Sunday

September 25, 2016
**calculus**

Find the dimensions of the rectangle with the largest area if the base must be on the x-axis and its other two corners are on the graph of: (a) y=16-x²,-4<=x<=4 (b)x²+y²=1 (c)|x|+|y|=1 (d)y=cos(x),-pi/2<=x<=pi/2

*Monday, May 2, 2016 by Jay*

**calculus**

Evaluate lim (1³ +2³ +3³ +…+ n3)/n^4 n →∞ by showing that the limit is a particular definite integral and evaluating that definite integral.

*Monday, May 2, 2016 by Jay*

**calculus**

Evaluate π ∫ tan² x/3 dx 0

*Monday, May 2, 2016 by Jay*

**calculus**

Use the Fundamental Theorem of Calculus to find G'(x) if: G(x)=∫ up(x²) bottom(1) cost dt

*Monday, May 2, 2016 by Jay*

**calculus**

Use the Fundamental Theorem of Calculus to find G'(x) if: /x² G(x)= / cos t dt / 1

*Monday, May 2, 2016 by Jay*

**calculus**

I'm having trouble on this question: Find the area of the region in the first quadrant that is bounded above by the curve y= sq rt x and below by the x-axis and the line y=x -2.

*Monday, May 2, 2016 by Jay*

**Calculus**

A conical cistern is 10 ft. across the top and 12 ft. deep. If water is poured into the cistern at the rate of 1 cubic foot per second, how fast is the surface rising when the water is 8 ft. deep?

*Monday, May 2, 2016 by Claire*

**Calculus**

A particle travels along the parabola y=ax^2+x+b. At what point do its abscissa and ordinate change at the same rate?

*Monday, May 2, 2016 by Alexa*

**Calculus**

A light hangs 15 ft. directly above a straight walk on which a man 6 ft. tall is walking. How fast is the end of the man's shadow travelling when he is walking away from the light at a rate of 3 miles per hour?

*Monday, May 2, 2016 by Sandra*

**calculus too hard help**

if y=x^x^x^x... dy/dx=? plz show working thanks got no ideal at all

*Monday, May 2, 2016 by sam*

**Calculus - urgent**

A lamina. defined by y>=0 with edges y=0, y=3/2(1-x^2) and x=-y+2y^2, for which the density is given by p(x,y)=y. a) define domain as union of type 1 and type 2 region. b) Calculate mass of lamina.

*Monday, May 2, 2016 by Alex*

**calculus**

Given the area is in the first quadrant bounded by y²=x, the line x=4 and the 0X What is the volume generated when this area is revolved about the 0X? the answer is 25.13 but I don't know how. help me please

*Sunday, May 1, 2016 by ced*

**Calculus**

A cardioid r=1+cos(theta) A circle r=3*cos(theta) a) Define the domain of the region enclosed inside both the cardioid and the circle. b) Use polar coordinates to calculate the area. (We can use symmetry about x-axis)

*Sunday, May 1, 2016 by Alex*

**Calculus**

Air expands adiabatically in accordance with the law PV^1.4=Const. If at a given time the volume is 14 cubic feet and the pressure is 40 pounds per square inch, at what rate is the pressure changing when the volume is decreasing 1 cubic foot per second?

*Sunday, May 1, 2016 by Alexa*

**Calculus**

One ship is sailing south at a rate of 5 knots, and another is sailing east at a rate of 10 knots. At 2 P.M. the second ship was at the place occupied by the first ship one hour before. At what time does the distance between the ships not changing?

*Sunday, May 1, 2016 by Sandra*

**Calculus**

An island is 3 mi from the nearest point on a straight shoreline; that point is 6 mi from a power station. A Utility company plans to lay electrical cable underwater from the island to the shore and then underground along the shore to the power station. Assume ...

*Saturday, April 30, 2016 by Laura*

**Calculus**

Optimization: A man on an island 16 miles north of a straight shoreline must reach a point 30 miles east of the closet point on the shore to the island. If he can row at a speed of 3 mph and jog at a speed of 5 mph, where should he land on the shore in order to reach his ...

*Saturday, April 30, 2016 by Sammy*

**calculus**

Assume that the radius ,r , of a sphere is expanding at a rate of 10in./min. The volume of a sphere is V=43πr^3. Determine the rate at which the volume is changing with respect to time when r=5in. The volume is changing at a rate of how many in^3/min.?

