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When a spring does work on an object, we cannot find the work by simply multiplying the spring force by the object's displacement. The reason is that there is no one value for the force-it changes. However, we can split the displacement up into an infinite number of tiny parts and then approximate the force in each as being constant. Integration sums the work done in all those parts. Here we use the generic result of the integration.
In Figure, a cumin canister of mass $m=0.40 \mathrm{~kg}$ slides across a horizontal frictionless counter with speed $v=0.50 \mathrm{~m} / \mathrm{s}$. It then runs into and compresses a spring of spring constant $k=750 \mathrm{~N} / \mathrm{m}$. When the canister is momentarily stopped by the spring, by what distance $d$ is the spring compressed?
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1.2
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textbook question answering
|
|
what is the total volume of the measuring cup?
|
1000
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visual question answering
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△ABC的两内角平分线OB、OC相交于点O,若∠A=110°,则∠BOC=()
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145°
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geometry problem solving
|
|
Subtract all large rubber spheres. Subtract all big shiny cylinders. How many objects are left?
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4
|
math word problem
|
|
Find $m\angle H$
|
97
|
geometry problem solving
|
|
As shown in the figure, if CB = 4.0, DB = 7.0, and D is the midpoint of AC, then the length of AC is ()
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6cm
|
geometry problem solving
|
|
What time is shown? Answer by typing a time word, not a number. It is (_) after eight.
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quarter
|
math word problem
|
|
Is the number of tiny gray bicycles that are on the left side of the brown metal sedan greater than the number of things that are to the left of the tiny green bicycle?
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Yes
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visual question answering
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|
如图是一株美丽的勾股树,其中所有四边形都是正方形,所有的三角形都是直角三角形,若正方形A、B的面积分别为5、3,则最大正方形C的面积是()
|
8
|
geometry problem solving
|
|
Which object comes next?
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E
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figure question answering
|
|
Subtract all red things. Subtract all tiny matte balls. How many objects are left?
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5
|
math word problem
|
|
Are there fewer metallic fighters than rubber objects?
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Yes
|
visual question answering
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|
How many objects are preferred by more than 90 percent of people in at least one category?
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0
|
figure question answering
|
|
Is the number of tiny objects that are behind the small metal jet less than the number of tiny things left of the tiny sedan?
|
Yes
|
visual question answering
|
|
Which organism with be most affected if algae was eliminated?
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Common water flea
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textbook question answering
|
|
How many items sold less than 5 units in at least one store?
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2
|
figure question answering
|
|
如图,在Rt△ABC中,∠ACB=90°,D是AB的中点,AB=10,则CD的长为()
|
5
|
geometry problem solving
|
|
The passage below describes an experiment. Read the passage and then follow the instructions below.
Linda applied a thin layer of wax to the underside of her snowboard and rode the board straight down a hill. Then, she removed the wax and rode the snowboard straight down the hill again. She repeated the rides four more times, alternating whether she rode with a thin layer of wax on the board or not. Her friend Bob timed each ride. Linda and Bob calculated the average time it took to slide straight down the hill on the snowboard with wax compared to the average time on the snowboard without wax.
Figure: snowboarding down a hill. Identify the question that Linda and Bob's experiment can best answer.
|
Does Linda's snowboard slide down a hill in less time when it has a layer of wax or when it does not have a layer of wax?
|
textbook question answering
|
|
what is the highest amount this class measures?
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400
|
visual question answering
|
|
Is the sum of smallest two bar is greater then the largest bar?
|
No
|
figure question answering
|
|
Fill in the blank to describe the model. The model has 4 dots divided into 2 equal groups. There are (_) dots in each group.
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2
|
math word problem
|
|
How many people in the image were born after the end of World War II?
|
0
|
visual question answering
|
|
The derivative of f(x) at x=2 is ____ that at x=5
|
equal to
|
textbook question answering
|
|
Is Periwinkle the maximum?
|
no
|
figure question answering
|
|
Is Medium Periwinkle the smoothest?
|
no
|
figure question answering
|
|
Is Black greater than Deep Sky Blue?
|
no
|
figure question answering
|
|
What is the age gap between these two people in image?
|
11
|
visual question answering
|
|
$\overline{AB}$ is a diameter, $AC=8$ inches, and $BC=15$ inches. Find the radius of the circle.
|
8.5
|
geometry problem solving
|
|
What is the age gap between these two people in image?
|
4
|
visual question answering
|
|
As shown in the figure, the two chords AB and CD in the circle intersect at E, ∠D = 35.0, ∠AEC = 105.0, then ∠C = ()
|
70°
|
geometry problem solving
|
|
Are there more big red rubber double buss in front of the large red double bus than big green things?
