Tuesday

December 1, 2015
**[Calculus] U-substitution for Integrals**

Integrate from 1 to 5 of (3x-5)^5 dx = Integrate from a to b of f(u) du where (I have solved this part) u = 3x-5 du = 3 a = 0 b = 12 The original value of the integral is 165888 via calculator here's my last question, and it has to be in terms of u: f(u) = ? (Again, in ...
*Monday, February 23, 2015 by Ian*

**Calculus 2**

Consider a trough with triangular ends where the tank is 10 feet long, top is 5 feet wide, and the tank is 4 feet deep. Say that the trough is full to within 1 foot of the top with water of weight density 62.4 pounds/ft^3, and pump is used to empty the tank until the water ...
*Monday, February 23, 2015 by Lauren*

**Calculus 2**

Let a thing rod of length a have a density distribution function p(x)+10e^(-.1x), where x is measured in cm and p in grams per centimeter. A) if the mass of the rod is 30 g, what is the value of a? B) For the 30g rod, will the center of mass lie at its midpoint, to the left, ...
*Monday, February 23, 2015 by Jordan*

**calculus**

State whether or not the following statements are true. Justify your reasoning.? a. Vector a • (Vector b + Vector c) = Vector a • Vector b + Vector a • Vector c b. Vector a × (Vector b + Vector c) = Vector a × Vector b + Vector a × Vector c c. ...
*Monday, February 23, 2015 by anon*

**Pre-Calculus (Trigonometry)**

An angle in standard position such that sinÈ = 5/13. Determine the possible values of È, to the nearest degree. Answer: I got 23°. (How do I get the second one?)
*Sunday, February 22, 2015 by Lucina*

**calculus**

given the velocity of a particle traveling along the y-axis by v(t)=tsin(t^2)
*Sunday, February 22, 2015 by sam*

**Calculus**

When given the f graph, how do you determine extrema of F(x)? Concavity of F(x)?
*Sunday, February 22, 2015 by Anonymous*

**calculus**

Find the integral of (sin^5 x)(cos^5 x)
*Sunday, February 22, 2015 by tolu*

**calculus**

A woman is attached to a bungee cord from a bridge that is 38m above a river. Her height in meters above the river t seconds after the jump is y(t)=19(1 + e^-1xcos(t)) for t>0. What is her velocity at t=1 and t=4?
*Saturday, February 21, 2015 by Zee*

**Calculus**

Evaluate: the integral from pi/8 to pi/6 csc2xcot2xdx
*Saturday, February 21, 2015 by Anonymous*

**Calculus**

Evaluate by U-substitution: the integral of xcubedroot(x-2) dx
*Saturday, February 21, 2015 by Anonymous*

**Calculus **

A spring has a natural length of 18 cm. If a 22-N force is required to keep it stretched to a length of 24 cm, how much work W is required to stretch it from 18 cm to 21 cm? (Round your answer to two decimal places.) Arg, another question that has me stumped! Would love some ...
*Friday, February 20, 2015 by Mr. Garvoti *

**Calculus **

If 54 J of work are needed to stretch a spring from 15 cm to 21 cm and 90 J are needed to stretch it from 21 cm to 27 cm, what is the natural length of the spring? Any help would be appreciated!
*Friday, February 20, 2015 by Mr. Garvoti *

**AP calculus**

If 54 J of work are needed to stretch a spring from 15 cm to 21 cm and 90 J are needed to stretch it from 21 cm to 27 cm, what is the natural length of the spring?
*Friday, February 20, 2015 by Sam*

**Calculus Physics**

A 1559-kg car moves at 15.0 m/s. What is the magnitude of the horizontal net force needed to bring the car to a halt in a distance of 50.0 m?
*Thursday, February 19, 2015 by danny*

**Calculus Physics**

A particle is subject to a time-dependent force: F(t)=5t√. If the particle's mass is 7 kg, what will its velocity be at t=6.7 seconds, assuming its initial velocity at t=0 is equal to 0.
*Thursday, February 19, 2015 by danny*

**Algebra**

How do you know which rule to use when it doesn't specify? All it says is find the derivative of the function. I haven't had algebra/calculus in over 20 years, I'm completely lost. Please help
*Thursday, February 19, 2015 by Averi*

