unique_id stringlengths 2 7 | problem stringlengths 9 11.6k | answer stringlengths 0 2.49k | answer_type stringclasses 11
values | category stringclasses 16
values | difficulty stringclasses 5
values |
|---|---|---|---|---|---|
957247 | Evaluate $$\displaystyle\int \frac{dx}{\sin x + \sec x}$$ | \frac2{\sqrt3} \tanh^{-1}(\sqrt{\frac23}\sin\frac t2)-2\tan^{-1}(\sqrt2\cos\frac t2)+C | Expression | Mathematics | University |
641430 | Multiply
$\left(
\begin{array}{c}
-\frac{1}{2} \\
-\frac{1}{3} \\
-\frac{1}{2} \\
\frac{3}{2} \\
\frac{11}{6} \\
\end{array}
\right)$ and
$\left(
\begin{array}{ccccc}
-\frac{8}{3} & \frac{7}{6} & 0 & -\frac{1}{6} & \frac{3}{2} \\
\end{array}
\right)$. | \begin{pmatrix} \frac{4}{3} & -\frac{7}{12} & 0 & \frac{1}{12} & -\frac{3}{4} \\ \frac{8}{9} & -\frac{7}{18} & 0 & \frac{1}{18} & -\frac{1}{2} \\ \frac{4}{3} & -\frac{7}{12} & 0 & \frac{1}{12} & -\frac{3}{4} \\ -4 & \frac{7}{4} & 0 & -\frac{1}{4} & \frac{9}{4} \\ -\frac{44}{9} & \frac{77}{36} & 0 & -\frac{11}{36} & \fr... | Matrix | Mathematics | University |
1273654 | Set up an initial value problem that can be solved for the amount {eq}\displaystyle \rm A {/eq} of salt in the tank at time {eq}\displaystyle t {/eq}. | dA/dt = 1 - 2A/(240-t), A(0) = 60 | Expression | Mathematics | University |
546690 | What time is Emma by Jane Austen set in? | late 18th century | String | Other | Junior High School |
111213 | What is the present value of $13,150 to be received 4 years from today if the discount rate is 5 percent? | $10,818.51 | Float | Finance | Senior High School |
344166 | Differentiate the function {eq}f(x) = x^{4x^2}{/eq} with respect to {eq}x{/eq}. | 4x^(4x^2 + 1) ( 2 \ln x + 1 ) | Expression | Mathematics | University |
709865 | Solve $\frac{\mathrm{d} y}{\mathrm{d} x} = 2 + \sqrt{y - 2x + 3}$ | {eq}y = \frac{1}{4}x^2 + (\frac{C}{2}+2)x + \frac{C^2}{4} - 3{/eq} | Expression | Mathematics | University |
476855 | When two point charges are a distance d part, the electric force that each one feels from the other has magnitude F.
In order to make this force twice as strong, what would be the change in the distance?