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No
|
visual question answering
|
|
如图,在ABCD中,AB=AC,∠CAB=40°,则∠D的度数是()
|
70°
|
geometry problem solving
|
|
Use a sector paper sheet with a central angle of 120.0 and a radius of 6.0 to roll into a conical bottomless paper cap (as shown in the picture), then the bottom perimeter of the paper cap is ()
|
4πcm
|
geometry problem solving
|
|
Is this function continuous at each point?
|
No
|
textbook question answering
|
|
如图,AB是⊙O的直径,EF,EB是⊙O的弦,点E是FEB的中点,EF与AB交于点C,连接OF,若∠AOF=40°,则∠F的度数是()
|
35°
|
geometry problem solving
|
|
What is the age gap between these two people in image?
|
9
|
visual question answering
|
|
What is the limit as x approaches -1?
|
3
|
textbook question answering
|
|
How many bars have values smaller than 6?
|
0
|
figure question answering
|
|
Is this function odd or even?
|
odd
|
textbook question answering
|
|
Subtract all brown blocks. Subtract all large blue rubber things. How many objects are left?
|
7
|
math word problem
|
|
What is the age gap between these two people in image?
|
7
|
visual question answering
|
|
What is the age gap between these two people in image?
|
8
|
visual question answering
|
|
Use the graph to answer the question below. Which month is the wettest on average in Christchurch?
|
May
|
textbook question answering
|
|
Chase wants to buy 4 kilograms of oval beads and 5 kilograms of star-shaped beads. How much will he spend? (Unit: $)
|
18
|
math word problem
|
|
An administrator at the Department of Motor Vehicles (DMV) tracked the average wait time from month to month. According to the table, what was the rate of change between August and September? (Unit: minutes per month)
|
-3
|
math word problem
|
|
What would happen to the population of adult spiders if predator ate all the spider eggs?
|
Adults spider population would decrease
|
textbook question answering
|
|
Subtract all rubber balls. Subtract all yellow shiny things. How many objects are left?
|
6
|
math word problem
|
|
Find $m \angle 3$.
|
38
|
geometry problem solving
|
|
What is the sum of the digits on either end of the sign in the corner?
|
0
|
visual question answering
|
|
Based on the food web, what would likely happen if the number of large roach would decrease?
|
The population of predatory insects would decrease.
|
textbook question answering
|
|
Is the number of gray rubber objects in front of the small yellow aeroplane greater than the number of big cyan matte fighters?
|
Yes
|
visual question answering
|
|
Subtract all big red metallic spheres. Subtract all big brown matte things. How many objects are left?
|
6
|
math word problem
|
|
What is the age gap between these two people in image?
|
1
|
visual question answering
|
|
In the figure above, the ratio of the length of line AB to the length of line AC is 2 : 5. If AC = 25, what is the length of line AB?
|
10
|
geometry problem solving
|
|
如图,一块直角三角板60°的角的顶点A与直角顶点C分别在两平行线FG,DE上,斜边AB平分∠CAG,交直线DE于点H,则∠BCH的大小为()
|
30°
|
geometry problem solving
|
|
What is the perimeter of the rectangle?
|
6
|
math word problem
|
|
Subtract all small balls. Subtract all blue rubber things. How many objects are left?
|
2
|
math word problem
|
|
Does Firebrick have the maximum area under the curve?
|
yes
|
figure question answering
|
|
As shown in the figure, AB is the diameter of ⊙O, CD is the chord of ⊙O, ∠ADC = 26.0, then the degree of ∠CAB is ()
|
64°
|
geometry problem solving
|
|
What is the age gap between these two people in image?
|
22
|
visual question answering
|
|
Is Coral the roughest?
|
no
|
figure question answering
|
|
如图,E,F分别是菱形ABCD的边AB,AD的中点,且AB=5,AC=6.则EF的长为()
|
4
|
geometry problem solving
|
|
Subtract all red matte cubes. Subtract all small green metal objects. How many objects are left?
