Monday

November 30, 2015
**Pre-Calculus**

f(x) = cos(x) on the interval [−2π, 2π] (a) Find the x-intercepts of the graph of y = f(x). (Enter your answers as a comma-separated list.) (b) Find the y-intercepts of the graph of y = f(x). (Enter your answers as a comma-separated list.) (c) Find the ...
*Sunday, November 29, 2015 by Sam*

**Calculus- Damon, Steve, Reiny**

I forgot to mention that I am trying to find sigma squared.. given that the mean is r and p(x)= (1/r)(e^(-x/r)) on the interval [0,infinity), where r>0.. note: sigma squared= integral sign (-inf, inf) (x-M)^2 p(x) dx i got (r^2 - 2r)^(1/2) for sigma, but my answer is wrong...
*Saturday, November 28, 2015 by Christina*

**Calculus**

I tried to integrate this: intergral sign with an interval from -inifinity to + infinity function: (x-r)^2 (1/r) (e^(-x/r)) with respect to dx..... I know that Steve set up the u-substitution but I seem to never arrive at an answer... It seems like I keep integrating and ...
*Saturday, November 28, 2015 by Christina*

**Calculus**

How do you integrate (x-r)^2 (1/r) (e^(-x/r)) from the interval negative infinity to positive infinity?
*Friday, November 27, 2015 by Sanaya*

**Calculus**

How do you integrate (x-r)^2 (1/r) (e^(-x/r)) from the interval negative infinity to positive infinity?
*Friday, November 27, 2015 by Christina*

**Math calculus **

The top and bottom margins of a poster are 8 cm and the side margins are each 8 cm. If the area of printed material on the poster is fixed at 382 square centimeters, find the dimensions of the poster with the smallest area?
*Friday, November 27, 2015 by MArıam *

**calculus**

integrate (e^t + e^-t)²
*Friday, November 27, 2015 by ligas*

**Integral Calculus**

Integrate (tan^-1 X)/(1+x²) dx please help, I don't know how to start this one
*Friday, November 27, 2015 by ligas*

**Integral Calculus**

Integrate (tan^-1 X)/(1+x²) dx please help, I don't know how to start this one
*Friday, November 27, 2015 by ligas*

**calculus**

integrate (e^t + e^-t)²
*Friday, November 27, 2015 by ligas*

**Pre Calculus HELP!?**

The length of a day in Philadelphia, Pennsylvania, is given by the sinusoidal function, f(t), which represents the number of hours of daylight t days into the year: f(t)= 10+2.8sin(2pi/365)*(t-1.35). How many hours of daylight are there on the 100th day of the year? Round the ...
*Thursday, November 26, 2015 by Ellie*

**Pre-Calculus HELP!!**

The length of a day in Philadelphia, Pennsylvania, is given by the sinusoidal function, f(t), which represents the number of hours of daylight t days into the year: f(x)=11+2.2sin(2pi/365)t-1.25).How many hours of daylight are there on the twelfth day of the year? Round the ...
*Thursday, November 26, 2015 by Ellie*

**calculus**

integrate (e^t + e^-t)²
*Wednesday, November 25, 2015 by ligas*

**Pre-Calculus HELP!**

Explain how the transformations of the functions f(x)=15sin(x) and f(x)=sin(x)+15 differ. I see that f(x)=sin(x)+15 experiences a vertical shift, but I am not sure about the transformation that f(x)=15sin(x) experiences. Thank you for your help!
*Wednesday, November 25, 2015 by Ellie*

**Calculus 1**

Use a graph to give a rough estimate of the area of the region that lies beneath the given curve. Then find the exact area. y = x^−3, 2 ≤ x ≤ 5
*Wednesday, November 25, 2015 by TayB*

**Calculus 1**

Use a graph to give a rough estimate of the area of the region that lies beneath the given curve. Then find the exact area. y = cube root(x) , 0 ≤ x ≤ 27
*Wednesday, November 25, 2015 by TayB*

**Calculus III**

Evaluate ∭W f(x,y,z)dV for the function f and region W specified: f(x,y,z) = 18(x+y) W: y≤ z≤x ; 0≤y≤x ; 0≤x≤1 ∭W (18(x+y))dV =
*Tuesday, November 24, 2015 by Steven*