*Saturday, April 30, 2016 by Marquese*

**Calculus**

Find the area of the largest rectangle having one side on the x-axis and inscribed in a triangle formed by the lines y=x, y=0 and 3x+y=20.

*Saturday, April 30, 2016 by Sandra*

**Calculus**

Find the area of the largest rectangle with sides parallel to the coordinate axes which can be inscribed in the area bounded by the two parabolas y=26-x^2 and y=x^2+2

*Friday, April 29, 2016 by Alexa*

**Calculus**

An object's velocity after t seconds is v(t)= 38-2t feet per second. a. How many seconds does it take for the object to come to a stop (velocity = 0)? b. How far does the car travel during that time? c. How many seconds does it take the car to travel half the distance in ...

*Friday, April 29, 2016 by Adam*

**Calculus**

A bucket begins weighing 15 pounds, including the sand it holds. The bucket is to be lifted to the top of a 50 foot tall building by a rope of negligible weight. However, the bucket has a hole in it, and leaks 0.1 pounds of sand each foot it is lifted. Find the work done ...

*Friday, April 29, 2016 by Joey*

**College Algebra/pre-calculus**

The question is to evaluate each logarithm: My professor wants us to show work. Could you please tell me if I'm on the right track? Thank you!!! 1. log6^(1/36)= -2 2. ln(1/e^4)= 1/e^2 3. log7^1= 0 4. log4^64= ln64/ln4= 3 5. log10^8= ln8/ln10= .9031 6. log3^(radical 3)= I ...

*Friday, April 29, 2016 by Need Help*

**Pre Calculus**

A cylinder shaped can needs to be constructed to hold 200 cubic centimeters of soup. The material for the sides of the can costs 0.02 cents per square centimeter. The material for the top and bottom of the can need to be thicker, and costs 0.06 cents per square centimeter. ...

*Friday, April 29, 2016 by Joey*

**Pre Calculus**

A piece of cardboard measuring 13 inches by 11 inches is formed into an open-top box by cutting squares with side length x from each corner and folding up the sides. a. Find a formula for the volume of the box in terms of x b. Find the value for x that will maximize the volume...

*Friday, April 29, 2016 by Joey*

**Calculus**

Find the dimensions of the largest right circular cylinder that can be inscribed in a sphere of radius 6 inches.

*Thursday, April 28, 2016 by Sandra*

**Calculus**

An open box is formed from a piece of cardboard 12 inches square by cutting equal squares out of the corners and turning up the sides, find the dimensions of the largest box that can be made in this way.

*Thursday, April 28, 2016 by Alexa*

**Math, Pre-Calculus.**

A postal airplane leaves lsland A and flies 91 miles to Island B. It drops off and picks up mail and flies 63 miles to lsland C. After unloading and loading A- mail, the plane returns to lsland A at an average rate of 300 miles per hour. How long does it take the pilot to ...

*Thursday, April 28, 2016 by Daniel López*

**Calculus**

Evaluate as limit approaches 0. (Without using l'hopital's rule. ( Sqrt(4+sin(x))-2 ) / (3x)

*Thursday, April 28, 2016 by Brian*

**Calculus**

find the point on the plane 5x+4y+z=12 that is nearest to (2,0,1)

*Thursday, April 28, 2016 by Lyndsay*

**Pre-Calculus**

suppose y is directly proportional to x. if y=6 when x=4, find the constant of proportionality and write the formula for y as function of x. Use your formula to find x when y=8.

*Wednesday, April 27, 2016 by Monica*

**Calculus **

Find the 4th Taylor polynomial, P4, generated by f(x) = 1/x at center a = 2 ?

*Wednesday, April 27, 2016 by ChrismB*

**Calculus**

Sketch the region enclosed by the curves given below. Decide whether to integrate with respect to x or y. Then find the area of the region. y=4cos(x),y=4−8x/π. I thought it was the integral of 4cos(x)- the integral of 4- 8x/π on the interval 0 to π/2. This...

