Saturday

October 10, 2015
**Pre-Calculus**

he amount M (in billion of dollars) of mortgage debt outstanding in the US from 1990 to 2001 can be approximated by the function M(t)= 29.9t^2 + 3892 where t=0 represents 1990. Rewrite the function so that t=0 represents 2000.
*Monday, February 16, 2015 by Tara*

**Calculus**

Integrate Cos^7(2x) Explanation would be helpful
*Monday, February 16, 2015 by Pen*

**Calculus**

determine the absolute extreme values of the function f(x)=sinx-cosx+6 on the interval 0<=x<=2pi. This is what i did: 1.) i found the derivative of the function which is f'(x)=cosx+sinx 2.) I set f'(x)=0 and got sinx/cosx=-1 which is tanx=-1 and then x=3π/4...
*Sunday, February 15, 2015 by Sara*

**multivariable calculus**

show that a=!0 , the equation p=2asin0cos0 describes the sphere centered(a,0,0) at radius|a|
*Sunday, February 15, 2015 by robert*

**Pre-Calculus**

If r = 1, will a sequence be convergent or divergent?
*Sunday, February 15, 2015 by Lucina*

**calculus**

Find limit of 2x+1-cosx/3x as x approaches 0?
*Sunday, February 15, 2015 by sential *

**Calculus**

Can someone please explain how to solve this type of question? Determine the maximum and minimum value of the function f(x)=3x3^x - 1
*Saturday, February 14, 2015 by Sara*

**Calculus**

would the derivative of f(x)=(7^x)(x^7) be f'(x)=(7^x ln7) (7x^6)?
*Saturday, February 14, 2015 by Sara*

**Calculus**

a certain radioactive substance is decaying so that at time t, measured in years, the amount of the substance, in grams, is given by the function f(t)=3e^-3t. What is the rate of decay of the substance after half a year: I first found the derivative of f(t)=3e^-3t which is f&#...
*Saturday, February 14, 2015 by Sara*

**Calculus**

How would I answer this question? Differentiate the function f(x)=sqrt(cosxsinx)
*Friday, February 13, 2015 by Sara*

**Calculus**

1. is the derivative of the function f(x)=5e^(4x-9z) f'(x)= -25e^(4x-9z)? 2. Is the derivative of the function f(x)=e^(2x)-e^(-2x) f'(x)=2e^(2x)+2e^(-2x)? 3. If f(x)=e^-x^-1, would f'(2)=-1/4e^(1/4)?
*Friday, February 13, 2015 by Sara*

**Calculus help and please check answer for a)**

The decay of a certain substance is modeled by the function N(t)=100(3+e^(-t/3), where the number of particles is represented by N in a time of t hours. a) what is the initial number of particles? - I set t as 0 and got an answer of 400 particles initially b) determine the ...
*Friday, February 13, 2015 by Sara*

**math calculus**

what is the difference between the function 2^x and (1/2)^x?
*Friday, February 13, 2015 by Sara*

**Calculus**

A wealthy patron of a small private college wishes to endow a chair in mathematics with a gift of G thousand dollars. Suppose the mathematician who occupies the chair is to receive $110 thousand dollars per year in salary and benefits. If money costs 8% per year compounded ...
*Friday, February 13, 2015 by C*

**calculus- min value of function**

The answer is -1/2 but how? Which of the following is the minimum value of the function f(x)= sinxcosx? a) 0 b) -1/2 c) -1 d) does not exist
*Friday, February 13, 2015 by Sara*

**Calculus**

I am not too sure if I did this question correct. Thanks in advanced! Data table: Time after Consumption (min): 30 60 90 120 150 180 Amount of Codeine in Blood (mg): 27.0 23.5 21.2 18.7 16.6 14.5 1.) create a scatter plot of the data and determine a suitable equation to model ...
*Friday, February 13, 2015 by Sara*

**pre- calculus**

In how many ways can a family of six be seated at a round table if the mother and father must sit together?
*Friday, February 13, 2015 by Anonymous*

