Saturday

August 1, 2015

August 1, 2015

**pre-calculus 11 **

I am asked to solve the absolute value equation of |1/2x +1| =x+1 graphically. I can solve this algebraically and consider two cases for the absolute value one being positive and the other negative. I know this will be a straight line and when I solved it algebraically x=0 the...
*Wednesday, June 10, 2015 by george *

**pre-calculus 11 **

I have the question y=-|x^2 -9| I am asked for the piecewise function. I have written y={-x^2 +9 if x less than equal to -3} { x^2 -9 if x is greater than equal to 3} I am wondering if I have my are signs backwards.My reasons for choosing the signs I have is if I plug a ...
*Wednesday, June 10, 2015 by george *

**Pre calculus/ Advanced Functions**

Samuel is investigating the rate of change of the function f(x) = cos x on the interval xE[0, 2pi]. He notices that the graph of f(x) passes through the x-axis at pi/2. He also determines the instantaneous rate of change at x = 0, pi and 2pi by inspection. Based on this ...
*Tuesday, June 9, 2015 by Anonymous*

**pre-calculus 11**

abs x^2/2 -1 =x+3 solve algebraically so if I divide thru by 2 i get x^2 -2= 2x+3 simplifying x^2-2x-5 =0 solve by quadratic formula to get =3.449 and -0.445 both of which are extraneous roots if I take negative then I get -x^2 +2=2x+6 simplify to x^2 +2x +4 if taking using ...
*Tuesday, June 9, 2015 by george *

**Calculus 1**

True or false. Explain. The line x=1 is a vertical asymptote of f(x)=(x^2+x-2)/(x^2-1)
*Tuesday, June 9, 2015 by TayB*

**Calculus**

A manufacturer of a product has a monthly cost for producing x items given by C(x) = 10+2x. The selling price function for this product is p(x) = 50-.01x. Find the maximum profit the company can expect monthly
*Monday, June 8, 2015 by Schaun*

**Calculus**

An architect needs to design a rectangular room with an area of 77ft^2. What dimensions should he use in order to minimize the perimeter? I keep getting stuck on this problem. I know when I take square root of 77, it gives me 8.77. But how do I get there. xy= 77, y= 77/x P= 2x...
*Sunday, June 7, 2015 by LittlePanda*

**Calculus**

A rectangle is bounded by the x axis and the semicircle = square root 25-x^2. What length and width should the rectangle have so that its area is a maximum? When I worked the problem out(which is a bit detailed). I started with y = square root 25-x^2 then A = 2x square root 25...
*Saturday, June 6, 2015 by LittlePanda*

**Calculus**

Describe the solid whose volume is represented by the following definite integrals. The integral of 2pi(x-1)e^x from 2 to 7.
*Friday, June 5, 2015 by Alex*

**Calculus**

v(t)= t^3 - 3t^2 + 3t Are there any times after t = 0 where the particle comes to a stop? Does the particle ever slow down?
*Wednesday, June 3, 2015 by Anonymous*

**calculus**

Can I have a website of Beginner calculus books?
*Tuesday, June 2, 2015 by ken*

**Calculus**

An airplane has airspeed of 724 k/h at bearing of North 30 degrees East. If the wind velocity is 32 from west. find the ground speed and direction of plane. Teacher gives solution of 740.5 k/hr and 57.9 degrees. Can anyone show steps?
*Monday, June 1, 2015 by Trey*

**Calculus**

A(x) = x^2 + 128/x find A'(x) and A"(x)
*Sunday, May 31, 2015 by Anonymous*

**math**

Consider the distribution of mathematics SAT scores of students in honors calculus at a liberal arts college. What would you expect the shape and variation of the distribution to be? A. Symmetric with little variation B. Symmetric with large variation C. Skewed right with ...
*Thursday, May 28, 2015 by scoobs2usa*

**Calculus**

For f(x)=(1-x)/(1+x) and g(x)=x/(1-x) , find the simplified form for f [g(x)] and state the domain
*Wednesday, May 27, 2015 by Tom*