*Wednesday, April 27, 2016 by Kevin*

**pre-calculus**

Rewrite the following expression as an algebraic function of x sin(arccos(x/2)) I know sine is y, which is opposite over hypotenuse. I also know that arccos is the inverse of cosine. I'm confused on what the question is asking and what to do with the x. Please help! Thanks

*Wednesday, April 27, 2016 by Em*

**Calculus**

Find the 4th Taylor polynomial, P4, generated by f(x) = 1/x at center a = 2 ?

*Wednesday, April 27, 2016 by ChrismB*

**Calculus**

give a parametrization of the ellipse x^2/25 + y^2/9 =1 that travels once counter clockwise in an interval at belongs to (0, 2pi)?

*Wednesday, April 27, 2016 by ChrismB*

**calculus**

A rectangular closed box with a square base is to have a capacity of 27 cubic inches determine the least amount of material required.

*Wednesday, April 27, 2016 by gillian*

**calculus**

What are the dimensions of a rectangular field of area A that requires the least amount of fencing.

*Wednesday, April 27, 2016 by gillian*

**calculus**

A rectangular lot has a perimeter of 320meters determine the maximum area of the lot

*Wednesday, April 27, 2016 by gillian*

**Pre-Calculus **

Determine the balance A for P dollars invested at rate R compounded N times per year for T years. Round each amount to the nearest cent P= $1000, R=3% t=10 years N=A 2=? 4=? 12=? 365=? Compounded continuously=?

*Tuesday, April 26, 2016 by Juniper*

**Pre-Calculus **

g(x)= x^2+7 Find the inverse of g(x) and state the domain and range for the inverse of g(x) using interval notation

*Tuesday, April 26, 2016 by Juniper*

**Calculus**

Two cars leave an intersection at the same time. Car X is travelling East at 50 km/hr and Car Y is travelling South at 60 km/hr. Find the rate at which the cars are separating after 30 minutes. I want its complete solution

*Tuesday, April 26, 2016 by ChrismB*

**Calculus**

Along reservoir has the shape of a right circular cone having a radius of 40m at the top and a height of 10m at the centre. it is being filled at a constant rate of 40 m^3/min.Find the rate at which the water level is rising when the height is 5m?

*Tuesday, April 26, 2016 by ChrismB*

**Calculus**

A spherical balloon is being inflated and the radius of the balloon is increasing at a rate of 2cm/min. At what rates are the volume and surface area of the balloon increasing when the radius is 5cm?

*Tuesday, April 26, 2016 by ChrismB*

**Calculus 2**

Suppose that a spring has a natural length of 25 cm, and that 8 J of work is needed to stretch from a length of 50 cm to 80 cm. How far beyond its natural length will a force of 32 N keep the spring stretched? **I've tried calculating the spring constant ...

*Monday, April 25, 2016 by David*

**Calculus II**

So I'm trying to integrate a function using partial fractions. Here is the integral of interest: ∫(3x^2+5x+3)/[(x+2)(x^2+1)]dx. Since the numerator's degree of the polynomial is lesser than that of the denominator's degree, it is clear to separate. However, ...

*Monday, April 25, 2016 by Justin*

**Calculus**

Sand pouring from a conveyor belt forms a conical pile the radius of which is 3/4 of the height. If the sand is filling up at a constant rate of 1/2m^3/min, at what rate is the height of the pile is growing 3 min after the pouring starts?

*Monday, April 25, 2016 by ChrismB*

**Calculus II**

So I have Maclaurin series for sinx = ∑(-1)^n[x^(2n+1)]/(2n+1)!. I need to write out new series for sin(x^2). This will be equivalent to squaring the whole Maclaurin series of sinx, right? I'm just confused as to what terms are squared, and thus what the final ...

*Monday, April 25, 2016 by Justin*

**Calculus**

two small planes take off from the same airport at the same time. One travels north at 200 km/h, and the other, west at 150 km/h. If the planes fly at the same altitude, how fast are they separating after 2 hours?

*Monday, April 25, 2016 by Sarah*

**Calculus**

A ladder 6m long rests against the vertical wall. How far is the top of the ladder sliding down the wall when the bottom of the ladder is 4m from the wall and sliding at a speed of 1m/s?

*Monday, April 25, 2016 by Asfand*

**Calculus**

A spherical water balloon is being filled with water at the rate of 125 cubic inches per minute. At what rate is the radius increasing when the radius is 10 inches? At what rate is the surface area increasing?