**Calculus**

If f is an exponential function of the form f(x)=C times a^x with growth factor 5 and f(5)=14. What is f(6)? I know f(6) is 70 but how do you set up the equation to get 70?
*Tuesday, November 24, 2015 by Dale*

**calculus**

what are the inflection points of 5x^2-45/x^2-25
*Monday, November 23, 2015 by marissa*

**Calculus**

Integrate e^(-t/r) WITH RESPECT TO dt?
*Monday, November 23, 2015 by Sanaya*

**Calculus**

The amount remaining of a radioactive substance after t hours is given by A(t) = 100ekt. After 12 hours, the initial amount has decreased by 4%. How much remains after 48 hours? What is the half-life of the substance?
*Monday, November 23, 2015 by Bill*

**Pre-calculus**

Initially 600 milligrams of a radioactive substance was present. After 7 hours the mass had decreased by 3%. Construct an exponential model A(t) = A0ekt for the amount remaining of the decaying substance after t hours. Find the amount remaining after 24 hours.
*Monday, November 23, 2015 by Kim*

**Calculus**

find the maximum volume of a cylinder whose height and radius do not exceed a combined total of 12cm
*Monday, November 23, 2015 by Emma*

**Calculus**

Let f(x)=5x^(9/5)−45x^(4/5). Find the largest open interval(s) where f(x) increases.
*Monday, November 23, 2015 by Kevin*

**Calculus**

Calculate μ and σ, where σ is the standard deviation, defined by the following. σ^2 = integral between (−∞,∞) (x-μ)^2 p(x) dx The smaller the value of σ the more tightly clustered are the values of the random variable X about the...
*Sunday, November 22, 2015 by Christina*

**Calculus**

How do you integrate e^(-t/r) dt?
*Sunday, November 22, 2015 by Sanaya*

**Calculus**

Calculate μ and σ, where σ is the standard deviation, defined by the following. σ^2 = integral between (−∞,∞) (x-μ)^2 p(x) dx The smaller the value of σ the more tightly clustered are the values of the random variable X about the...
*Sunday, November 22, 2015 by Anonymous*

**Calculus**

How do you integrate e^(-t/r)?
*Sunday, November 22, 2015 by Sanaya*

**Calculus**

Integrate x/(6x-5) dx The answer is 1/6 x + 5/36 ln abs (36x-30) + C... But I don't understand why it is 5/36 times ln.. I thought that when you factored out the 5 you would get 5 times ln abs (36x-30)..
*Saturday, November 21, 2015 by Sanaya*

**Calculus**

A window is designed to be the area between a parabolic section and a straight base. The height is 0.640 m and the base is 1.60 m. What is the area of the window?
*Saturday, November 21, 2015 by Anonymous*

**Calculus**

Calculate integral [0, infinity) xe^(-x) dx
*Saturday, November 21, 2015 by Sanaya*

**Calculus**

Find the solution t the differential equation dz/dt = 2te^z that passes through the origin. My answer is -In (1-t^2), but my answer is populating as incorrect. Can someone help please?
*Friday, November 20, 2015 by Latoya*

**Calculus**

Solve the initial value problem 2y" + 5y' - 3y = 0 y(0) =7, y'(0) = 7 Can someone please help. The answer I came up with is 35 exp(-x) - 28 exp(-3x/2), but my answer is wrong.
*Friday, November 20, 2015 by Latoya*

**Calculus**

For the vector field G⃗ =(yexy+3cos(3x+y))i⃗ +(xexy+cos(3x+y))j⃗ , find the line integral of G⃗ along the curve C from the origin along the x-axis to the point (3,0) and then counterclockwise around the circumference of the circle x2+y2=9 to the point (...
*Friday, November 20, 2015 by A*

**Calculus**

Integral sign 8x/(x-1) dx Is it 8x+8ln abs (x-1)+C ?
*Thursday, November 19, 2015 by Sanaya*