**Calculus**

Use the table below to evaluate d/dx [f[g(2x)]] at x = 1 x 1 2 3 4 f(x) 6 1 8 2 f '(x) 6 1 8 2 g(x) 1 4 4 3 g '(x) 9 5 5 -4
*Wednesday, May 27, 2015 by Tom*

**Calculus**

at what time does this equation reaches 10000? show steps. thanks w(t)=(t-10)(t-20)+4500
*Tuesday, May 26, 2015 by Reza*

**Calculus**

A box with a square base and no top is to have a volume of 32 ft3. What dimensions use the least amount of material (in other words what dimensions give minimum outside surface area)?
*Sunday, May 24, 2015 by Maddie*

**Calculus math**

how do i solve these quadratics? c=10000 9a+3b+c=7975 36a+6b+c=6400 im unsure of how to solve as a and b are unknowns...
*Thursday, May 21, 2015 by Dg*

**Calculus**

Which of the following functions is continuous at x = 5? I put a for my answer, could someone please check this? a. f(x)=(x^2-25)/(x+5) b. (x^2-25)/(x-5), x cannot equal 5 20 when x equals 5 c.(x^2-25)/(x-5), x cannot equal 5 0 when x equals 5 d. all of the functions are ...
*Thursday, May 21, 2015 by Tom*

**calculus **

Peter the punter decided to place $10,000 into a high growth share portfolio. After 3 weeks his investment was looking rather sad, with the value of his portfolio falling $2,025. Unperturbed, Peter stuck with his original plan to hold the stock for at least 6 months. But after...
*Thursday, May 21, 2015 by Roney*

**Calculus and quadratic equations**

Peter the punter decided to place $10,000 into a high growth share portfolio. After 3 weeks his investment was looking rather sad, with the value of his portfolio falling $2,025. Unperturbed, Peter stuck with his original plan to hold the stock for at least 6 months. But after...
*Wednesday, May 20, 2015 by Roney*

**Calculus**

Which of the following statements is/are true? I.If f '(c) = 0, then f has a local maximum or minimum at x = c. II.If f is continuous on [a, b] and differentiable on (a, b) and f '(x) = 0 on (a, b), then f is constant on [a, b]. III.The Mean Value Theorem can be ...
*Wednesday, May 20, 2015 by Tom*

**Calculus**

The function's value will always be greater than or equal to the local linear approximation of a function f if, for all x in an interval containing the point of tangency, f " > 0 f " < 0 f ' > 0 f ' < 0
*Wednesday, May 20, 2015 by Tom*

**Calculus**

The function's value will always be greater than or equal to the local linear approximation of a function f if, for all x in an interval containing the point of tangency, f " > 0 f " < 0 f ' > 0 f ' < 0
*Wednesday, May 20, 2015 by Tom*

**Calculus**

(a) Consider the region in the xy-plane consisting of the points (x; y) satisfying x > 0, y > 0, and lying between the curves y = x^2 + 1, y = 2x^2 2 and the two axes. Draw a diagram of this region. (b) This region is rotated about the y-axis to form a solid glass vase. ...
*Tuesday, May 19, 2015 by Yoyo*

**Calculus**

If the integral from 0 to 8 of f(x)=4, then calculate the integral of f(4x) from 0 to 2.
*Tuesday, May 19, 2015 by Yoyo*

**Calculus**

Let f : R --> R be an odd function. Explain why, for any positive number a, the integral from -a to a of f(x) = 0.
*Tuesday, May 19, 2015 by Jack *

**Calculus**

The following definite integral gives the area of the region between the graph of the function f(x) = Icosx - x^2I (I=modulus), the x-asis, and the lines x=-2 and x=2. the integral of mod cosx - x^2 from -2 to 2. Describe a different region whose area is given by this integral...
*Tuesday, May 19, 2015 by Alex*

**Calculus**

Let f for all Real numbers, be an odd function. Explain why, for any positive number a, the integral from -a to a of f(x) = 0.
*Tuesday, May 19, 2015 by Jim*

**Quadratic Functions and Calculus **

Peter the punter decided to place $10,000 into a high growth share portfolio. After 3 weeks his investment was looking rather sad, with the value of his portfolio falling $2,025. Unperturbed, Peter stuck with his original plan to hold the stock for at least 6 months. But after...
*Tuesday, May 19, 2015 by Roney*