1. {eq}\frac{d}{2}
{/eq}
2. d
3. {eq}\frac{d}{4}
{/eq}
4. 2d | {eq}\frac{d}{\sqrt{2}}{/eq} | Expression | Physics | Senior High School |
670739 | What type of structures of copolymers have a higher probability of crystallization? | Alternating and block copolymers | List | Chemistry | University |
773222 | A neutral molecule is identified as a tetrafluoride, {eq}\rm
XF_4
{/eq}, where {eq}\rm
X
{/eq} is an unknown atom. If the molecule has a dipole moment of {eq}\rm
0.63\ D
{/eq}, can you give some possibilities for the identity of {eq}\rm
X
{/eq}? | Sulfur | String | Chemistry | Senior High School |
105263 | How is the expression
$$\frac{df}{dz}=\lim_{\delta z \to 0} \frac{f(z+\delta z)-f(z)}{\delta z}$$
transformed into
$$\frac{df}{dz}=e^{-i\alpha}\left(\frac{\partial u}{\partial x}\cos (\alpha) +i\frac{\partial v}{\partial y}\sin (\alpha)\right)+\left(\frac{\partial u}{\partial y}\sin (\alpha) +i\frac{\partial v}{\partia... | \frac{df}{d\epsilon} = f_x\frac{dx}{d\epsilon} + f_y\frac{dy}{d\epsilon} | Expression | Mathematics | University |
1945073 | Convert the following matrix to reduced row echelon form:
$\left(
\begin{array}{cccc}
4 & -8 & -1 & 0 \\
5 & -6 & 10 & -5 \\
5 & 6 & 0 & 4 \\
\end{array}
\right)$. | $\left(\begin{array}{cccc}1 & 0 & 0 & \frac{157}{350} \\0 & 1 & 0 & \frac{41}{140} \\0 & 0 & 1 & -\frac{96}{175} \\ \end{array}\right)$ | Matrix | Mathematics | University |
347517 | Consider a four-year project with the following information: Initial fixed asset investment = $510,000; straight-line depreciation to zero over the four-year life; zero salvage value; price = $20; variable costs = $10; fixed costs = $150,000; quantity sold = 81,000 units; tax rate = 34 percent. How sensitive is OCF to ... | With a 1% increase in quantity sold, OCF increases by 1.116%
With a 1% decrease in quantity sold, OCF decreases by 1.116% | Percentage | Business | University |
217435 | What structures direct lymph into the bloodstream? | The right lymphatic duct and the thoracic duct | List | Biology | Senior High School |
949505 | Which form of cancer in the female reproductive system ranks second in occurrence?
A. Ovarian
B. Cervical
C. Endometrial
D. Vaginal | A | Multiple Choice | Biology | Senior High School |
1995478 | How do you evaluate the integral of #[ (e^7x) / ((e^14x)+9) dx ]#? | {7/126(14/(9e^(-7x))-ln|14/(9e^(-7x))+1|) + C} | Expression | Mathematics | University |
70552 | How do you evaluate the integral #int (x-1)/(x+1)dx#? | x -2lnabs(x+1) +C | Expression | Mathematics | University |
610416 | Convert the following matrix to reduced row echelon form:
$\left(
\begin{array}{cccccc}
2 & -4 & 1 & 5 & 0 & 4 \\
1 & -8 & 2 & 7 & -4 & 10 \\
-5 & 10 & 6 & -10 & -6 & -8 \\
\end{array}
\right)$. | $\left(\begin{array}{cccccc}1 & 0 & 0 & 1 & \frac{4}{3} & -\frac{2}{3} \\0 & 1 & 0 & -\frac{23}{34} & \frac{25}{51} & -\frac{65}{51} \\0 & 0 & 1 & \frac{5}{17} & -\frac{12}{17} & \frac{4}{17} \\ \end{array}\right)$ | Matrix | Mathematics | University |
823476 | The King Company is producing two types of products: A and B. Both products are produced on the same machining operation. The machines operate on two 8-hour shifts. 5 days a week and 50 weeks per year. The manager wants to. Maintain a 20% capacity cushion. The demand forecast, batch sizes, processing times, and setup t... | D | Multiple Choice | Business | University |
989844 | Auto Art sells original works of art on a prepaid basis as each piece is uniquely designed to the customer's specifications. For one project, the cash flows are $9,500 and -$10,300 for years 0 and 1, respectively. Based on the internal rate of return, should this project be accepted if the required return is 12 percent... | B | Multiple Choice | Business | University |
1444884 | Does cellular respiration happen in humans or just in plants? | both humans and plants | Boolean | Biology | Junior High School |
778400 | A farmer produces both corn and wheat. if he must give up 10 bushels of corn to get 15 bushels of wheat, then what is his opportunity cost of 1 bushel of wheat? | 2/3 of a bushel of corn | Fraction | Economics | Senior High School |
91446 | What genre is The Devil in the White City? | Non-fiction | String | History | Junior High School |
1447262 | Find the double integral {eq}\iint_Ry^2dA, {/eq} where R is the region enclosed by y= 2 - x and {eq}y= x^2. Start by graphing the region R. | 423/28 | Fraction | Mathematics | University |
1840152 | Show that $\mathbb{R}^2-\{(0,0)\}$ is homeomorphic to $\mathbb{R}×S^1.$ | The homeomorphism between $\mathbb{R}^2 \setminus \{0\}$ and $\mathbb{R} \times S^1$ can be established through the functions $f(p) = (\ln \lVert p \rVert, \frac{p}{\lVert p \rVert})$ and its inverse $g(x,z) = e^xz$. | Expression | Mathematics | University |
1135445 | How do I express the following optimization problem as either LP, QP, QCQP or SOCP?
