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What is 1 percent of 7 billion?

What number is 1 more than 5?

What does 'much' mean in math?

How many times shorter is one inch than one foot?

What is 9 divided by 15?

What is 8 divided by 60?

What is 100 divided by 4?

50% (2 ratings)

What is the difference between postulate and theorem?

What is 30 divided by 8?

What is 100 divided by 16?

5 inches is what fraction of a foot?

What is 0.12 as a fraction?

What is 75 divided by 2?

Use the cross product to find the sin(theta) where theta is the angle between v and w where v = i + j and w = i + j + k.

What is 119% as a fraction in its simplest form?

Suppose that you are climbing a hill whose shape is given by z = 483 - 0.03x2-0.03y2, and that you are at the point (50, 60, 300). In which direction (unit vector) should you proceed initially in orde

What are the multiples of 56?

Calculate the double integral. 8x/(1 + xy) dA, R = [0, 8] x [0, 1]R

What is 4.25 as a fraction?

What is the square root of 115?

Write 25% as a decimal

What is one tenth of 50?

Parametrize the intersection of the surfaces using t = y as the parameter. (If there are multiple correct answers, give only one answer.) y^2 - z^2 = x - 2, y^2 + z^2 = 16.

Evaluate the integral from 5 to infinity of (1)/[ (x)(sqrt(x^2 - 25)) ]dx

What irrational number is between 5 and 7?

Why must the remainder be less than the divisor?

The length of the day in Boulder (Latitude 40 degrees N) can be modeled approximately by L(t) = 3 cos (2 /365 (t + 10) )+ 12 where L is given in hours and t is the day of the year. a) Evaluate L(355);

Is a kilogram bigger than a gram?

What is 100 divided by 5?

What is 90 divided by 2?

Evaluate the following limit: Limit as x goes to infinity of 1/(10^(2x)) * 1/(x^2).

What is 16 divided by 8?

Let f(x) = (2x^2 - 3x + 2)/(4x^2 + 4x + 7). Evaluate f prime (x) at x = 5.

How do you use benchmark fractions?

Find the general solution of the given second-order differential equation. 3y'' + 2y' + y = 0

Find the volume V of the described solid S. A cap of a sphere with radius r and height h V = ___

Find the radius of convergence, R, and the convergence interval for x of the series sum of (x - 8)^n / (n^7 + 1) from n = 0 to infinity.

How do we begin to evaluate the integral cosxln(sinx)dx?

What is 30 divided by 40?

Find a parametrization, using cos(t) and sin(t), of the following curve: The intersection of the plane y=3 with the sphere x2+y2+z2=58

Lasha Talakhadze of the Republic of Georgia broke a world record in the snatch and grab and clean and jerk weight lifting competition in Rio with 105 , 258 kilograms respectively. Determine the amount

Find the centroid of the region bounded by the given curves. Give your answers correct to two decimal places. y = x^3, x + y = 2, y = 0.

Find a vector parametrization of the curve x = -5Z^2 in the xz-plane. Use t as the parameter in your answer.

What is 28 divided by 3?

For the following sequences evaluate the ratio \frac{a_n + 1}{a_n}. Simplify your answer. (a) a_n = \frac{2^n}{(2n-1)!} (b) a_n = \frac{(2n)!}{3^{2n + 1}}

Evaluate the indefinite integral as a power series: Integral of (x)/(1 + x^3) dx.

What is 32 divided by 8?

How many hundred thousands are in a million?

40 is 50 percent of what number?

Integrate f(x,y,z)=16xz over the region in the first octant (x,y,z%3E=0) above the parabolic cylinder z=y2 and below the paraboloid z=8-2x2-y2

Solve for y. 2x - 3y = 8

Find the limit for the following functions if they exist. lim(x,y)-%3E(0,0) (x+14y)^2/(x^2 + 196y^2), and lim(x,y)-%3E(0,0) (5x^3 + 7y^3)/(x^2 + y^2)

A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2 feet per second. How fast is the top of the ladder sliding down the wal

A temperature of 20 C is equivalent to approximately what in F?