**Calculus**

Find the x-coordinates of any relative extrema and inflection point(s) for the function f(x) = 3x^(1/3) + 6x^(4/3). You must justify your answer using an analysis of f '(x) and f "(x). I found the first and second derivative which i think is (8x+1)/(x^(2/3), and the ...
*Monday, May 18, 2015 by Tom*

**Calculus**

The position function of a particle in rectilinear motion is given by s(t) s(t) = t^3 - 9t^2 + 24t + 1 for t ≥ 0. Find the position and acceleration of the particle at the instant the when the particle reverses direction. Include units in your answer.
*Monday, May 18, 2015 by Tom*

**Calculus**

Please check my answers. Solve the following equations and/or system of equations for the unknown variables. 1. x^2-3x-12=0 x= 3 + sqrt(57) / 2, x= 3 - sqrt(57) / 2 2. x+y=8 , 3x+2y=2 x=-14, y=22 3. 3x + 2y =10 , x+y=5 , y+z =9 x=0,y=5, z=4 4. 1/x-p1z=0, 1-p2z=0, I-p1x-p2y=0 ...
*Monday, May 18, 2015 by John*

**Calculus**

Given h(x)=(6x^2+x)/x , find h'(0)
*Monday, May 18, 2015 by Fred*

**Calculus**

If f(5) = 7, then lim f(x) ------------------x-> 5
*Monday, May 18, 2015 by Andrew*

**Calculus**

If f(5) = 7, then lim f(x) x-> 5
*Monday, May 18, 2015 by Andrew*

**Calculus**

I really need help with this calculus question. I ve been struggling to figure it out. Imagine making a tent in the shape of a right prism whose cross section is an equilateral triangle (the door is on one of the triangular ends). Assume we want the volume to be 2.6m^3, to ...
*Sunday, May 17, 2015 by AG*

**Calculus 2**

How would you find the following. A step by step process would greatly be appreciated. 1) Convert the polar equation to a rectangular equation. r^2 = 8sin2θ
*Sunday, May 17, 2015 by Mira*

**calculus **

velocity of a particle- the displacement s (in meters) of a particle moving in a straight line is given by the equation of motion s=4t^3+6t+2, where t is measured in seconds. Find the velocity of the particle s at times t=a t=1 t=2 t=3
*Saturday, May 16, 2015 by Anonymous*

**calculus **

velocity of a ball- if a ball is thrown into the air with a velocity of 40 ft/s, its height (in feet) after t seconds is given by y=40t-16t^2. find the velocity when t=2
*Saturday, May 16, 2015 by Anonymous*

**calculus **

find the derivative of the function at the given number F(x)= 1/ √x at 4
*Saturday, May 16, 2015 by Anonymous*

**calculus**

find an equation of the tangent line to the curve at the given point. graph the curve and the tangent line y=x/x-1 at (2,2) )
*Saturday, May 16, 2015 by Anonymous*

**Calculus**

Solve the following differential equation with initial conditions: y"=e^(-2t) + 10^(4t); y(0)=1, y'(0) = 0
*Friday, May 15, 2015 by Pax*

**Calculus**

Suppose a certain country's population has constant relative birth and death rates of 97 births per thousand people per year and 47 deaths per thousand people per year respectively. Assume also that approximately 30000 people emigrate (leave) from the country every year. ...
*Friday, May 15, 2015 by Pax*

**Calculus**

The table below shows the temperature (in °F) t hours after midnight in Phoenix on March 15. The table shows values of this function recorded every two hours. (10 points) a. Estimate the value of T'(6). Give units in your answer. b. What is the meaning of T'(6)? t ...
*Friday, May 15, 2015 by Tom*

**Calculus**

The slope of the line normal to the curve e^x − x^3 + y^2 =10 at the point (0, 3) is ____
*Thursday, May 14, 2015 by Pax*

**Calculus**

Center at (2,-5), conjugate axis parallel to the y-axis, slopes at assymptotes numerically one-sixteenth times the length of the latus rectum, and distance between foci is 2 sqr t145.
*Thursday, May 14, 2015 by Ruby Ann*