**Calculus**

Let f(x)=cosxsqrt(1+sinx). A. Let F(x)=the integral of f(x)dx and F(0)=5/3, find F(pi/2). I got 3.386 with U-substitution B. If G(x)=the integral of f(x)sinxdx and G(0)=1/3, find G(x). I got a reply to this but I did not understand the explanation. How would I solve this with ...
*Friday, February 13, 2015 by Anonymous*

**Pre-Calculus**

Each second after shut-off, the speed of the blade is 2/3 of the speed in the previous second. After the first 8 s, the saw has turned 258 times. What was the speed of the saw before the motor shut off, to the nearest tenth of a turn per second? I get 805.4 but I don't ...
*Friday, February 13, 2015 by Lucina*

**calculus**

Two forces of 7 lb. and 14 lb. act on a body at right angles to each other. Find the angle their resultant force makes with the force of 14 lb.
*Friday, February 13, 2015 by Jasmine*

**Calculus**

The integral of sin(7x)cos(7x)dx
*Friday, February 13, 2015 by Anonymous*

**Calculus**

Integration with substitution The integral of f'(g(5x))g'(5x)dx
*Friday, February 13, 2015 by Anonymous*

**Calculus**

Let f(x)=cosxsqrt(1+sinx) A. If F(x)=the integral of f(x)dx and F(0)=5/3, find F(pi/2). B. If G(x)=the integral of f(x)sinx dx and G(0)=1/3, find G(x).
*Friday, February 13, 2015 by Anonymous*

**Calculus**

f'(x) if x is less than or greater than 1 Let F'(x)={ g'(x) if x>1 Where f'(x)=x/(x^2-2)^2 and g'(x)=3x-4 A. If f(1)=3/2, find f(x) B. If F(x) is continuous at x=1, find g(x). C. Express F(x). D. If F(x) is continuous at x=1, determine if F(x) is ...
*Friday, February 13, 2015 by Anonymous*

**Calculus**

Integration with trig functions Integral of [(1-sinx)/cos^2x] dx
*Thursday, February 12, 2015 by Anonymous*

**Calculus**

I am not too sure if I did this question correct. Thanks in advanced! Data table: Time after Consumption (min): 30 60 90 120 150 180 Amount of Codeine in Blood (mg): 27.0 23.5 21.2 18.7 16.6 14.5 1.) create a scatter plot of the data and determine a suitable equation to model ...
*Thursday, February 12, 2015 by Sara*

**Calculus**

Integration with U-Substitution Integral of [x/sqrt(x+1)] dx I'm getting confused with how to deal with the x when I find the derivative of (x+1) because they don't match.
*Thursday, February 12, 2015 by Anonymous*

**Calculus**

Suppose f"(x)=6x-2 A. If f'(1)=5, find f'(x). I got f'(x)=3x^2-2x+4 B. Fine the average rate of change of f on [-1,4]. C. Fine the value of x guaranteed by the mean value theorem for r on [-1,4]. D. If f(-1)=-2, find f(x) I am not sure how to do B, C, and D.
*Thursday, February 12, 2015 by Anonymous*

**Calculus**

Integrate: Indefinite integral of [(sqrt(x))-1]^2 / [sqrt(x)] dx
*Thursday, February 12, 2015 by Anonymous*

**Pre-calculus**

Hello, Consider a geometric sequence with t3= 18 and t7= 1458. Are there one or two values for the common ratio? How does this affect the sequence (I got one, but the way this question mentions 2 ratios, I get the feeling there are 2 values.) My work: 1458 = 18r^4 81 = r^4 3 = r
*Thursday, February 12, 2015 by Lucina*

**calculus**

integral sqrt(1-x^2) . sin^-1 x dx
*Thursday, February 12, 2015 by akki*

**calculus**

integral sec^-1 x dx
*Thursday, February 12, 2015 by akki*

**Calculus**

What would an example of a logarithmic function that contains a radical within it and a quotient within it where you would need to use chain rule and quotient rule to take derivative look like? How would taking the derivative of the function in its original form look different...
*Thursday, February 12, 2015 by Robin*