What is the first consecutive odd integer that follows 7?

Describe the level surfaces of the function: f(x,y,z) = x^2+3y^2+5z^2

Given a_{n}=\frac{\sqrt{n^2-1}}{2n+1}, find \lim_{n \to \infty }a_{n}. Does \sum_{n=1}^{\infty}a_{n} converge or diverge? Explain why. Suppose b_{n} are such that \sum_{i=1}^{n}b_{i}=a_{n}. Does the s

The rate at which velocity changes is called

A spacecraft moves along a path described by the parametric equations; x = 10*(sqrt(1+t^4)-1) and y = 40t^(3/2), for the first 100 seconds after launch. Here, x and y are measured in meters, and t is

What is 40/100 in simplest form?

What is 15 divided by 12?

What is 43 divided by 3?

Find the derivative of the function.F(x) = x2et7dt

A steel pipe is being carried down a hallway 9 ft wide. At the end of the hall there is a right-angled turn into a narrower hallway 6 ft wide. What is the length of the longest pipe that can be carrie

Bismuth-210 has a half-life of 5.0 days. A sample originally has a mass of 800 mg. Find a formula y(t) for the mass remaining after (t) days. Find the mass remaining after 30 days. When is the mass re

A poster is to have an area of 180 in^2 with 1 inch margins at the bottom and sides and a 2 inch margin at the top. Find the exact dimensions that will give the largest printed area.

Find the radius of convergence, R, of the series: \sum_{n=2}^{\infty} (-1)^n \frac{xn}{8^nln\;n}

Evaluate the integral of 4*tan(x) sec^3(x) dx. (Use C for the constant of integration.)

Use Green's theorem to compute the area inside the ellipse( x^2/13^2)+(y^2/6^2)=1. Use the fact that the area can be written as dub intD dxdy=(1/2) int partialD (-y dx+x dy) . Hint: x(t)=13cos(t).

200 ounces of a drink that contains 60% fruit juice is mixed with x ounces of filtered water. If 100 ounces of filtered water is used, what percent of juice does that resulting juice contain?

When was the word integer introduced?

Determine whether the following sequence converges or diverges. If it converges, find the limit. a_n = ((-1)^n)/(2*sqrt(n)).

What is 150 divided by 4?

What is 20 divided by 15?

Find the cross product axb, and verify that it is orthogonal to both a and b. a = j + 7k b = 2i - j +4k

What is 25 divided by 10?

Find the arc length parametrization of the circle in the plane z=9 with a radius of 4 and center located at (1,4,9).

What are examples of things weigh more than a ton?

Show that the line integral is independent of path by finding a function f such that f = F. C2xe ydx + (2y x2e y)dy, C is any path from (1, 0) to (5, 1)

Find the interval of convergence of the following series. The sum of (-1)^n * ((x + 2)^n)/(n^2) from n = 0 to infinity.

Convert 63 degrees F to Celsius

What is 40 divided by 7?

Evaluate the iterated integral \int_{2}^{3}\int_{-1}^{2}\frac{1}{(x+y)^{2}}dydx

What is 16 divided by 6?

Use Green's Theorem to calculate the circulation of F = (y)I + (2xy)j around the unit circle, oriented counterclockwise.

What is 140 divided by 2?

A) Find the area between x-axis and under the curve of f(x) = x^2 +x+3 over the interval ~[1,3] B) Evaluate \int^4_{0}f(x)dx \left\{\begin{matrix} 12x, x%3C 1 \\ 8 x\geq 1 \end{matrix}\right.

What is half of 78?

What set of numbers does 0 belong to?

What is 64 divided by 6?

What is the second Taylor polynomial P_2(x) for f(x) = sqrt(x) about a = 4?

Find the average value of the function f(x) = 7 sin2x cos3xon the interval [-pi, pi]. (Round your answer to two decimal places.)

Find the third degree Taylor polynomial of f(x) = sqrt(1 + 2x) centered at a = 0.

How are equivalent ratios like equivalent fractions?

Is one-third more than one-half?