\begin{array}{ll} \text{minimise}_{x,y,t} & a||\mathbf{x}||_2^2 + b||\mathbf{y}||_2^2 \\ \text{subject to}& ||\mathbf{x}+\mathbf{y}||_2^2 \le t. \end{array}
where $a,b \in \mathbb{R}_+$ and $\mathbf{x},\mathbf{y}\in \mathbb{R}^n$. Is my... | Minimize z
subject to
u <= t
v = 1/2
w_i = x_i + y_i for all i
2uv >= sum_i w_i^2
2vz >= sum_i (sqrt(a)x_i)^2 + (sqrt(b)y_i)^2 | Expression | Mathematics | University |
201866 | How large would your annual payments be for a 30-year, $110,000 amortized loan at a nominal annual rate of 7% with annual end-of-year payments? | $8,864.50 | Float | Mathematics | University |
1017313 | How do you say 'seriously' in Spanish? | en serio | String | Other | Primary School |
1566801 | Find the area of the finite part of the paraboloid {eq}\; y = x^2 + z^2 \; {/eq} cut off by the plane {eq}\; y = 25 {/eq}. | 530.95 | Float | Mathematics | University |
290080 | A pendulum clock has a heavy bob supported on a very thin steel rod that is 1.00000 m long at 21.0. The clock keeps perfect time at 21.0 degree C. At 33.0 degree C after how many hours will the clock be off by 3.00 s? | 11.9 h | Float | Physics | Senior High School |
1375803 | Calculate the volume of the cone whose radius is 3 units, height is 4 units and whose apex is at the origin in the xy-plane. Use spherical coordinates. | 12π | Expression | Mathematics | University |
680190 | Operating data for Conard Corporation are presented below.
2014 2013
Net sales $751,930$603,830
Cost of goods sold 477,180412,330
Selling expenses 117,61083,130
Administrative expenses 74,87049,980
Income tax expense 35,85018,190
Net income 46,420 40,200
Prepare a schedule showing a vertical analysis for 2014 and 2... | Vertical Analysis
2014
Amount Percentage
Net sales $751,930 100%
Cost of goods sold 477,180 63.5%
Gross profit 274,750 36.5%
Selling expenses 117,610 15.6%
Administrative expenses 74,870 10%
Total operating expenses 192,480 25.6%
Income before taxes 82,270 10.9%
Income tax expense 35,850 4.8%
Net income 46,420 6.1%
20... | List | Business | Senior High School |
1289904 | How long did the Scientific Revolution last? | 1543 -1687 | String | History | Junior High School |
774752 | Suppose you are buying your first home, a condominium, for $300,000. The down payment is $15,000 and you have arranged for a 30-year amortized mortgage at a 6.5% nominal rate of interest with the first payment due in one-month. If you pay an additional $500 per month in addition to the monthly payment, how soon will th... | 206 months or 17.18 years | Float | Finance | University |
2054284 | A simple pendulum of length 1.0 meter with a bob of mass m swings with an angular amplitude of 60 degrees. What would be the tension in the string when its angular displacement is 45 degrees? | 1.121mg | Expression | Physics | University |
402510 | Is it possible to calculate the radius of Earth based on two height measurements, and knowing the distance between the observers? If so: how? I have the following situation: Here I can use the Pythagorean theorem to find R = ($a^2/2s$)-$s/2$ but what if the observers are on 2 different heights? (Like the picture but yo... | If the line between the two observers is tangent to the Earth, the radius R can be calculated by solving d = sqrt{h1(h1+2R)} + sqrt{h2(h2 + 2R)}, where d is the distance between the two observers, and h1 and h2 are the heights of the two observers, respectively. If the line between the two observers is not tangent to ... | Expression | Physics | Senior High School |
1730557 | As the unemployment rate rises, A. the rate of voluntary turnover increases. B. early retirement plans become less attractive to Baby Boomers. C. people available for work tend to have high qualifications. D. it becomes harder to fill jobs with skilled workers. | C | Multiple Choice | Economics | Senior High School |
1934476 | Find all points of inflection for f(x) = tan(3x) on the domain (-π,π). | x=-2π/3, -π/3, 0, π/3, 2π/3 | List | Mathematics | University |
749759 | Aerobic respiration uses oxygen to break down energy-rich food molecules and store their energy in the form of ATP.