*Monday, April 25, 2016 by Anonymous*

**Calculus**

A bead moves on a circular wire x^2 + y^2 = 25. As it passes the point (3,4), the x-coordinate is decreasing at a rate of 2 units per second. At what rate is the y changing?

*Monday, April 25, 2016 by Anonymous*

**Calculus**

A man is 2 m tall is walking at a rate of 1 m per second in a straight line away from a 10 m lamppost. How fast is the tip of his shadow moving away from the lamppost?

*Monday, April 25, 2016 by Anonymous*

**Calculus**

Two cars leave an intersection at the same time. Car X is travelling East at 50 km/hr and Car Y is travelling South at 60 km/hr. Find the rate at which the cars are separating after 30 minutes.

*Monday, April 25, 2016 by Andreyall*

**Calculus**

A spherical balloon is being inflated and the radius is increasing at a constant rate of 2 cm per minute. At what rates are the volume and surface area of the balloon increasing when the radius is 5 cm? For this problem do I plug in the 5 cm into the Volume formula ( 4/3 pi r^...

*Monday, April 25, 2016 by Andreyall*

**Calculus**

Two cars leave an intersection at the same time. Car X is travelling East at 50 km/hr and Car Y is travelling South at 60 km/hr. Find the rate at which the cars are separating after 30 minutes.

*Monday, April 25, 2016 by Kaya*

**Calculus**

two small planes take off from the same airport at the same time. One travels north at 200 km/h, and the other, west at 150 km/h. If the planes fly at the same altitude, how fast are they separating after 2 hours?

*Monday, April 25, 2016 by Kaya*

**Calculus**

A boat is held at a dock by a bow line which is wound about a circular windlass 3 feet higher than the bow of the boat. How fast is the bow line increasing its length at the instant the boat is 4 feet from the dock if the boat is drifting at a rate of 7 feet per second from ...

*Monday, April 25, 2016 by Kaya*

**CALCULUS**

Water is draining from a small cylindrical tank into a larger one below it. The small cylindrical tank has a radius of 4 feet and a height of 6 feet; the large cylindrical tank has a radius of 8 feet and a height of 16 feet. The small tank is initially full of water, and the ...

*Monday, April 25, 2016 by Anonymous*

**AP Calculus **

A race car is running practice laps in preparation for an upcoming race. To judge how the car is performing, the crew takes measurements of the car's speed S(t) (in miles per hour, or mph) every minute. The measurements are given in the table below. t (min) --- S(t) (mph 0...

*Monday, April 25, 2016 by Anonymous*

**Calculus**

An equation of the line with slope -1 that passes through the point (2,5) is y=-x+7

*Sunday, April 24, 2016 by Ryan*

**Calculus quick question pls**

Why is there no vertical asymptote on F(x) = x/(x^2+1) What i learned is that to find vertical asymptote you have to set the denominator To 0 and solve for x ? In that case I find that x=-1,1

*Sunday, April 24, 2016 by Amelia*

**calculus**

Find the maximum value of the function f(x)=(x^2+9x-3) / x^2

*Sunday, April 24, 2016 by Jay*

**calculus**

Find the critical numbers for the function f(x) = 2x / sqrt(x-1)

*Sunday, April 24, 2016 by Jay*

**Calculus**

a(t)=4sin3t;v(0)=1,s(0)=6 I'm trying to find expression for s(t). Should I wait till the end to add find and add constant. I got [1/9(13t-4sin(3t))+6] and it was wrong.

*Sunday, April 24, 2016 by Anon*

**Calculus!!**

Consider the differential equation given by dy/dx = xy/2. A. Let y=f(x) be the particular solution to the given differential equation with the initial condition. Based on the slope field, how does the value of f(0.2) compare to f(0)? Justify your answer. B. Find the particular...

*Saturday, April 23, 2016 by Anonymous*

**AP Calculus**

Suppose that f has a continuous second derivative for all x, and that f(0)=1, f'(0)=2, and f''(0)=0. A. Does f have an inflection point at x=0? Explain your answer. B. Let g'(x) = (3x^2 + 2)f(x) + (x^3 + 2x + 5)f'(x). The point (0,5) is on the graph of g. ...