A cube is located such that its top four corners have the coordinates (-1, -2, 2), (-1,3,2), (4, -2, 2) and (4,3,2). Give the coordinates of the center of the cube.

Find the absolute maximum and absolute minimum of the function f(x,y)=xy-2y-4x+8 on the region on or above y=x^2 and on or below y=7.

Compute the length of the curve r(t)= (2t, ln t, t2) over the interval

Use the arc length formula to find the length of the curve y = sqrt(2 - x^2), 0 less than or equal to x less than or equal to 1. Check your answer by noting that the curve is part of a circle.

What is 7/14 in simplest form?

Convert 2.5 pounds to ounces

Find the limit of: limit as t goes to 0 of [(e^?7t) i + (t^2/sin^2(t)) j + sin(6t) k]

Find the arc length of the curve below on the given interval by integrating with respect to x. y = (x^3)/3 + 1/(4x); [1, 3]. (Give an exact answer, using radicals as needed.)

What is 250 divided by 2?

Determine if the following ODE is exact, and if so, solve it. x/y dy = (ln 1/y) dx

A bee with velocity vector r'(t) starts out at (-4,3,1) at t=0 and flies around for 7 seconds. Where is the bee located at time 7 if integral from t 0 to 7 r'(u)du=0?

Round 31 to the nearest ten

What is 160 divided by 2?

At what points does the helix r(t) = sin t, cos t, t intersect the sphere x^2 + y^2 + z^2 = 8^2?

Is 6 a divisor of 18?

What is 70 divided by 3?

What is 29 divided by 2?

What is 200 degrees Celsius in Fahrenheit?

Compute the flux of the vector field F=8x^2y^2zk through the surface S which is the cone sqrt(x^2+y^2)=z, with 0=%3Cz=%3CR, oriented downward.(a) Parameterize the cone using cylindrical coordinates.

What is 40 divided by 15?

Consider the solid shaped like an ice cream cone that is bounded by the functions z = x2 + y2 and z = 18 - x2 - y2. Set up an integral in polar coordinates to find the volume of this ice cream cone.

What are the odd integers between 2 and 15?

What is 72 divided by 7?

Suppose the solid W is one-quarter of a circular cylinder of height 8 and radius 4 centered about the z-axis in the first octant. Find the limits of integration for an interated integral of the form W

What is 0.125 in fraction form?

How many months are in 3 years?

Find the directional derivative of the function f(x,y) = tan^(-1)(xy) at the point (3,2) in the direction of the vector v = 5i + 4j.

What is 75 divided by 8?

Find the derivative with respect to \theta if y=\ln \frac{e^{9\theta}}{1+e^{9\theta}}

Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the curves y = sqrt(x - 1), y = 0, and x = 5 about the line y = 3.

Find the length of the curve:r(t) = 9i + t2j + t3k, 0 %3C= t %3C= 1

A population is modeled by the differential equation given below. dP/dt = 1.3P(1 - P/4200) (a) For what values of P is the population increasing? (b) For what values of P is the population decreasing?

Let C be the curve of intersection of the parabolic cylinder x^2 = 2y, and the surface 3z = xy. Find the exact length of C from the origin to the point ( 5 , 25 / 2 , 125 / 6 ).

What is two thirds times four?

86 is 45% of what number?

What is 22 divided by 4?

What is 48% as a fraction?

Round 739 to the nearest hundred.

Determine the sum of the following series (-4^(n-1))/5^n from n = 1 to infinity.

Find the centroid of the region bounded by the given curves. y = 6 sin 2x, y = 6 cos 2x, x = 0, x = pi/ 8

Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. f(x, y) = 10x + 10y; x^2 + y^2 = 50.

Find the number of multiples of 7 between 30 and 300

What is the product of a number and its reciprocal?

Find the derivative of the function g(x) = integral of 1/sqrt(3 + t^4) dt from tan x to 4x^2.

A sphere of radius 3 inches is sliced with two parallel planes: one passes through the equator and the other is H inches above the first plane. The resulting portion of the sphere between the two plan

What is 84 divided by 6?