**Calculus, Riemann Sums**

Measurements of a lake’s width were taken at 15-foot intervals, as shown: x= 0 15 30 45 60 75 90 105 120 f(x)= 0 15 18 20 19 23 24 22 12 Estimate integral (0,120) f(x) dx with n = 4, using Midpoint approximation. For this question, I ended up with 7200 but compared to the...
*Tuesday, May 12, 2015 by Pax*

**Calculus **

Problem: Find the general solution to the following differential equation: x y' +x = ycos(1/x) I assume that you do separation of variables here: x(dy/dx) +x = ycos(1/x) xdy+x = (ycos(1/x)) dx ....? I'm stuck on how to simplify this. Thank you!
*Tuesday, May 12, 2015 by Sarah*

**Pre-Calculus (absolute values)**

I want to find the invariant points( points that are fixed) algrebraically of x^2 - 25 and its reciprocal. Would I set up my equation like this? 0 = x^2 -25 or 0 = 1/ x^2 - 25 Thanks
*Tuesday, May 12, 2015 by Lucina*

**Calculus**

f(x)=xe^-x^2. What interval is this function increasing.
*Monday, May 11, 2015 by Andrew*

**pre calculus **

Given that sinx= 3/5 and that x terminates in Quadrant 2 , determine the values for cosx and tanx Find Cos x/2
*Monday, May 11, 2015 by Anonymous*

**Pre-calculus ( Absolute value)**

Why does |7 + 3x| = x -1 have no solution? I could plug in, for example 5, and the answer would be positive. Thank you =)
*Sunday, May 10, 2015 by Lucina*

**Pre-Calculus**

Can someone please explain on how to solve this equation so I can do the others that are similar to this one? Find the solutions of the equations that are in the interval [0,2pi) cos x cot^2 x= cos x Thank you!
*Saturday, May 9, 2015 by Anonymous*

**Calculus**

Let g be a function that is defined for all x, x ≠ 2, such that g(3) = 4 and the derivative of g is g′(x)=(x^2–16)/(x−2), with x ≠ 2. a.Find all values of x where the graph of g has a critical value. b.For each critical value, state whether the ...
*Friday, May 8, 2015 by Gary*

**calculus**

Integral of 1/[x^2(1+x^2)]
*Friday, May 8, 2015 by ben*

**calculus(urgent pls) **

Integral of 1/[x^2(1+x^2)]
*Friday, May 8, 2015 by ben*

**Calculus, derivatives**

The curve is given by x^2+2r(sqrt(y))=xy What is dx/dr when y is constant?
*Friday, May 8, 2015 by Andy*

**Calculus(URGENT PLS!!!)**

Find the integral of (e^cosx)sinx
*Friday, May 8, 2015 by ben*

**Calculus **

Find the area of the region bounded by f(x)=5xsqrt(121−x2) and the x-axis. The area is = to
*Friday, May 8, 2015 by Lis *

**Calculus - Derivative**

The curve is given by x^2+2r(sqrt(y))=xy What is dx/dy when r is constant?
*Friday, May 8, 2015 by Fred*

**Calculus**

The local linear approximation of a function f will always be greater than or equal to the function's value if, for all x in an interval containing the point of tangency f '(x) < 0 f '(x) > 0 f "(x) < 0 f "(x) > 0
*Thursday, May 7, 2015 by Gary*

**Calculus**

The function g is defined for x>0 with g(1)=2, g'(x)=sin(x+1/x), and g"(x)=(1-1/x^2)cos(x+1/x). A. Find all values of x in the interval 0.12<=x<=1 at which the graph of g has a horizontal tangent line. B. On what subintervals of (0.12,1), if any, is the graph...
*Thursday, May 7, 2015 by Sarah*

**Calculus**

Consider a differentiable function f having domain all positive real numbers, and for which it is known that f'(x)=(4-x)x^-3 for x>0. A. Find the x-coordinate of the critical point of f. Determine whether the point is a relative maximum, a relative minimum, or neither ...
*Thursday, May 7, 2015 by Sarah*