List the major inputs and outputs of aerobic respiration. | Inputs: Glucose and Oxygen
Outputs: Carbon dioxide, Water, and 36 ATPs | List | Biology | Junior High School |
1424188 | What is the formula mass of water? | 18.02 amu | Float | Chemistry | Junior High School |
1034187 | Let $P(x)$ be a real polynomial of degree 6 with the following property: For all $-1\leq x\leq 1$, we have $0\leq P(x)\leq 1$. what is the maximum possible value of the leading coefficient of $P(x)$? | 16 | Integer | Mathematics | University |
178818 | Find the volume of the solid whose base is the region bounded by the x-axis, the curve {eq}y=\sqrt{x^2+25} {/eq}, x=0 and x=2 and which has the property that each cross-section perpendicular to the x-axis is an equilateral triangle. | 22.80533 | Float | Mathematics | University |
1113895 | Imagine you are an astronaut who has landed on another planet and wants to determine the free-fall acceleration on that planet. In one of the experiments you decide to conduct, you use a pendulum 0.47 m long and find that the period of oscillation for this pendulum is 1.43 s. What is the acceleration due to gravity on ... | 9.07 m/s^2 | Float | Physics | Senior High School |
290069 | An annuity has an expected $900 payment annually for 4 years at an interest rate of 6%.What is the present value of the annuity? | $3,118.60 | Float | Finance | Senior High School |
1202286 | Integrate (x^2 - 3 x - 4) e^{-2 x}\ dx and don't simplify. | - \frac{\left(x^2 - 2x - 5\right)e^{-2 x}}{2} + C | Expression | Mathematics | University |
783176 | If its tax rate is 30%, calculate the WACC or weighted average cost of capital.
Jack has found a really cheap small cap food stock that markets snacks. It has 10 mm shares outstanding, a share price of $15, 40 mm in debt, and 10 mm in cash. It has a cost of debt of 10%. It expects to generate 30 mm in EBITDA, operatin... | 10.95% | Percentage | Business | University |
29145 | Perform the indicated calculation: 35.453 g/mol + 1.0 g/mol
Express your answer with the correct number of significant figures and include units. Don't forget to use the correct format for scientific notation. | 36.4 g/mol | Float | Chemistry | Senior High School |
1426136 | What is the number in front of each molecule in a chemical equation that tells how many of each molecule is present? | coefficient | String | Chemistry | Junior High School |
232985 | Compute the present value of $1,200 received at the end of each year for the next six years discounted at 8% compounded annually. | $5548 | Float | Mathematics | University |
1483036 | Why is the camel such an important animal in the middle east
1.(a) the camel can carry a large amount of people and goods
2.(b)the camel has an incredible ability to adapt to harsh conditions
3.(c)the camel is easily trained and very obedient
4.(5)the camel is extremely loyal to its owners | b | Multiple Choice | History | Primary School |
1656422 | 1. The oversupply of hospitals and in-patient beds in the U.S. produced by the Hill-Burton legislation is the result of: A. The advent of managed care B. Change in the focus of medical education C. Technological advances D. Clinical guidelines E. A and C | E | Multiple Choice | History | University |
1425285 | Four identical particles, each having charge {eq}q
{/eq} and mass {eq}m
{/eq}, are released from rest at the vertices of a square of side {eq}L
{/eq}. How fast is each particle moving when their distance from the center of the square doubles? | v = \sqrt{\frac{2.707kq^2}{mL}} | Expression | Physics | Senior High School |
2096689 | The following are selected accounts for the Alpha Dog Company after all Fiscal Year December 31, 2016, adjusting entries & closing entries have been posted. All balances are normal.