Find the dimensions of the box with volume 8000 cm^3 that has minimal surface area. (Let x, y, and z be the dimensions of the box.)

Solve the following differential equation: y''+10y'+25y=0

Find the centroid of the region bounded by the curves y = 2x^3 - 2x and y = 2x^2 - 2. Sketch the region and plot the centroid to see if your answer is reasonable.

How many mm is a dime?

What is 120 divided by 15?

Operations that undo each other are called

Round the number 14.587020 to 4 significant digits

What is the GCF of 48 and 60?

How many feet is 3 meters?

Find the derivative of the following functions: A) f(x) = e^(x^2 + x) - sqrt(ln x). B) f(x) = x^3 e^x. C) f(x) = (e^x)/(1 + x^2).

What is 9.5 as a fraction?

Find the volume of the wedge-shaped region contained in the cylinder x^2+y^2=49 and bounded above by the plane z=x and below by the xy-plane.

What is 6 to the 6th power?

Compute the length of the curve C with parametrization r(t) = (e^t, sqrt(2)t, e^(-t)), -1 less than or equal to t less than or equal to 1.

Determine whether the geometric series is convergent or divergent. 10 - 4 + 1.6 - 0.64 + ... If it is convergent, find its sum.

Find the absolute maximum and absolute minimum values of the function, if they exist, over the indicated interval. f(x) = 1/3x^3 - 5x; [-8, 8].

Find the exact area of the surface obtained by rotating the given curve about the x-axis. Using calculus with Parameter curves.x = 6t - 2t3, y = 6t2, 0 t 1

1. Determine whether the geometric series is convergent or divergent and find its sum. 9 + 8 + 64//9 + 512/81 + ... 2. Determine whether the geometric series is

Round 76 to the nearest ten.

Solve the given initial-value problem. The DE is a Bernoulli equation. x2? dy/dx ? 2xy = 6y4, y(1) = 1/4

What is half of 500?

Find the linear approximation of the function f(x, y, z) =x2 + y2 + z2 at (2, 6, 9) and use it to approximate the number 2.022 + 5.992 + 8.972. (Round your answer to five decimal places.)

What is 80 divided by 4?

20,000 pounds equals how many English tons?

What are the first 5 multiples of 7?

A particle starts at the point (-3, 0), moves along the x-axis to (3, 0), and then along the semicircle y = sqrt(9 - x^2) to the starting point. Use Green's Theorem to find the work done on this particle by the force field F(x, y) = %3C3x, x^3 + 3xy^2%3E

What is 39 percent as a fraction?

Find the area inside one leaf of the rose: r = 3sin(4theta).

Use Stokes' Theorem to evaluate S curl F dS. F(x, y, z) = 4y cos z i + ex sin z j + xey k, S is the hemisphere x2 + y2 + z2 = 49, z %3E= 0, oriented upward.

What is one half of 22?

20 percent of what number is 14?

What is 3,000 divided by 12?

What is the square root of 117?

Find a cubic function f(x) = ax3 + bx2 + cx + d that has a local maximum value of 4 at x = -4 and a local minimum value of 0 at x = 2.

Use polar coordinates to find the volume of the solid bounded by the paraboloid z = 7 - 6x^2 - 6y^2 and the plane given by z = 1. Show steps needed to compute this answer by hand calculation.

What is 21 divided by 7?

Show that the vector field F(x,y,z)=(4ycos(-2x),-2xsin(4y),0) is not a gradient vector field by computing its curl. How does this show what you intended?

What is two-fifths of 30?

How to find the annual interest rate

What is the percent composition of sulfur in sulfur dioxide?

Set up the iterated integrals for both orders of integration. Then evaluate the double integral using the easier order. Double integral y dA, D is bounded by y = x - 56; x = y^2

Find the surface area of the solid obtained by rotating the parametric curve c(t) = (cos^3 t, sin^3 t) about the x-axis for 0 less than equal t less than equal pi/2.

Find Values of m so that the function y = e^mx is a solution of the given differential equation: y'' - 5y' + 6y = 0

Solve the differential equation dR/dx=a(R2+16). Assume a is a non-zero constant, and use C for any constant of integration that you may have in your answer.