**Calculus**

If f is a function such that [(f(b)-f(a))/(b-a)]=2 , then which of the following statements must be true? a.f(a) = f(b) = 2 b.The slope of the tangent line to the function at x = a is 2. c.The average rate of change of the function on the interval [a, b] is 2 d.The linear ...
*Thursday, May 7, 2015 by Gary*

**Calculus**

True or False If f is continuous at x = c, then f is differentiable at x = c.
*Thursday, May 7, 2015 by Gary*

**Calculus**

The local linear approximation of a function f will always be greater than or equal to the function's value if, for all x in an interval containing the point of tangency f '(x) < 0 f '(x) > 0 f "(x) < 0 f "(x) > 0
*Thursday, May 7, 2015 by Gary*

**Calculus**

Find the average value of the function f(x)= 8/ (3+x)^2 on the interval [0,2]
*Thursday, May 7, 2015 by Anonymous*

**Calculus**

A cable that weighs 3 lb/ft. is used to lift a golf cart which weighs 700 lbs up to the deck of a boat which is 300 ft above a loading dock. Find the work done.
*Thursday, May 7, 2015 by Anonymous*

**Calculus**

The region bounded by y= e^x, y=0, x= -1 and x=1 is rotated about the x-axis, find the volume generated.
*Thursday, May 7, 2015 by Anonymous*

**Calculus**

Find the volume of the solid obtained by rotating the region bounded by y= x^(1/3), and y= x about the line y=1
*Thursday, May 7, 2015 by Anonymous*

**Calculus**

Find the volume of the solid obtained by rotating the region bounded by y= x^2, y=0, and x=3 about the x-axis.
*Thursday, May 7, 2015 by Anonymous*

**calculus 1 (I need help)**

The portion of the ellipse x^2/9+y^2/4=1 with x greater than or equals to 0 is rotated about the y-axis to form a solid S. A hole of radius 1 is drilled through the center of S, along the y-axis. Find the exact volume of the part of S that remains. Show all steps. (Hint: use ...
*Wednesday, May 6, 2015 by linda*

**calculus**

Use table of integrals to evaluate the integral of x^4 sinxdx.
*Wednesday, May 6, 2015 by beam *

**Calculus**

Find the average value of the function f(x)= 8/ (3+x)^2 on the interval [0,2]
*Wednesday, May 6, 2015 by Joe*

**Calculus**

A cable that weighs 3 lb/ft. is used to lift a golf cart which weighs 700 lbs up to the deck of a boat which is 300 ft above a loading dock. Find the work done.
*Wednesday, May 6, 2015 by Joe*

**Calculus**

The region bounded by y= e^x, y=0, x= -1 and x=1 is rotated about the x-axis, find the volume generated.
*Wednesday, May 6, 2015 by Joe*

**Calculus**

Find the volume of the solid obtained by rotating the region bounded by y= x^(1/3), and y= x about the line y=1
*Wednesday, May 6, 2015 by Joe*

**Calculus**

Find the volume of the solid obtained by rotating the region bounded by y= x^2, y=0, and x=3 about the x-axis.
*Wednesday, May 6, 2015 by Joe*

**Calculus**

Find the area of the region bounded by the curves y=x^2 - 2x and y= x + 4
*Wednesday, May 6, 2015 by Joe*

**Pre-Calculus**

Evaluate. 1-|200+||-2|(-5)^3|| I get 49 as an answer
*Wednesday, May 6, 2015 by Lucina*

**calculus**

find the exact arc length of the curve: y=0.5(e^x + e^-x) for 0 is less than or equal to x and x is less than or equals to ln2.
*Wednesday, May 6, 2015 by may*

**Calculus **

What is the derivative of tan(1-x)^(1/2)?
*Wednesday, May 6, 2015 by Lola*

**Calculus**

The graph of f '(x) is continuous and decreasing with an x-intercept at x = -3. Which of the following statements must be true?
*Monday, May 4, 2015 by joe9*

**Calculus max/min**

d=0.767. There are two parallel sidewalks that are separated by the park that is 600 feet wide. You are standing on the south sidewalk facing east. On the north sidewalk, 2000 feet ahead of you, is a bus stop. You can walk on the sidewalk at 5.5+d feet per sec. You can walk ...
*Sunday, May 3, 2015 by John*