**Calculus**

Evaluate the integral. Problem#1 Integral sign 4dx/[(x+3)(x^2 +3x) Does it matter where A, B, and C is placed over. Is there a particular order? Is it ..... (A/x)+(B/(x+3))+(c/(x+3)^2=4 Or ... (A/x+3)+(B/x)+(C/(x+3)^2)=4 I am confused because I get different answers each time ...
*Thursday, November 19, 2015 by Sanaya*

**Calculus**

Evaluate using long division. The integral of x/6x-5 dx How do I divide this?
*Thursday, November 19, 2015 by Sanaya*

**Calculus 1 **

Find each limit: (a) lim x->1 (ln(x)+2x-2)/(x^2-1) (b) lim x->infinity (x^2)/(e^x)
*Thursday, November 19, 2015 by TayB*

**Calculus 1 **

Find the local maximum and minimum for the function f(x)=2x^3-3x^2-120x+10
*Thursday, November 19, 2015 by TayB*

**Calculus III**

Use symmetry to evaluate the double integral ∫∫R(10+x^2⋅y^5) dA, R=[0, 6]×[−4, 4]. (Give your answer as an exact number.) ∫∫R(10+x^2⋅y^5) dA=
*Wednesday, November 18, 2015 by Stevo*

**Pre Calculus 1**

thirty percent of a radioactive substance decays in four years. assuming the decay is exponential, find the half life of the substance. the beginning of 1975 the population of a country was 40 million and growing at a rate of 3% per year. Assume that the growth is exponential...
*Wednesday, November 18, 2015 by Yasmine*

**Business Calculus**

The skeleton has lost 56 percent of their carbon-14. The constant proportionality is approximately k=0.000124. Estimate the age of the bones.
*Wednesday, November 18, 2015 by Amy*

**Calculus**

Evaluate using long division. The integral of x/6x-5 dx How do I divide this?
*Tuesday, November 17, 2015 by Rucha*

**math (Calculus III)**

In this example we should use the beta function. But I'm a bit lost, because I don't know how to change the limits of the integral to fit the one that is needed when using B-function. The problem goes like this: integrate cos^7(x) dx, limits of the integral are from 0 ...
*Tuesday, November 17, 2015 by Marie*

**Calculus**

Find the first partial derivatives and evaluate each at the given point. Function w = sqrt(5x^2 + y^2 − 4z^2) Point (2, −4, 2) wx(2, −4, 2) = wy(2, −4, 2) = wz(2, −4, 2) =
*Tuesday, November 17, 2015 by Calculus Help *

**Calculus**

Find the four second partial derivatives and evaluate each at the given point. Function f(x, y) = x^3 + 2xy^3 − 9y Point (9, 2) fxx(9, 2) = fxy(9, 2) = fyx(9, 2) = fyy(9, 2) =
*Tuesday, November 17, 2015 by Calculus Help *

**Calculus**

Find the first partial derivatives and evaluate each at the given point. Function w = 2x^2y − 6xyz + 10yz^2 Point (2, 5, −3) wx(2, 5, −3) = wy(2, 5, −3) = wz(2, 5, −3) =
*Tuesday, November 17, 2015 by akash*

**Calculus**

A pharmaceutical corporation has two locations that produce the same over-the-counter medicine. If x1 and x2 are the numbers of units produced at location 1 and location 2, respectively, then the total revenue for the product is given by R = 700x1 + 700x2 − 2x1^2 −...
*Tuesday, November 17, 2015 by akash*

**calculus**

You have been hired by a farmer to design a fenced-in rectangular enclosure for emus. The emus will require 720 square feet of area in which to roam, and the fence will cost 20 dollars per foot. The rectangular area will adjoin an existing wall, so a fence is only needed on ...
*Tuesday, November 17, 2015 by carl*

**Calculus**

A tennis ball is dropped from a height of 32 feet, rebounding to 1/2 its former height with each bounce. How far will the ball have traveled VERTICALLY when it comes to a rest?
*Monday, November 16, 2015 by Sean*

**Pre-Calculus**

Big Bob is trying to shape up for the summer. He begins on the first day of his exercise program with 3 sit ups. Each day he will do 4 more sit ups than the day before. On what day will Big Bob do 115 sit ups?
*Monday, November 16, 2015 by Claire*