There is a rectangular box whose length x, width y and height z are changing at the following rates: the length x is decreasing at a rate of 2 ft/hour, the width y is increasing at a rate of 1 ft/hour

What is 2 percent as a fraction in simplest form?

Solve 3 - 3 * 6 + 2

Find all critical points of f(x) = -3x^4 + 16x^3 - 24x^2 + 36 and classify each as a relative minimum, relative maximum, or neither one.

What is 0.375 as a fraction in simplest form?

What is 162 divided by 3?

Find fx(1, 0) and fy(1, 0) and interpret these numbers as slopes for the following equation. f(x, y) = sqrt(4 - x^2 - 3y^2) fx(1, 0) = fy(1, 0) =

What is 42 divided by 6?

Round 65 to the nearest ten.

A particle moves along the curve below. y = 8 + x3 As it reaches the point (1, 3), the y-coordinate is increasing at a rate of 4 cm/s. How fast is the x-coordinate of the point changing at that instan

Solve the given differential equation by using an appropriate substitution. The DE is homogeneous. (x - y)dx + x dy = 0

What is 135 divided by 2?

What is the square root of 96?

What is 10.5 as an exponent?

For the surface with parametric equations r(s, t) = (st, s + t, s - t), find the equation of the

Find the solution r(t) of the differential equation with the given initial condition: r'(t) = %3Csin2t, sin2t, 7t%3E, r(0) = %3C8, 7, 6%3E

Using disk or washers, find the volume of the solid obtained by rotating the region bounded by the curves y = x^2 and y = 4 about the line y = 4.

Find an equation of the tangent plane to the given surface at the specified point. z = 6(x - 1)^2 + 4(y + 3)^2 + 4, (2, -2, 14).

If a vector has direction angles alpha = pi/4 and beta = pi/3, find the third direction angle gamma.

Find the work done by the force field F in moving an object from A to B. F(x,y)= 2y^{\frac{3}{2}}\mathbf{i} +3x\sqrt{y}\mathbf{j} A(1,1), B(2,9)

What is 9 as a fraction in simplest form?

What percent of 29 is 3?

Find the indicated partial derivative. R(s, t) = tes/t; Rt(0, 3)

Find the volume of the solid formed by revolving the region bounded by the graphs of y = x^4 + 2x^2 + 1, y = 1, and x = 1 about the line x = 2.

What is the square root of 108?

A worker on a scaffolding 75 ft above the ground needs to lift a 500 lb bucket of cement from the ground to a point 30 ft above the ground by pulling on a rope weighing 0.5 lb/ft. How much work is req

Consider the equation below. f(x) = 9 sin x + 9 cos x 0 x 2pi a) Find the intervals on which f is increasing. Find the intervals on which f is decreasing. b) Find the local minimum and maximum values

How to convert cm2 to m2?

What is two-thirds plus two-thirds?

Consider the vector field F(x,y,z)=xi+yj+zk. a) Find a function f such that F= f and f(0,0,0)=0. b) Use part a to compute the work done by F on a particle moving along the curve C given by r(t)=(1+3si

80 percent of what number is 20?

Consider the solid that lies above the square (in the xy-plane), R = [0, 2] x [0, 2], and below the elliptic paraboloid z = 25 - x^2 - 2y^2. (A) Estimate the volume by dividing R into 4 equal squares and choosing the sample points to lie in the lower

Find the centroid of the region in the first quadrant bounded by the given curves; y = x^3 and x = y^3.

What is 45 divided by 2?

What is 8 divided by 32?

What is 12 divided by 5?

Find the area enclosed by the ellipse x2/a2 + y2/b2 = 1

A spherical shell centered at the origin has an inner radius of 3 cm and an outer radius of 4 cm. The density of the material increases linearly with the distance from the center. At the inner surface

What is 90 divided by 6?