*Saturday, April 23, 2016 by Anonymous*

**Calculus **

Water is draining from a small cylindrical tank into a larger one below it. The small cylindrical tank has a radius of 4 feet and a height of 6 feet; the large cylindrical tank has a radius of 8 feet and a height of 16 feet. The small tank is initially full of water, and the ...

*Saturday, April 23, 2016 by Anonymous*

**Calculus **

Let M be the region under the graph of f(x) = 3/e^x from x=0 to x=5. A. Find the area of M. B. Find the value of c so that the line x=c divides the region M into two pieces with equal area. C. M is the base of a solid whose cross sections are semicircles whose diameter lies in...

*Saturday, April 23, 2016 by Anonymous*

**Calculus **

A race car is running practice laps in preparation for an upcoming race. To judge how the car is performing, the crew takes measurements of the car's speed S(t) (in miles per hour, or mph) every minute. The measurements are given in the table below. t (min) --- S(t) (mph 0...

*Saturday, April 23, 2016 by Anonymous*

**AP Calculus**

Consider a curve given implicitly by the equation (1+x)y^3 + (x^4)y - 85 = 0. A. Calculate dy/dx at a general point (x,y). B. Write the equation of the tangent line to the curve at the point (3,1). C. At (3,1), y(x) is defined implicitly as a function of x. Let g(x) be the ...

*Saturday, April 23, 2016 by Anonymous*

**Calculus**

If f(2) = 2.5 and f'(2) = -2.5, then f(2.5) is approximately: A. 2.5 B. -2.5 C. -2 D. 2 E. 1.25

*Saturday, April 23, 2016 by Anonymous*

**Calculus **

The rate of decay is proportional to the mass for radioactive material. For a certain radioactive isotope, this rate of decay is given by the differential equation dm/dt = -.022m, where m is the mass of the isotope in mg and t is the time in years. A. If m(0)=20, write a ...

*Saturday, April 23, 2016 by Anonymous*

**Calculus **

The equation dy/dx = -6x^2/y gives the slope at any point on the graph of f(x). The range of f(x) is [0, infinity] and f(1) = 2. A. Find the equation of the tangent line to f(x) at the point (1,2). B. Write the function f(x). C. Determine the domain of the function f(x).

*Saturday, April 23, 2016 by Anonymous*

**Calculus**

Compute the curvature. r(t)=(t^2,2t^3/3) t >0 The answer is 1/2t(1+t^2)^3/2 I have tried multiple times but i cannot arrive to this answer.

*Saturday, April 23, 2016 by Lyndsay*

**Calculus Help**

Evaluate lim x-->25 5 - square root x / x - 25 I don't get how the answer is -1/10

*Friday, April 22, 2016 by Anonymous*

**Calculus I**

The area enclosed by the curve y^2 = x(2 − x) is given by what definite integral? Should I begin by square rooting both sides? Not really sure.

*Friday, April 22, 2016 by Jer*

**Calculus I**

Which of the following represents the volume of the solid formed by revolving the region bounded by the graphs of y =x^3, y = 1, and x = 2, about the line x = 2?

*Friday, April 22, 2016 by Jer*

**Calculus I**

The base of a solid is the circle x^2 + y^2 = 9. Cross sections of the solid perpendicular to the x-axis are squares. What is the volume, in cubic units, of the solid?

*Friday, April 22, 2016 by Jer*

**Calculus I**

Find the volume of the solid formed by rotating the region bounded by the graph of y equals 1 plus the square root of x, the y-axis, and the line y = 3 about the x-axis.

*Friday, April 22, 2016 by Jer*

**Calculus**

What did I do wrong? An object is formed so that its base is the quarter circle y = sqrt(64 − x^2) in the first quadrant, and its cross sections along the x-axis are squares. What is the volume of the object? (Assume the axes are measured in centimeters.) I have already ...

*Thursday, April 21, 2016 by Ana*

**Math (Calculus)**

The function f(x)=-2x^3+10.2x^2+202.275x+0.87 is increasing on the open interval (?,?). It is decreasing on the open interval (-oo,?) and the open interval (?,+oo) The function has a local maximum at ? I used derivative -6x^2+20.4x+202.275 and find the root but it doesn't ...