**Calculus**

Partial fractions of (2x^2 +8x+24)/(x+2)^2 (x^2 +4) I see a repeated quadratic and an irreducible quadratic..
*Sunday, November 15, 2015 by Rucha*

**pre calculus**

find 2 solutions of tan θ=.6524 in both degrees and radians. I know the answer are 33.12 degrees/.578 radians and 213.12 degrees/3.72 radians, but how do you find this? Thanks!!!!
*Sunday, November 15, 2015 by elle*

**Calculus 1**

Use Newton's method to approximate the indicated root of the equation correct to six decimal places. The root of x^4 − 2x^3 + 5x^2 − 5 = 0 in the interval [1, 2]
*Sunday, November 15, 2015 by TayB*

**Calculus 1**

Consider the function below. f(x)= (x^2)/((x-4)^2) Find the interval where the function is concave up. (Enter your answer using interval notation.) Find the intervals where the function is concave down. (Enter your answers using interval notation.) For interval where the ...
*Sunday, November 15, 2015 by TayB*

**Calculus 1**

Find the absolute minimum and absolute maximum values of f on the given interval. f(t) = 16 cos t + 8 sin 2t, [0, π/2]
*Saturday, November 14, 2015 by TayB*

**calculus**

Use the Left and Right Riemann Sums with 100 rectangle to estimate the (signed) area under the curve of y=−2x+1 on the interval [0,50]. Write your answer using the sigma notation.
*Friday, November 13, 2015 by Mark*

**Calculus**

Use the Left and Right Riemann Sums with 80 rectangle to estimate the (signed) area under the curve of y=e^(3x)−5 on the interval of [10,20]. Write your answer using the sigma notation
*Friday, November 13, 2015 by Mark*

**Calculus 1**

Use Newton's method to find the coordinates, correct to six decimal places, of the point on the parabola y = (x − 5)^2 that is closest to the origin.
*Friday, November 13, 2015 by TayB*

**Calculus 1**

Use Newton's method to find all roots of the equation correct to six decimal places. (Enter your answers as a comma-separated list.) 7/x = 1 + x^3
*Friday, November 13, 2015 by TayB*

**Calculus 1**

Use Newton's method to find the coordinates, correct to six decimal places, of the point on the parabola y = (x − 5)^2 that is closest to the origin.
*Friday, November 13, 2015 by TayB*

**Calculus 1**

Of the infinitely many lines that are tangent to the curve y = −4 sin x and pass through the origin, there is one that has the largest slope. Use Newton's method to find the slope of that line correct to six decimal places.
*Friday, November 13, 2015 by TayB*

**Pre-Calculus**

1) For tax purposes a manufacturer is allowed to depreciate the value of a machine by 10% each year. If the original value of the machine was $10,000, what would be its value for tax purposes at the end of 6 years. (Assume the depreciation is computed at the end of each year...
*Thursday, November 12, 2015 by Anon*

**Integral Calculus - Series**

Find if series is convergent or divergent. Series from n=2 to infinity (4n+7)/(3n^3 -8n)
*Thursday, November 12, 2015 by John*

**Calculus 1**

Of the infinitely many lines that are tangent to the curve y = −4 sin x and pass through the origin, there is one that has the largest slope. Use Newton's method to find the slope of that line correct to six decimal places.
*Thursday, November 12, 2015 by TayB*

**Calculus**

Find the area of the unbounded shaded region. Y= 7/ SQRT (7-X)
*Thursday, November 12, 2015 by akash*

**Calculus**

A professional athlete signs a four-year contract in which the earnings can be modeled by c = 300,000 + 750,000t, where t represents the year. (a) Find the actual value of the athlete's contract. =7200000 (b) Assuming an annual inflation rate of 4%, what is the present ...
*Thursday, November 12, 2015 by akash*

**Calculus**

Find the area of the unbounded shaded region. Y= 7/ SQRT 7-X
*Thursday, November 12, 2015 by Please Help Me ! *