**Calculus**

What would an example of a logarithmic function that contains two trig functions within it where you would need to use chain rule and product rule to take derivative look like? How would taking the derivative of the function in its original form look different when using log ...
*Thursday, February 12, 2015 by Robin*

**calculus**

A small airplane has an air speed of The pilot wishes to fly to a destination that is 480 km due west from the plane’s present location. There is a wind from the south.
*Tuesday, February 10, 2015 by josh*

**Pre-Calculus**

On a campus of 9000 students, a single student returned to campus with a case of measles on Monday January 5th. The infirmary is keeping track of the number of students who have been diagnosed with the disease Day # of students infected 1. 2 2. 5 3. 9 4. 28 5. 64 6. 81 7. 320...
*Tuesday, February 10, 2015 by Guadalupe*

**Pre-Calculus**

The Gateway Arch in St. Louis, Missouri is not a parabola but a shape known as a catenary. The name is given to the shaoe formed by the Graph of the hyperbolic cosine (cosh). The arch has a height of 625 feet andna span of 600 feet. The hyperbolic cosine is defined as: Cosh x...
*Tuesday, February 10, 2015 by Guadalupe*

**Pre-Calculus**

A corpse was discovered in a motel room at midnight and uts temperature was 82°F. The temperature dropped to 80.5°F two hours later. Given k is a constant for the object in question, S is the surrounding temperature, t represents the time and theta(of time) is the ...
*Monday, February 9, 2015 by Guadalupe*

**Calculus**

Write the definite integral for the area of the region lying in the upper half of the ellipse given by 4x^2+y^2=4
*Monday, February 9, 2015 by Anonymous*

**Calculus**

The rate of growth of a particular population is given by dP/dt=50t^2-100t^3/2 where P is the population size and t is the time in years. The initial population is 25,000. Find the population function. Estimate how many years it will take for the population to reach 50,000.
*Monday, February 9, 2015 by Anonymous*

**Calculus**

An object has a constant acceleration of 72 feet per second squared, an initial velocity of 17 feet per second, and an initial position of 10 feet. Find the position function describing the motion of this object.
*Monday, February 9, 2015 by Anonymous*

**Calculus**

Use a(t)=-32 ft/second squared as the acceleration due to gravity. A ball is thrown vertically upward from the ground with an initial velocity of 56 feet per second. For how many seconds will the ball be going upward?
*Monday, February 9, 2015 by Anonymous*

**Calculus**

Use a(t)=-32 ft/second squared as the acceleration due to gravity. A ball is thrown vertically upward from the ground with an initial velocity of 96 feet per second. How high will it go?
*Monday, February 9, 2015 by Anonymous*

**Calculus**

Sketch the region enclosed by the curves x= 49-y^2 and x = y^2 - 49. Decide whether to integrate with respect to x or y. Then find the area of the region.
*Monday, February 9, 2015 by Jason*

**Calculus **

If Y = SecXTanX, find y" 4y' 4y. I can easily do the second part of the question if I could if only I could find d first and second derivative of SecXTanX, pls do help.
*Monday, February 9, 2015 by Francis *

**Math- Calculus**

I need help with these problems, I cannot find a similar example to help me in the book: 1. Find lim x->infinity (e^(-2x) + sin x). 2. Find the derivative of sqrt(9-x) using the limit process. 3. Find lim x-> -infinity (x + sqrt(x^2 + 2x)). 4. Show that the equation e^x...
*Monday, February 9, 2015 by Amber*

**Calculus**

Can someone show me a step by step process, along with explanations on how to do this problem? Thank you. :) Evaluate the integral ∫ [(x^2 - 1)/(x^2 + 1)]dx?
*Monday, February 9, 2015 by Aria*