Account Amount
Common Stock, $5 par $150,000
Treasury Stock, at a cost $10 per share 20,000
Dividends Payable 5,000
Paid in Capital in e... | Alpha Dog Company
Balance Sheet (partial) On December 31, 2016
Stockholders' Equity:
Paid in Capital:
Common stock, $5 par value, 50,000 shares authorized; 30,000 shares issued and 28,000 outstanding$150,000
Preferred Stock, $100 par, 5% cumulative, 5,000 shares authorized, 350 shares issued and outstanding 35,000
Pai... | List | Business | University |
1149817 | Compute the (pseudo)inverse of
$\left(
\begin{array}{ccc}
-3 & -3 & 0 \\
-4 & -2 & -3 \\
4 & -1 & 0 \\
\end{array}
\right)$. | \frac{1}{45}\left(
\begin{array}{ccc}
-3 & 0 & 9 \\
-12 & 0 & -9 \\
12 & -15 & -6 \\
\end{array}
\right) | Matrix | Mathematics | University |
1288890 | How does $$(R^2 +[|x|]^2)^{0.5}$$ expand as $$R + \frac{[|x|]^2}{2R} + \text{(more terms)}$$ around the point $x = 0$? | $$R+\frac{x^2}{2 R}-\frac{x^4}{8 R^3} +\frac{x^6}{16 R^5}-\frac{5 x^8}{128 R^7}$$ | Expression | Mathematics | University |
806481 | A child's achievement seems more influenced by _____ in the united states than in other nations. | income and ethnicity | String | Other | Senior High School |
1443192 | Find the theoretical yield of {eq}NaCl
{/eq} using 0.016 mols {eq}HCl
{/eq} with {eq}HCl + NaOH \rightarrow NaCl + H_2O
{/eq} as the equation for the reaction. | 0.016 mol | Float | Chemistry | Senior High School |
949910 | An 88-pound boy has a severe allergic reaction to a test allergen that has been administered. Which dosage of subcutaneous epinephrine would be appropriate for him? | 0.4 mg | Float | Health | Senior High School |
288225 | Find the general solution for the differential equation \(\displaystyle \frac{\mathrm{d} y}{\mathrm{d} x} = y - 8\) | y = e^(x+c) + 8 | Expression | Mathematics | University |
858268 | What are the steps that 1-pentyne goes through to become N-ethyl pentanamide? | 1. Convert 1-pentyne to pentanal using H2SO4 and HgSO4 at 60°C.
2. Oxidize pentanal to pentanoic acid using KMnO4.
3. React pentanoic acid with ethylamine and heat to produce N-ethyl pentanamide. | List | Chemistry | University |
492809 | Which factors can affect the amount of friction acting on an object on a solid surface? | The mass of the object, the type of surface, and whether the object is still or moving are all factors that affect friction. | List | Physics | Junior High School |
79840 | A train starts from station A and for the first kilometer, it travels with a uniform acceleration. Then, for the next two kilometers, it travels with a uniform speed.