**Calculus**

A professional athlete signs a four-year contract in which the earnings can be modeled by c = 300,000 + 750,000t, where t represents the year. (a) Find the actual value of the athlete's contract. =7200000 (b) Assuming an annual inflation rate of 4%, what is the present ...
*Thursday, November 12, 2015 by Calculus Help *

**Calculus**

A professional athlete signs a four-year contract in which the earnings can be modeled by c = 300,000 + 750,000t, where t represents the year. (a) Find the actual value of the athlete's contract. (b) Assuming an annual inflation rate of 4%, what is the present value of the...
*Thursday, November 12, 2015 by Calculus Help *

**Calculus**

Use integration by parts to evaluate the definite integral. S 12 x/sqrt of x+4 dx 0
*Thursday, November 12, 2015 by Justin *

**Calculus 1**

Use Newton's method to find all roots of the equation correct to six decimal places. (Enter your answers as a comma-separated list.) (x − 9)^2 =ln x
*Thursday, November 12, 2015 by TayB*

**Calculus 1**

Use Newton's method with initial approximation x1 = −2 to find x2, the second approximation to the root of the equation x^3 + x + 1 = 0. *I got -1.307692 for my answer but it said that was wrong, so then I tried rounding it to two decimal places and got -1.31 and ...
*Thursday, November 12, 2015 by TayB*

**Calculus 1**

A piece of wire 23 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 maximize the total area? (b) How much wire should be used for the square in order ...
*Wednesday, November 11, 2015 by TayB*

**Calculus**

Evaluate using Integration by Parts. x^2 cos(3x) dx
*Wednesday, November 11, 2015 by Anonymous*

**Pre-Calculus**

A parallelogram has adjacent sides 7 cm and 15 cm. If the shorter diagonal is 10 cm long, find the length of the longer diagonal.
*Tuesday, November 10, 2015 by starmario12*

**Calculus**

Evaluate the definite integral using the properties of even and odd functions. S 2 (1/2 t^4+3)dt -2
*Tuesday, November 10, 2015 by Please Help *

**pre-Calculus**

Evaluate the definite integral using the properties of even and odd functions. S 2 (1/2 t^4+3)dt -2
*Tuesday, November 10, 2015 by Calculus Help *

**Calculus**

The marginal cost of a product is modeled by dC/dx =12/Cube root (12x+5) where x is the number of units. When x = 13, C = 160. (a) Find the cost function. (Round your constant term to two decimal places.) C= Ans- 3/2(12x+5)^2/3 +115.61 ???? (b) Find the cost of producing 70 ...
*Tuesday, November 10, 2015 by akash*

**Calculus**

Find the local maximum and local minimum of the function. f(x) = x^3 − 12x^2 − 27x + 7
*Monday, November 9, 2015 by Callie*

**Calculus-antiderivative**

Find f. f ''(θ) = sin θ + cos θ, f(0) = 5, f '(0) = 3 My steps: f'(θ)=cosθ-sinθ+C When f'(0)=3, C=-2, so f'(θ)=cosθ-sinθ-2. f(θ)=-sinθ-cosθ-2x+D When f(0)=5, D=6, so f is -sinθ-cosθ-...
*Monday, November 9, 2015 by Callie*

**Calculus**

Find the critical numbers of the function. (Use n to denote any arbitrary integer values.) f(θ) = 12 cos θ + 6 sin2θ My answer was pi/2 and 3pi/2, but those were wrong. I don't understand the 'n' part, either.
*Monday, November 9, 2015 by Callie*

**Calculus**

How do you integrate 2x^5 • e^x^2 ? I would say that this cannot be evaluated because the answer is more complicated than the original problem. Am I correct? Or is it doable?
*Monday, November 9, 2015 by Rucha*

**Calculus**

Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 17 + 4x − x^2, [0, 5] I got -13 and 17, but the answers were wrong. Take the derivative for the critical values, right? To get 2 as a critical value. What from there?
*Monday, November 9, 2015 by Callie*

**Calculus **

The rate of growth dP/ dt of a population of bacteria is proportional to the square root of t with a constant coefficient of 9, where P is the population size and t is the time in days (0¡Üt¡Ü10). The initial size of the population is 700. Approximate the...
*Monday, November 9, 2015 by Beth*