Write an equivalent series with the index of summation beginning at n = 1. sum n=0 infty (-1)n+1(n+1)xn

Find the inflection point(s), if any, of the following function: f(x) = (x - 8)^4/3

Use implicit differentiation to find an equation of the tangent line to the curve at the given point. y sin 8x = x cos 2y, (?/2, ?/4)

What is 200 divided by 6?

A Bernoulli differential equation is one of the form \frac{dy}{dx} + P(x)y = Q(x)y^n. Observe that, if n=0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u=y^{1-n} tr

Calculate the derivative using implicit differentiation:{partial w / partial z}, {x^2w+w^8+wz^2+9yz=0}. Find dw/dz

You are given the following. F(x,y,z) =(x - 2z)i + (x +y + z)j + (x - 2y)k (a) Find the curl. i + j + k (b) Find the divergence of the vector field.

What is 6 cubed?

What are the factors of 45?

Find the derivative of the function y=arctan(sqrt(1+x/1-x))

Solve the differential equation by variation of parameters. y'' + 3y' + 2y = cos(e^x)

Suppose that f(2)=-5, g(2)=4, f'(2)=-1, and g'(2)=3. a) h(x) = 4f(x) - 2g(x) Find h'(2). b) h(x) = f(x)g(x) Find h'(2). c) h(x) = f(x)/g(x) Find h'(2). d) h(x) = g(x)/(1+f(x)) Find h'(2).

Give an equation of the plane whose trace in the yz-plane has equation y = 7z, and in the xy-plane has equation y =-4x

Find the absolute maximum and minimum of the function f(x,y)=y(x)^(1/2)-y^2-x+3y on the domain 0 less than x less than 9, 0 less than y less than 3. Absolute minimum value: attained at Absolute maxim

a) Find the point at which the given lines intersect. r = (3,3,0) + t(3,-3,3) r = (6,0,3) + s(-3,3,0) b) Find the equation of the plane that contains these lines.

Find the exact length of the curve x = 6 + 6t^2, y = 3 + 4t^3, 0 less than or equal to t less than or equal to 5.

Use a power series to approximate the definite integral, I, to six decimal places, i.e., so that the error is less than 0.0000005. Integral of 0 to 0.3 1/(1 + x^5) dx.

Evaluate the following limit: Limit as x goes to 0 of ((1/1 + 2x^5) - 1 + 2x^5 - 4x^10)/(6x^15).

What is 90 divided by 3?

What is the square root of 172?

Find the area lying outside r = 4sin(theta) and inside r = 2 + 2sin(theta).

Write the equations in cylindrical coordinates. (a) 5z = 7x^2 + 7y^2 z = ___________ (b) 5x^2 + 5y^2 = 7^y r = ___________

Find the solution of the differential equation that satisfies the given initial condition. du/dt = (2t + sec^2(t))/(2u), u(0) = -8

Suppose xy = -2 and dy/dt = -2. Find dx/dt when x = 4.

Why do fractions need a common denominator?

What is 1 liter in cups?

Round 6.724 to the nearest hundredth

What is 47 divided by 3?

What does 'how much' mean in math?

Sketch a contour diagram of each function. Then, decide whether its contours a predominantly lines, parabolas, ellipses or hyperbola. 1. z = -4x2 2. z = x2 - 4y2 3. z = y - 4x2 4. z = x2 + 3y2

Find the equation of the tangent line to the curve f(theta) = theta*csc(theta) - (1/2)*cot(theta) at theta = pi/2.

Show that the ellipsoid 3x^2 + 2y^2 + z^2 = 9 and the sphere x^2 + y^2 + z^2 - 8x - 6y -8z + 24 = 0 are tangent to each other at the point (1,1,2)

What are the prime numbers between 30 and 45?

What is the square root of 130?

Determine the force due to hydrostatic pressure on the flat vertical side of a tank which has the shape in feet of the boundaries y=0, y=10lnx, y=10ln(-x) and the line y=10ln24. Note that water has density 62.4 lb/ft^3

Compute Delta y and dy for the given values of x and dx = Delta x. (Round your answers to three decimal places.) y = sqrt x , x = 1 , Delta x = 1

Evaluate the following limits: a) limit as x goes to two of (x^3 - 2x^2)/(10x-20) and b) limit as x goes to zero of (2x)ln(x^2).