Finally, the train decelerates uniformly for another kilometer before coming to rest at station B. If the time for the whole journey is six minutes, dra... | 16.666 m/s | Float | Physics | Senior High School |
1232438 | How can I solve the equation $\dfrac x9 = \log_2x$ ? | x = $e^{-W(-\frac{ln(2)}{9})}$ , $e^{-W_{-1}(-\frac{ln(2)}{9})}$ | Expression | Mathematics | University |
1368363 | If I'm evaluating $\int^b_a r dz$, where $r$ is a variable in spherical coordinates and $z$ is a variable in rectangular coordinates, do I need to transform $dz$ in spherical coordinates? If so, how would I do that? | z = rcos(φ), dz = cos(φ)dr - rsin(φ)dφ | Expression | Mathematics | University |
1136770 | Use the Laplace transform to solve the problem {eq}y'' + 6y' + 34y = 0, y(0) = 3, y'(0) = 1 {/eq}. | y(t) = 3e^(-3t)cos(5t) + 2e^(-3t)sin(5t) | Expression | Mathematics | University |
1709035 | What is the Taylor series of f(x) = 1/x about x = 2? | {eq}f(x)= \sum_{n=0}^{\infty} \frac{(-1)^n (x-2)^n } { 2^{n+1} }{/eq} | Expression | Mathematics | University |
1421193 | Given that one solution of {eq}x^2 y'' + 6x y' + 4y = 0
{/eq} is {eq}\displaystyle \frac{1}{x}
{/eq}, use reduction of order to find the second linearly independent solution. | -1/(3x^4) | Expression | Mathematics | University |
1703453 | If I have two sets of data, x and y, and I am required to apply a weighting factor, 1/x, to the regression line, does that mean I should plot 1/y versus 1/x and then get the regression? | Compute \(\frac{dSSQ}{da}\) and \(\frac{dSSQ}{db}\) for \(SSQ=\sum_{i=1}^n \frac 1{x_i}(a+bx_i-y_i)^2\), and set them to be zero. This gives two linear equations to solve for the two unknowns \(a\) and \(b\). | Expression | Mathematics | University |
415815 | What is the gravitational force on a 60 k person on the earth, due to the moon? | 0.002 N | Float | Physics | Senior High School |
441446 | Is the following table for $D_4$ correct? $$\begin{array}{c|c|c|c|c|c|c|c|c|} * & 1 & g & g^2& g^3& f& fg & fg^2 & fg^3 \\ \hline 1 & 1 & g & g^2 & g^3 & f & fg & fg^2 & fg^3 \\ \hline g & g & g^2 & g^3 & 1 & fg^3 & f & fg & fg^2 \\ \hline g^2 & g^2 & g^3 & 1 & g & fg^2 & fg^3 & f & fg \\ \hline g^3 & g^3 & 1 & g & g^2... | Yes | Boolean | Mathematics | University |
1527949 | What mass in grams would 5.7L of hydrogen gas occupy at STP? | 0.54 g | Float | Chemistry | Senior High School |
469620 | Sagon Corporation manufactures and sells one product.
The following information pertains to the company's first year of operations:
The company does not have any variable manufacturing overhead costs or variable selling and administrative costs.
During its first year of operations, the company produced 29,000 units ... | b | Multiple Choice | Business | University |
604257 | Given two aqueous solution whose respective #pH# values are #6# and #3#, how much more acidic is one solution compared to the other? | 1000 | Integer | Chemistry | Senior High School |
1345673 | A sphere of radius {eq}R
{/eq} and surface charge density {eq}\eta
{/eq} is positioned with its center distance {eq}2R
{/eq} from an infinite plane with surface charge density {eq}\eta
{/eq}.
(a) At what distance from the plane, along a line toward the center of the sphere, is the electric field zero? Expres... | x =(2 - √2)R | Expression | Physics | University |
369032 | This 30-year-old female comes to the clinic because of excessive vomiting for the last three days. She is in her 24th week and has had no problems with vomiting in her early pregnancy. What is the correct diagnostic code assignment for this case?
ICD-10-CM Code(s): | O21.9 | String | Health | Senior High School |
703858 | A regulated natural monopoly is most likely to spend more money on employee healthcare under which of the following types of regulation?