*Thursday, April 21, 2016 by Anonymous*

**Calculus **

A closed box with square base is to be built. the bottom and the top of the box are to be made of a material costing $2/ft^2, and all four sides are to be made of a material costing $1/ft^2. what are the dimensions of the box of the greatest value that can be constructed for $12?

*Wednesday, April 20, 2016 by yaniv*

**Calculus**

A stone is dropped from the edge of a roof, and hits the ground with a velocity of −170 feet per second. Assume the acceleration due to gravity is -32 feet per second squared. How high (in feet) is the roof?

*Wednesday, April 20, 2016 by Anonymous*

**Calculus (easy)**

What is the polar form of (-2-2i)?

*Wednesday, April 20, 2016 by Desperate Student*

**Calculus**

Let 𝑆 be the region (in the first quadrant) bounded by a circle 𝑥^2 + 𝑦^2 = 2, 𝑦^2 = 𝑥 and the 𝑥-axis (ii) Find the volume of the solid generated by rotating the region 𝑆 about the 𝑦-axis (c) Find the surface area...

*Wednesday, April 20, 2016 by Desperate Student*

**Calculus**

Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) limit n approaches infinity of an = e^(−6/sqrt(n))

*Tuesday, April 19, 2016 by Misty*

**Calculus **

Equation: Suppose that the demand of a certain item is x = -0.7 p + 20. Evaluate the elasticity at E = 8. I'm not sure what steps to take to solve this. I know that elasticity is equal to the absolute value of [(p/q) x (dp/dq)]

*Tuesday, April 19, 2016 by James*

**Calculus**

The Riemann sum s for f(x)=4x^2, 0<=x<=1, taking the sample points to be the right endpoints is given by s=4n^2+6n+2/3n^2. True or False?

*Tuesday, April 19, 2016 by Alice*

**Calculus (Urgent, please)**

Find the area of the region enclosed by the intersection of the circle x^2+y^2=4 and the parabola y=x^2. Show work

*Tuesday, April 19, 2016 by Alice*

**calculus.can you help me on these as well@sir collins**

integrate sin^7xdx

*Tuesday, April 19, 2016 by newton*

**calculus very hard help**

integrate:cos^10xdx even with the previous hint a tutor here gave me i still don,t know it

*Tuesday, April 19, 2016 by newton*

**advanced calculus**

Many carnivals have a version of the double Ferris wheel. A large central arm rotates clockwise. At each end of the central arm is a Ferris wheel that rotates clockwise around the arm. Assume that the central arm has length 200 feet and rotates about its center. Also assume ...

*Tuesday, April 19, 2016 by please help me*

**Calculus**

Let 𝑅 be the region bounded by the four straight lines 𝑦=𝑥, 𝑥+𝑦=4, 𝑦=𝑥−2 and 𝑥+ 𝑦 = 2. Find the surface area of the surface obtained by rotating the region 𝑅 about the 𝑥-axis for 1 ...

*Tuesday, April 19, 2016 by Desperate Student*

**Calculus I**

For what values of a and b is the line -4x+y=b tangent to the curve y=ax^3 when x=4? Can anyone give me the hint?

*Tuesday, April 19, 2016 by Anonymous*

**Calculus I**

if f(x)=24, find f'(11)? How can i find it?

*Tuesday, April 19, 2016 by Anonymous*

**Calculus**

Find the arc length of the curve 𝑥(𝑡)=cos𝑡+ү05;sin𝑡, 0≤𝑡≤𝜋/2 𝑦(𝑡) = sin 𝑡 − 𝑡 cos 𝑡 ^2

*Monday, April 18, 2016 by Desperate Student*

**Calculus**

Compute (f^-1) (2) if f(x) = 7x + 3cos(x) + 2sin(x).... We tried solving it in the form (f^-1)(a) = (1/f'(f^-1(a))... or is this a u-sub problem? We are trying to figure out whose way is right with one getting the answer as 1/2 and the other 1/10... we are getting mixed up...

*Monday, April 18, 2016 by Robin*

**calculus**

Find f'x given f(x)= 1/(1+(1/(1+(1/x))))

*Monday, April 18, 2016 by Jay*

**math calculus**

Find the intervals on which the function f(x)=x²/³(10-x) is increasing and decreasing. Sketch the graph of y=f(x)and identify any local maxima and minima. Any global extrema should also be identified.

*Monday, April 18, 2016 by Jay*