What is 6 divided by 9?

What is 3.5 squared?

Evaluate the integral using the indicated trigonometric substitution. (Use C for the constant of integration.) x3x2 + 64dx, x = 8 tan

Find the arc length function for the curve y = 2x^3/2 with starting point P0(25, 250).

An aquarium 4 m long, 3 m wide, and 2 m deep is full of water. Find the work needed to pump half of the water out of the aquarium. (Use the fact that the density of water is 1000 kg/m^3, and use 9.8 m/s^2 for g.)

Solve the initial value problem for r as a vector function of t. Differential equation: dr/dt = -7ti - 5tj - 5tk Initial condition : r(0) = 5i+j+2k

What is 56 divided by 6?

Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x, y, z) = (2x + y)/z, (3, 6, -1) Find direction of maximum rate of change (in unit vector)

A lamina occupies the region inside the circle x^2 + y^2 = 10y but outside the circle x^2 + y^2 = 25. Find the center of mass if the density at any point is inversely proportional to its distance from

Find the two x-intercepts of the function f(x) = -8x\sqrt{x+1} and find the optimum value. Also find the point/s at which the optimum exists.

Find all points on the graph of the function f(x) = 2 cos x + cos2 xat which the tangent line is horizontal. (Use n as your arbitrary integer.)

Consider the following equation. f(x,y) = y4/x, P(1,2). u=1/3(2i+swrt5j) a) Find the gradient of f. b) Evaluate the gradient at the point P. c) Find the rate of change of f at P in the direction of th

What is a proportion?

A piece of wire 18 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. (a) How much wire should be used for the square in order to maximi

Trevor bought 8 gallons of paint to paint his house. He used all but 1 quart. How many quarts of

What is 14 squared?

Find the volume of the given solid. Under the plane 7x + 2y - z = 0 and above the region enclosed by the parabolas y = x^2 and x = y^2.

Find the second Taylor polynomial T2(x) for f(x)=ex2based atb=0. For values of x near 0,T2(x) = ex2. Approximate the value of 1ex20dxby computing 1T2(x)0dx.

Find the solution r(t) of the differential equation with the given initial condition: r'(t) =

What is 10 percent of 70,000?

For the following function, determine the intervals on which the following functions are increasing and decreasing and classify each of the critical points as a relative minimum, a relative maximum, o

What is 7/8ths as a decimal?

What is 10 of 10?

Use the gradient to find the directional derivative of the function at P in the direction of Q. f(x,y) = 3x^2 - y^2 + 4, P(5, 3), Q(2, 2).

A curve C is given by a vector function r(t), 4 t 6, with unit tangent T(t), unit normal N(t), and unit binormal B(t). Indicate whether the following line intergrals are positive, negative or zero.

Consider the helix r(t)=(cos(-2t),sin(-2t),4t). Compute, at t=pi/6: the unit tangent vector T

Find the arc length of the curve f(x)=ln(cos x) over the interval [0, pi/4]

Gravel is being dumped from a conveyor belt at a rate of 40 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is

What is 10,000 divided by 24?

Find the exact length of the curve y = 2 + 2x^(3/2) for 0 less than or equal to x less than or equal to 1.

What is 156 minutes in hours?

A) Solve the given differential equation by undetermined coefficients y'' + 4y = 7 sin 2x B) Solve the given intial-value problem 5y'' + y' = -4x, y(0) = 0, y'(0) = -5y

What is the square root of 2.25?

A warehouse selling cement has to decide how often and in what quantities to reorder. It is cheaper, on average, to place large orders, because this reduces the ordering cost per unit. On the other ha

Find the square root of the fraction 64/100

Use the Chain Rule to find dz/dt.z = x2 + y2 + xy, x = sin t, y = 9et

If a ball is thrown vertically upward with a velocity of 80 ft/s, then its height after t seconds is S = 80t - 16t^2. What is the velocity of the ball when it is 96 ft above the ground on its way up?

What is 52 divided by 8?

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