Select one:
a. All of the above.
b. Administrative regulation.
c. Price regulation.
d. Profit regulation. | a | Multiple Choice | Economics | University |
1295262 | At which of these points is an insurance contract accepted?
a. When the first premium is paid.
b. When the application is received.
c. When the binder is delivered.
d. When the insurance company has had enough time to review the application. | a | Multiple Choice | Finance | Senior High School |
307155 | By switching to polar coordinates, evaluate the integral {eq}\iiint_D (x^2+y^2)^{7/2} \,dx \,dy where {eq}D is the disk {eq}x^2+y^2=4^2 | {eq}\frac{2(4^9)\pi}{9}{/eq} | Fraction | Mathematics | University |
289592 | Find the eigenvalues of the following matrix:
$\left(
\begin{array}{ccc}
3 & 7 & -5 \\
1 & 2 & 5 \\
-1 & 6 & 8 \\
\end{array}
\right)$. | $\lambda = -3.15131$ or $\lambda = 4.86343$ or $\lambda = 11.2879$ | Float | Mathematics | University |
793514 | AAA Company is about to issue a bond with semiannual coupon payments, an annual coupon rate of 8%, and par value of $1,000. The yield to maturity for this bond is 6?%. What is the price of the bond if it matures in 5 years? | $1,085.30 | Float | Finance | University |
864562 | Evaluate the right Riemann sum for f(x)=x+1 on [0, 4] with n=50. | 12.16043 | Float | Mathematics | University |
36890 | Did Sam Shepard talk against gays before coming out himself? | No | Boolean | History | Junior High School |
489608 | Rewrite the integral with limits of integration {eq}i = 0{/eq} to {eq}1{/eq}, radical {eq}x{/eq} to {eq}1{/eq} , {eq}0{/eq} to {eq}1-y{/eq}, dz dy dx in the order {eq}dx dy dz{/eq} | {eq}I= \int_{0}^{1}\int_{0}^{1-z}\int_{0}^{y} dx dy dz{/eq} | Expression | Mathematics | University |
1846053 | Expand the function
{eq}\displaystyle f (x) = \begin{cases}-1,& -\pi < x < 0\\ 1, &0 \le x \lt \pi \end{cases}
{/eq}
in an appropriate cosine or sine series. | f(x)=1+(4/π)∑_{n=0}^{∞}[sin((2n+1)x)/(2n+1)] | Expression | Mathematics | University |
1243369 | Find a matrix where the kernel is a subspace of the range. Is the following correct? The matrix I had in mind: $$\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}$$ In this case, we see that the kernel is made up of a single vector, namely the zero vector, as that's the only solution that maps to the zero object. Next, w... | A = BC^T, where B = [[1, 0], [0, 1], [0, 0]] and C = [[0, 0], [1, 0], [0, 1]] | Matrix | Mathematics | University |
1693414 | How can I prove that for $d=2$, $v_2=2\int_{-1}^1 (1-x^2)^{1/2} \, dx$ using Corollary 3.8, and hence that $v_2=\pi$, given that $m(B)=v_2 r^2$, $v_2=\frac{m(B)} r^2$, and Corollary 3.8 states that if $\mathcal A = \{(x,y) : \mathbb R^d \times \mathbb R : 0 \le y \le f(x)\}$, then $\int_{\mathbb R^d} f(x) \, dx = m(\ma... | $v_2=2\int_{-1}^1\sqrt{1-x^2}dx$. | Expression | Mathematics | University |
1312730 | What is #f(x) = int x-xsec(x/2) dx# if #f((7pi)/4) = 0#? | #4i(Li_2(-ie^((ix)/2)) - Li_2(ie^((ix)/2))) +x^2/2-2x(ln(1-ie^((ix)/2)) - ln(1+ie^((ix)/2))) +C# | Expression | Mathematics | University |
208351 | Evaluate the following integral: {eq}\; \int \frac{\sqrt{36x^2 - 49}}{x^3} \, \mathrm{d}x, \; x > \frac{7}{6} {/eq}. | {eq}\frac{54 }{25} \left( 2 arcsec(6x/7) - \sin \left( arcsec(6x/7) \right) \right)+C{/eq} | Expression | Mathematics | University |