|
7
|
math word problem
|
|
The diagrams below show two pure samples of gas in identical closed, rigid containers. Each colored ball represents one gas particle. Both samples have the same number of particles. Compare the average kinetic energies of the particles in each sample. Which sample has the higher temperature?
|
sample A
|
textbook question answering
|
|
is f(3) > 0?
|
Yes
|
textbook question answering
|
|
Choose the answer for the missing picture.
|
A
|
figure question answering
|
|
What is the perimeter of the square?
|
16
|
math word problem
|
|
将一根长度为16cm自然伸直的弹性皮筋AB两端固定在水平的桌面上,然后把中点C竖直向上拉升6cm至D点(如图),则该弹性皮筋被拉长了()
|
4cm
|
geometry problem solving
|
|
Subtract all big matte balls. Subtract all green rubber objects. How many objects are left?
|
7
|
math word problem
|
|
What is the age gap between these two people in image?
|
8
|
visual question answering
|
|
What is the perimeter of the rectangle?
|
18
|
math word problem
|
|
A real estate agent drove around the neighborhood and counted the number of houses on each block. How many blocks have exactly 36 houses? (Unit: blocks)
|
1
|
math word problem
|
|
Complete the matrix.
|
D
|
figure question answering
|
|
What is the difference of largest and smallest bar?
|
47.6
|
figure question answering
|
|
Is Sky Blue less than Web Maroon?
|
no
|
figure question answering
|
|
What happens to fish if pelicans increase?
|
decrease
|
textbook question answering
|
|
Which year showed the largest difference in the data points between the two lines
|
2019
|
figure question answering
|
|
Find the missing value.
|
8
|
figure question answering
|
|
As shown in the figure, points A, B, C, and D are on circle O, and point E is on the extended line of AD. If ∠ABC = 60.0, then the degree of ∠CDE is ()
|
60°
|
geometry problem solving
|
|
According to the food web, what will happen if all the algae died due to pesticides?
|
Crabs and limpets will decrease
|
textbook question answering
|
|
What is the value of r at theta=3*pi/2?
|
-1
|
textbook question answering
|
|
A square is inscribed in a circle of area 18$\pi$ square units. Find the length of a side of the square.
|
6
|
geometry problem solving
|
|
Is the number of shiny buss less than the number of matte things?
|
Yes
|
visual question answering
|
|
ABCD is a square. Inscribed Circle center is O. Find the the angle of ∠AMK. Return the numeric value.
|
130.9
|
textbook question answering
|
|
How many countries have people working for more than 35 hours over the years?
|
2
|
figure question answering
|
|
Which model has the highest Acc score when Pretrain Loss is equal to 1.80?
|
RFT U13B
|
figure question answering
|
|
Look at the table. Then answer the question. At a price of $790, is there a shortage or a surplus?'
|
surplus
|
math word problem
|
|
A square is tangent to a line at point P in the figure above. What is the value of x?
|
30
|
geometry problem solving
|
|
How many miles per gallon do an average city bus get?
|
25
|
visual question answering
|
|
Subtract all yellow matte blocks. Subtract all tiny brown cylinders. How many objects are left?
|
5
|
math word problem
|
|
Is the number of brown suvs less than the number of brown rubber school buss?
|
No
|
visual question answering
|
|
Do the windows have a geometric shape that most houses have?
|
No
|
visual question answering
|
|
What's the computing and wirless total for semiconductor demand in 2014?
|
197.3
|
figure question answering
|
|
如图,D为△ABC内一点,CD平分∠ACB,BD⊥CD,∠A=∠ABD,若∠DBC=54°,则∠A的度数为()
|
27°
|
geometry problem solving
|
|
As shown in the figure, the straight lines AB and CD intersect at point O, OD bisects ∠AOE, ∠BOC = 50.0, then ∠EOB = ()
|
80°
|
geometry problem solving
|
|
How many times Dissatisfied more than satisfied?
|
3.9
|
figure question answering
|
|
How many algorithms have accuracies higher than 9?
|
0
|
figure question answering
|
|
Find the value of the square in the figure.
|
2
|
figure question answering
|
|
Which cat is larger?
|
white one
|
visual question answering
|
|
What is the sum of all the values in the ruling group?
|
12
|
figure question answering
|
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