**Calculus**

I am in a car and travel for 12 minutes. Below are the speeds in mph, recorded every two minutes. Use trapezoids, right-bound rectangles, and midpoint rectangles to estimate the distance I traveled. Min 0 2 4 6 8 10 12 Speed 20 22 35 46 50 50 20 Trapezoids: Right-bound ...
*Sunday, February 8, 2015 by Anonymous*

**Calculus**

By applying Rolle's theorem, check whether it is possible that the function f(x)=x^5+x−5 has two real roots. Answer: (input possible or impossible ) Your reason is that if f(x) has two real roots then by Rolle's theorem: f′(x) must be (input a number here) ...
*Sunday, February 8, 2015 by Sarah*

**Calculus**

At 2:00pm a car's speedometer reads 60mph, and at 2:10pm it reads 65mph. Use the Mean Value Theorem to find an acceleration the car must achieve. Answer( in mi/h2):
*Sunday, February 8, 2015 by Dee*

**Calculus**

Graph the function f(x)=x+4/x Graph the secant line that passes through the points (1,5) and (8,8.5) on the same set of axes Find the number c that satisfies the conclusion of the Mean Value Theorem for f on [1,8] c= Notice that if you graph the tangent line to the point (c,f(...
*Sunday, February 8, 2015 by Bob*

**Calculus**

Consider a regular tetrahedron whose face is an equilateral triangle of side 7. Find the area of the horizontal cross section A at the level z=3. A= ? Find the volume of the tetrahedron. Consider a regular tetrahedron whose face is an equilateral triangle of side 7. Find the ...
*Saturday, February 7, 2015 by Mwe*

**Calculus**

Find the volume of the solid whose base is the circle x^2+y^2=25 and the cross sections perpendicular to the x-axis are triangles whose height and base are equal. Find the area of the vertical cross section A at the level x=1.
*Saturday, February 7, 2015 by Mwe*

**pre cal**

The given equation is a partial answer to a calculus problem. Solve the equation for the symbol y'. 6y2y' − y − xy' = x y' =
*Friday, February 6, 2015 by mj jad*

**Calculus**

The volume of a solid
*Friday, February 6, 2015 by Francis*

**calculus**

Simplify the following power functions to the form y=kxp, where k and p are some numbers. (a) y=(18)/x√ is y=kxp. What are k and p?
*Thursday, February 5, 2015 by Lindsay*

**Calculus**

Find the anti-derivative of the integral [3sqrt(x)(2x^2-4)]dx
*Thursday, February 5, 2015 by Anonymous*

**Calculus**

Find the anti-derivative of the integral (7tan^2x+12)dx
*Thursday, February 5, 2015 by Anonymous*

**Calculus**

a) Find d/dm (x^4m^5 + y^3m +z^6) b) Find the first and second derivatives of: v = 3t^2 + 8t + 11 v' = v'' =
*Thursday, February 5, 2015 by Arin*

**Calculus**

Find the anti-derivative of the integral [(7t^2+6t-15)/t^4]dt
*Thursday, February 5, 2015 by Anonymous*

**Calculus**

Solve the differential equation f"(x)=x^2, f'(0)=3, f(0)=-1
*Thursday, February 5, 2015 by Anonymous*

**Calculus**

I am in a car and travel for 12 minutes. Below are the speeds in mph, recorded every two minutes. Use trapezoids, right-bound rectangles, and midpoint rectangles to estimate the distance I traveled. Min 0 2 4 6 8 10 12 Speed 20 22 35 46 50 50 20 Trapezoids: Right-bound ...
*Thursday, February 5, 2015 by Anonymous*

**Calculus**

Linda has $9000 to invest. She invested x dollars in an account that earned 3% simple interest and the remainder of the money in an account that earned 2.6% simple interest. In one year, both accounts together earned $250 interest. How much was invested in each account?
*Thursday, February 5, 2015 by Q*