849773 | Given the differential equation dP/dT = KP(P-K)(L-P), where K and L are unequal constants, is it possible to analytically find a solution only in terms of P, without assuming L > K > 0? How would one go about solving the equation then? | e^{-KT}+C=P^{\frac{1}{KL}}(P-K)^{\frac{1}{K(K-L)}}(P-L)^{\frac{1}{L(L-K)}} | Expression | Mathematics | University |
1824578 | A 16 ft ladder leans against a wall. The bottom of the ladder is 4 ft from the wall at time t = 0 and slides away from the wall at a rate of 3 ft/sec. Find the velocity of the top of the ladder at time t = 3. | -4.18 ft/s | Float | Physics | Senior High School |
1159610 | When a company changes from an accelerated method to the straight-line method of depreciation, this change should be handled as a:
A. change in accounting estimate
B. prior period adjustment
C. correction of an error
D. change in accounting principle | A | Multiple Choice | Business | University |
119746 | A basketball player tries to make a half-court jump shot, releasing the ball at the height of the basket. Assuming that the ball is launched at {eq}51.0^{\circ}
{/eq}, 14.0 m from the basket, what speed must the player give the ball? | 11.849 m/s | Float | Physics | Senior High School |
814853 | A point charge +6.8 {eq}\mu
{/eq}C is placed at the origin, and a second charge -4.5 {eq}\mu
{/eq}C is placed in the x -y plane at (0.35 m, 0.50 m ). Where should a third charge be placed in the plane so that the net force acting on it is zero? Express your answers using two significant figures. Enter the x and y coo... | 1.9 m, 2.7 m | Expression | Physics | University |
50500 | How much work must be done to stop an {eq}\rm
1150-kg
{/eq} car traveling at {eq}\rm
125 \ km/h
{/eq}?
Express your answer to two significant figures and include the appropriate units. | -6.9e+05 J | Float | Physics | Senior High School |
2104274 | A woman and her dog are out for a morning run to the river, which is located 4.03 km away. The woman runs at 3.88 m/s in a straight line. The dog is unleashed and runs back and forth at 5.63 m/s between his owner and the river, until she reaches the river. What is the total distance run by the dog (in meters)? | 5847.6 m | Float | Physics | Senior High School |
271425 | What two factors have the greatest influence on soil formation? | Temperature and rain | List | Other | Junior High School |
898405 | Two circular coils are concentric and lie in the same plane. The inner coil contains 120 turns of wire, has a radius of 0.012m, and carries a current of 6.5A. The outer coil contains 160 turns and has a radius of 0.017m. What must be the magnitude and direction (relative to the current in the inner coil) of the current... | 6.90 A | Float | Physics | Senior High School |
1974654 | A stone was dropped off a cliff and hit the ground with a speed of {eq}90 \frac {ft}{s}.
{/eq} What is the height of the cliff. (the downward acceleration from gravity is {eq}32 \frac {ft}{s^2}
{/eq}) | 126.5625 ft | Float | Physics | Senior High School |
219945 | Compute the (pseudo)inverse of
$\left(
\begin{array}{cc}
-\frac{1}{8} & -\frac{11}{4} \\
\frac{71}{16} & -\frac{19}{16} \\
\end{array}
\right)$. | \frac{8}{1581}\left( \begin{array}{cc} -19 & 44 \\ -71 & -2 \\ \end{array} \right) | Matrix | Mathematics | University |
97078 | Find the volume of the solid generated by revolving the region defined by {eq}y=3, \ y=\sqrt{3x}{/eq}, and the {eq}y{/eq}-axis about the line {eq}x=-1{/eq}. | \frac{57\pi}{5} | Fraction | Mathematics | University |
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