**calculus**

use symmetry to evaluate the double integral (1+x^2siny+y^2sinx)dA, R=[-pi,pi]x[-pi,pi]. let g(x) and h(y) be two functions: int(c to d)int(a to b)(g(x,y)+h(x,y))dxdy=int(c to d)int(a to b)g(x,y)dxdy+int(c to d)int(a to b)h(x,y)dxdy
*Monday, November 9, 2015 by Inna*

**Calculus**

how do you solve this trig identity? i don't get it at all! cos(a+b)cos(a-b)=cos^2a-cos^2b-1
*Monday, November 9, 2015 by sakura*

**Calculus**

Find the lim x→∞ of (ln(x))^2)/x using L'hospital's rule. I got - infinity when I did this, but I think I was looking at the numerator wrong when I took the derivative.
*Sunday, November 8, 2015 by Callie*

**Calculus**

Find the volume of the solid obtained by rotating the region under the graph of f(x)= 9-x^2 for 0<= x<=3 about the vertical axis x= -2. My answer: 81 pi/2
*Sunday, November 8, 2015 by Rucha*

**Pre-Calculus**

Two lookout towers are situated on mountain tops A and B, 4 mi from each other. A helicopter firefighting team is located in a valley at point C, 3 mi from A and 2 mi from B. Using the line between A and B as a reference, a lookout spots a fire at an angle of α = 42° ...
*Sunday, November 8, 2015 by Samantha*

**Calculus**

Find the area of the region between the graphs of f(x)=3x+8 and g(x)=x^2 +2x+2 over [0,2]. My answer: 34/3
*Sunday, November 8, 2015 by Rucha*

**calculus**

assume x and y are functions of t. Evaluate dy/dt for 2xy--4x/3y^3=48, with conditions dx/dt=-6,x=3, y=-2
*Sunday, November 8, 2015 by faye*

**Calculus**

Consider a sphere container with radius R. 1. Suppose it is filled to height h, below halfway, with water. Find the volume of the water. 2. What is the proportion of the sphere's total volume taken up by the water filled as described in problem #1? 3. Suppose it us filled ...
*Saturday, November 7, 2015 by Anonymous*

**Calculus-Reiny**

Yay! Reiny, you read the description of f(x) correctly. Recall the problem posted earlier: Let f(x)= abs of negative abs of x + pi/2 close abs and g(x)= abs of cosx. the wording might be confusing so here is another description of the equation (the "vertical line" ...
*Saturday, November 7, 2015 by Anonymous*

**Calculus**

suppose a sphere container of radius R=10 cm is fulled to a height of h=2 cm with a magic potion of density p=12g/mm^3. If the empty container weighs 500 g, how much does it weigh after the potion is poured in?
*Saturday, November 7, 2015 by Anonymous*

**Calculus**

Let f(x)= abs of negative abs of x + pi/2 close abs and g(x)= abs of cosx. the wording might be confusing so here is another description of the equation (the "vertical line" that I refer to is the line you draw as you draw the absolute value sign...for example "...
*Saturday, November 7, 2015 by Anonymous*

**Calculus**

Evaluate the integral. (Remember to use ln(|u|) where appropriate.) cot^3(3x) dx
*Saturday, November 7, 2015 by Anonymous*

**Calculus**

In a right triangle, the hypotenuse is of fixed length of 15 units, one side is increasing in length by 4 units per second while the third side is decreasing in size. At a certain instant the increasing side is of length 9 units. Find the rate of change of the third side at ...
*Saturday, November 7, 2015 by Bob*

**Calculus**

Find the Absolute Maximum and Absolute Minimum of f on (0,3]. f(x)=(x^3-4x^2+7x)/x Multiple choice question I know the minimum is (2,3) but the maximum is either nothing or (0,7) but I can't tell which one
*Saturday, November 7, 2015 by Henry*

**Calculus**

A company needs to make a cylindrical can that can hold precisely 2.1 liters of liquid. If the entire can is to be made out of the same material, find the dimensions of the can that will minimize the cost. Round your answer to the nearest four decimal places.
*Friday, November 6, 2015 by Coc*