**Calculus**

Integral sqrt(x-1/x^5)
*Thursday, February 5, 2015 by Akki*

**Survey of Calculus**

A total revenue function is given by R(x) = 1000(x^2 - 0.1x)^1/2 , where R(x) is the total revenue, in thousands of dollars, from the sale of x items. Find the rate at which total revenue is changing when 20 items have been sold. So far my answer is R'(x) = 1000 Coming ...
*Wednesday, February 4, 2015 by Shanxxix*

**Calculus 2**

integral of e^x(sqrt(1+e^(2x)))dx
*Wednesday, February 4, 2015 by Matt*

**Calculus 2**

use the method of equating coefficients. integral of (x^3+5x^2+12)/((x^2)(x^2+4)) dx
*Wednesday, February 4, 2015 by Matt*

**calculus**

At noon, Ship A is 100 km west of ship B. Ship A travels south at 35 km/h. Ship B travels North at 25 km/h. At 4 pm, how fast the distance between them change?
*Wednesday, February 4, 2015 by gerald*

**Calculus II**

Find the indefinite integral. ∫xe^-4xdx
*Wednesday, February 4, 2015 by Kris*

**calculus**

Hello! Just needed help with understanding this specific question. We never really wet over Euler's method so I'm not sure how to go about it. "Use Euler's method in order to solve the initial value problem below. dy/dx = x-3 and y=4 when x=1 Use Euler's ...
*Tuesday, February 3, 2015 by megan*

**calculus**

Find the value of the limit. lim ã(x+4) - 2 divided by x x->0 The 2 is outside of the square root. The answer is supposed to be 1/4 but I keep getting 0/0 no matter how many times I redo the algebra.
*Tuesday, February 3, 2015 by paula*

**Pre-calculus**

The area of a triangle wall on a barn is 160 square feet. Its length is 4 feet longer than twice the width. Find the length and width of the wall of the barn
*Tuesday, February 3, 2015 by Tamika*

**Pre-Calculus**

If h(x)=x^3, what is the difference between h(x) reflected about the x-axis and h(x) reflected about the y-axis?
*Tuesday, February 3, 2015 by Adrian*

**Pre-Calculus**

find the inverse of g(x)=(x+7)^3+4
*Tuesday, February 3, 2015 by Drue*

**Pre-Calculus**

Reflect f(x)=x^2 about the y-axis. What changes?
*Tuesday, February 3, 2015 by Christian*

**Pre-Calculus**

find all the maximums of the polynomial f(x)=x^2-8x+11 What is the global (absolute) maximum?
*Tuesday, February 3, 2015 by Andrea*

**Pre-Calculus**

Describe the function resulting from reflecting f(x)=x^3+2x^2-x+5 about the x-axis and then the y-axis. Does the order of the reflections matter?
*Tuesday, February 3, 2015 by Andrea*

**Pre-Calculus**

Describe the function resulting from reflecting f(x)=x^3+2x^2-x+5 about the y-axis and then shifting to the left by 4. Is this the same as performing the operations in the reverse order
*Tuesday, February 3, 2015 by Jose*

**Calculus - Differentiation**

Differentiate: y = 3/(1-6x^4)
*Monday, February 2, 2015 by Zac*

**calculus**

Find the x-coordinates where f '(x) = 0 for f(x) = 2x + sin(2x) in the interval [0, 2π].
*Monday, February 2, 2015 by Anonymous*

**calculus**

A particle moves on a line away from its initial position so that after t hours it is s = 6t^2 + 2t miles from its initial position. Find the average velocity of the particle over the interval [1, 4]. Include units in your answer.
*Monday, February 2, 2015 by Anonymous*

**Calculus**

Compute the area of a leaf given by the equation y^2 = (x^2−1)^2 for −1 ≤ x ≤ 1
*Monday, February 2, 2015 by Antonette*

**Math- Vector Calculus**

A manufacturer sells two products, one at a price of $3000 a unit and the other at a price of $12000 a unit. A quantity q1 of the first product and q2 of the second product are sold at a total cost of $5000 to the manufacturer. Express the manufacturer's profit, as a ...
*Saturday, January 31, 2015 by Javier*

