm\sqrt { 49 } & amp ; & amp ; \text { take the square root . } \\ x-2 & amp ; =\pm... | for example : ( x-2 ) ^2 = 81 be x^2- 2^2=81 , thus making it easier to solve ? |
what you should be familiar with before taking this lesson square roots special products of binomials what you will learn in this lesson so far you have solved linear equations , which include constant terms—plain numbers—and terms with the variable raised to the first power , $ x^1=x $ . you will now learn how to solv... | } \\ x & amp ; =\pm 8\end { align } $ now solve a few similar equations on your own . challenge question | do you always work on the left side of the equal sign first in problems like the challenge question ? |
what you should be familiar with before taking this lesson square roots special products of binomials what you will learn in this lesson so far you have solved linear equations , which include constant terms—plain numbers—and terms with the variable raised to the first power , $ x^1=x $ . you will now learn how to solv... | therefore , this equation has two solutions . the $ \pm $ is just an efficient way of representing this concept mathematically . for example , $ \pm 6 $ means `` either $ 6 $ or $ -6 $ '' . | what is the best way to tell the difference between the functions , and when to use which one ? |
what you should be familiar with before taking this lesson square roots special products of binomials what you will learn in this lesson so far you have solved linear equations , which include constant terms—plain numbers—and terms with the variable raised to the first power , $ x^1=x $ . you will now learn how to solv... | but this gives us $ \sqrt { x } $ , which is not helpful . in contrast , taking the square roots of expressions like $ x^2 $ or $ ( x-2 ) ^2 $ gives us nice expressions like $ x $ or $ ( x-2 ) $ . therefore , it 's actually helpful in quadratic equations to keep things factored , because this allows us to take the squa... | for the very last challenge question : how does the equation go from x^2 + 8x + 16 -- > ( x + 4 ) ^2 ? |
what you should be familiar with before taking this lesson square roots special products of binomials what you will learn in this lesson so far you have solved linear equations , which include constant terms—plain numbers—and terms with the variable raised to the first power , $ x^1=x $ . you will now learn how to solv... | what you should be familiar with before taking this lesson square roots special products of binomials what you will learn in this lesson so far you have solved linear equations , which include constant terms—plain numbers—and terms with the variable raised to the first power , $ x^1=x $ . you will now learn how to solv... | what does this symbol mean ? |
what you should be familiar with before taking this lesson square roots special products of binomials what you will learn in this lesson so far you have solved linear equations , which include constant terms—plain numbers—and terms with the variable raised to the first power , $ x^1=x $ . you will now learn how to solv... | but this gives us $ \sqrt { x } $ , which is not helpful . in contrast , taking the square roots of expressions like $ x^2 $ or $ ( x-2 ) ^2 $ gives us nice expressions like $ x $ or $ ( x-2 ) $ . therefore , it 's actually helpful in quadratic equations to keep things factored , because this allows us to take the squa... | are they called quadratic equations because we are squaring x and a square has four sides ( quad ) or because a x^2 makes a parabola which can cover all 4 ( quad ) quadrants ? |
what you should be familiar with before taking this lesson square roots special products of binomials what you will learn in this lesson so far you have solved linear equations , which include constant terms—plain numbers—and terms with the variable raised to the first power , $ x^1=x $ . you will now learn how to solv... | therefore , it 's actually helpful in quadratic equations to keep things factored , because this allows us to take the square root . solving $ 2x^2+3=131 $ and similar equations not all quadratic equations are solved by immediately taking the square root . sometimes we have to isolate the squared term before taking its... | what happens if you cant remember the equations ? |
what you should be familiar with before taking this lesson square roots special products of binomials what you will learn in this lesson so far you have solved linear equations , which include constant terms—plain numbers—and terms with the variable raised to the first power , $ x^1=x $ . you will now learn how to solv... | but this gives us $ \sqrt { x } $ , which is not helpful . in contrast , taking the square roots of expressions like $ x^2 $ or $ ( x-2 ) ^2 $ gives us nice expressions like $ x $ or $ ( x-2 ) $ . therefore , it 's actually helpful in quadratic equations to keep things factored , because this allows us to take the squa... | in the challenge question , how do we go from x^2+8x+16=9 to ( x+4 ) ^2=9 ? |
what you should be familiar with before taking this lesson square roots special products of binomials what you will learn in this lesson so far you have solved linear equations , which include constant terms—plain numbers—and terms with the variable raised to the first power , $ x^1=x $ . you will now learn how to solv... | } \\ x & amp ; =\pm 8\end { align } $ now solve a few similar equations on your own . challenge question | i do not understand how the expression in the challenge question can be factored as ( x+4 ) ^2 , what happens to the 8x ? |
what you should be familiar with before taking this lesson square roots special products of binomials what you will learn in this lesson so far you have solved linear equations , which include constant terms—plain numbers—and terms with the variable raised to the first power , $ x^1=x $ . you will now learn how to solv... | but this gives us $ \sqrt { x } $ , which is not helpful . in contrast , taking the square roots of expressions like $ x^2 $ or $ ( x-2 ) ^2 $ gives us nice expressions like $ x $ or $ ( x-2 ) $ . therefore , it 's actually helpful in quadratic equations to keep things factored , because this allows us to take the squa... | how do you get ( x+4 ) ^2 from 2 ( 4 ) ( x ) + ( 4 ) ^2 , why in the last problem do they factor it out as 2 ( 4 ) ( x ) + ( 4 ) ^2 ? |
what you should be familiar with before taking this lesson square roots special products of binomials what you will learn in this lesson so far you have solved linear equations , which include constant terms—plain numbers—and terms with the variable raised to the first power , $ x^1=x $ . you will now learn how to solv... | but this gives us $ \sqrt { x } $ , which is not helpful . in contrast , taking the square roots of expressions like $ x^2 $ or $ ( x-2 ) ^2 $ gives us nice expressions like $ x $ or $ ( x-2 ) $ . therefore , it 's actually helpful in quadratic equations to keep things factored , because this allows us to take the squa... | i see that 8x was dissected into 2 ( 4 ) x and the 4 was used in ( x+4 ) ^2 , but what happened to the 2x that was left ? |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.