**Calculus 2**

Find the radius of convergence and interval of convergence of the series. There is an infinity sign on top of the summation symbol and "n=1" underneath it. To the right of the summation symbol is x^n/5n! How would you find the radius of convergence and interval of ...
*Sunday, May 3, 2015 by Sena*

**Calculus**

A wedge is cut from a right circular cylinder of radius r by two planes, one perpendicular to the axis of the cylinder and the other making an angle (beta) with the first. Find the volume of the wedge by slicing perpendicular to the y-axis. Please show all steps
*Sunday, May 3, 2015 by Beam*

**calculus**

h(x)= x + cos(ax), where a is a positive constant such that 0 < a < 4. What values of a make h(x) strictly decreasing? I know h'(x) has to be less than zero for h(x) to be decreasing and h'(x) = 1-asin(ax). I'm not sure where to go from here...
*Saturday, May 2, 2015 by kaitlyn*

**Optimization Calculus**

A three sided fence is to be built next to a straight section of river, which forms the fourth side of a rectangular region. There is 96 ft of fencing available. Find the maximum enclosed area and the dimensions of the corresponding enclosure. I drew a picture of it and I got ...
*Saturday, May 2, 2015 by Nicole*

**Calculus**

h(x) = x+cos(ax) is a family of functions where a is a positive constant such that 0<a<4. Which values of a make h(x) strictly decreasing? Justify your answer. I can't figure this out and help would be appreciated. Thanks in advance!
*Saturday, May 2, 2015 by ashley*

**Calculus**

h(x)= x + cos(ax), where a is a positive constant such that 0 < a < 4. For what values of a will h(x) have a relative maximum at x=1? So I found the derivative and got h'(x) = 1- asin(ax). Then I plugged in 1 for x and set the derivative equal to zero, so I have 1 + ...
*Friday, May 1, 2015 by ashley*

**Calculus**

h(x)= x + cos(ax), where a is a positive constant such that 0 < a < 4. For what values of a will h(x) have a relative maximum at x=1? So I found the derivative and got h'(x) = 1- asin(ax). Then I plugged in 1 for x and set the derivative equal to zero, so I have 1 - ...
*Friday, May 1, 2015 by ashley*

**Calculus**

Imagine making a tent in the shape of a right prism whose cross-section is an equilateral triangle (the door is on one of the triangular ends). Assume we want the volume to be 2.2 m3, to sleep two or three people. The floor of the tent is cheaper material than the rest: assume...
*Thursday, April 30, 2015 by Lizz*

**Calculus**

What is the solution to the following system of equations -2x+3y+z=5 x+5y+2z=17 To do this, I used elementary operations and isolated x to get 13y+5z=37. Is that correct so far? How would I continue?
*Thursday, April 30, 2015 by Sara*

**Calculus**

How would I find the equilibrant of three vectors? I am given a graph of three different vectors which meet at the point (0,0)
*Thursday, April 30, 2015 by Sara*

**Calculus**

If 3(a,3,2)-2(3,b,b)=(-3,1,-2) determine a and b. Describe the set spanned by the vectors. I don't know how to answer this
*Thursday, April 30, 2015 by Sara*

**Calculus**

I'm not sure how to do this; I figured I should use separation of variables but I got the wrong equation. Help is appreciated, thanks! If dy/dx=(1+x)/(xy), x > 0, and y = –4 when x =1, when x =3, y = ? A. 6.433, −6.233 B. 3.898, −3.898 C. 4.711, −...
*Thursday, April 30, 2015 by ashley*

**Calculus**

What are the coordinates of the point on the graph of f(x)=(x+1)(x+2) at which the tangent is parallel to the line with equation 3x-y-1=0? a)(-3,2) b)(-1,0) c)(0,2) d)(1,6) To answer this, I put f(x)=(x+1)(x+2) into the form f(x)=x^2+3x+2 and found the derivative which is f&#...
*Thursday, April 30, 2015 by Sara*

**Calculus and Vectors **

A plane is flying south east at a constant speed of 900km/h. The wind is blowing towards the north at 100km/h. Determine the resultant velocity of the plane relative to the ground.
*Wednesday, April 29, 2015 by John*