**Calculus**

Compute the maximum and minimum amount of a drug remaining in a patient in the limit (that is, as time tends to infinity) given that the patient takes an 80 milligram dose once a day at the same time each day and the drug has a half life of 22 hours.
*Saturday, January 31, 2015 by Jona*

**Pre Calculus **

Can someone help me with this problem? Determine the number of positive integers less than 10,000 that can be formed from the digits 1, 2, 3, and 4 if repetitions are allowed. Thank you!
*Saturday, January 31, 2015 by Anonymous*

**Calculus**

Differentiate: y = (x^2 + 8x +3)^3
*Saturday, January 31, 2015 by Wes*

**Calculus**

Write 2.445353535353... as a fraction I'm learning integrals right now and this is part of the exercises under it. Is there a trick to this? Using integrals? Thank you very much!
*Saturday, January 31, 2015 by Alex*

**Calculus**

Hello, I really need help on these two homework problem. >< In problem #1, I believe it is related to the exponential functions and their derivatives section...in Calculus II? So, surely there should be a ln in the solution as well? I would like a step by step process ...
*Saturday, January 31, 2015 by Aria*

**Calculus**

Determine the interval(s) at which f(x) is concave up given that f′′(x)=−x2+x+6. a) (–2, 3) b) (–∞, –2), (3, ∞) c) (–∞, –3), (2, ∞) d) (–2, ∞) e) (–∞, 3)
*Friday, January 30, 2015 by joshua*

**Calculus **

Determine the interval(s) at which f(x) is concave up given that f′′(x)=−x2+x+6. Critical points are: -2 & 3
*Friday, January 30, 2015 by joshua*

**pre calculus **

12. Use the remainder theorem to find P (-2) for P(x) =x^3+2x^2-x-7. Specifically, give the quotient and the remainder for the associated division and the value of P (-2). Quotient =? Remainder =? P (-2) =?
*Friday, January 30, 2015 by gary *

**Calculus**

The volume, V cm3 , of a cone height h is pi x h^3 / 12 If h increases at a constant rate of 0.2 cm/sec and the initial height is 2 cm, express V in terms of t and find the rate of change of V at time t.
*Friday, January 30, 2015 by Akki*

**calculus**

(cx)={X if 0 is less than or equal x less than or equal 10 and 0.9x if 10<x
*Thursday, January 29, 2015 by john*

**calculus**

A trough is 9 feet long and 1 foot high. The vertical cross-section of the trough parallel to an end is shaped like the graph of y=x4 from x=−1 to x=1 . The trough is full of water. Find the amount of work in foot-pounds required to empty the trough by pumping the water...
*Thursday, January 29, 2015 by Catherine*

**Calculus**

A hot air ballon lifts off the earth 300m away from an observer and rises straight up at a rate of 80m/min. At what rate is the angle of inclination of the observers line of sight increasing at the time the balloon is 300, above the ground?
*Thursday, January 29, 2015 by Chris*

**calculus **

lim x->0 (Sin^3 3x - 3x^3)/(x^3) (x^4)
*Thursday, January 29, 2015 by Francis *

**Calculus**

1) An equation of the line contains points (7/9, 7) and (-7/9) is 2) Find the slope of the line tangent to the curve y=x^2 at the point (-0.6, 0.36) and find the corresponding equation of the tangent line
*Wednesday, January 28, 2015 by Seth*

**Calculus **

Evaluate lim x->0 (Sin^3 3x - 3x^3/x^3 x^4) I got zero (0) to be my answer by imputing 0 in place of x but am not so sure if the answer should be 0, am thinking it should be like 1/0 or something like that.
*Wednesday, January 28, 2015 by Francis *

**Calculus **

Find ¡Ò[dx/(x-2)(x+3)(x-4)] this is really confusing and I need help with it.
*Wednesday, January 28, 2015 by Francis *

**Calculus **

differentiate tan-1(2x/1-x^2)
*Tuesday, January 27, 2015 by Francis *