**business math**

How do you know which rule to use when it doesn't specify? All it says is find the derivative of the function. I haven't had algebra/calculus in over 20 years, I'm completely lost. Please help.
*Thursday, February 19, 2015 by Averi*

**Calculus**

On planet Calculi, acceleration due to gravity is -20 ft/sec^2. A ball is thrown upward with an initial velocity of 40ft/sec from an initial height of 50. a) Write the equation for the height of the ball, s(t), at time t. b) Find the velocity when the ball hits the ground. c) ...
*Thursday, February 19, 2015 by Anonymous*

**calculus**

When an oil well burns, sediment is carried up into the air by the flames and is eventually deposited on the ground. Less sediment is deposited further away from the well. Experimental evidence indicates that the density (in tons per square mile) at a distance r in any ...
*Thursday, February 19, 2015 by Randy*

**Calculus**

A spherical balloon with radius 3 inches is partially filled with water. If the water in the balloon is 4 inches deep at the deepest point, how much water is released when the balloon hits the wall and breaks?
*Wednesday, February 18, 2015 by Andy*

**Calculus Physics**

A particles with mass 3.7 kg moves in the x direction according to the following function: x(t)=−7+4t+3t2−4t3. (the units of each coefficient are meters, and time is measured in seconds). At time t=7.8, what is the net force acting on the particle?
*Wednesday, February 18, 2015 by danny*

**Calculus Physics**

A box and one force vector, F1 is shown. F1 = + 10 N. If the mass of the box is 3 kg, what is the magnitude and direction of a force, F2, that would need to be applied if the box was to have an acceleration of + 2 m/s 2 in the horizontal direction. (Indicate direction by ...
*Wednesday, February 18, 2015 by danny*

**Calculus**

Find the volume of the solid obtained by rotating the region bounded by y=8x+24, y=0 about the y-axis.
*Wednesday, February 18, 2015 by Cole*

**Pre-calculus**

Find the first two terms of a geometric sequence if t_3+ t_4 = 50 and t_4 + t_5 =100? t3= a(r^2) t4= a(r^3) t5= a(r^4) a(r^2)+ a(r^4)= 100 ------------------------- a(r^3)+ a(r^4) = 50 ar^3 ----- = 2 ar^2 r = 2 <-------
*Tuesday, February 17, 2015 by Lucina*

**Pre-Calculus**

Q.Determine the sum of each infinite geometric series. t_1= 8 r = -2^1/2 ---------------------------------------- A.This is a divergent series because the absolute value of r is greater than 1. ---------------------------------------- Q. The first term of an ...
*Tuesday, February 17, 2015 by Lucina*

**Calculus**

A craftsman wants to make a cylindrical jewelry box that has volume, V, equal to 60 cubic inches. He will make the base and side of the box out of a metal that costs 50 cents per square inch. The lid of the box will be made from a metal with a more ornate finish which costs ...
*Tuesday, February 17, 2015 by Shyan*

**calculus A**

A particle moves according to a law of motion s = f(t) = t3 - 12t2 + 21t, t 0, where t is measured in seconds and s in feet. v(t) = 3t^2 - 24t 21 a(t) = 6t - 24 e) Find the total distance traveled during the first 8 s. i) When is the particle speeding up? (Enter your answers ...
*Tuesday, February 17, 2015 by sohee*

**Calculus**

If f(x) = x4 + 6x,find f'(x).
*Tuesday, February 17, 2015 by Tay Tay*

**Calculus Chain rule**

How can derive this function?f(x) = 2/(9x^5+1)^5 The answer is The answer is -450x^4/(9x^5+1)^6 Can you please show why? Thank you
*Tuesday, February 17, 2015 by Tom*

**Calculus: Optimization**

I have no idea how to approach this problem, if someone knows just how to relate h, r with H,R, that would be extremely helpful and I can workout the rest! Thank you in advance. Given a right circular cone, you put an upside-down cone inside it so that its vertex is at the ...
*Tuesday, February 17, 2015 by Jazz*

**calculus 3**

A golf ball is driven down a horizontal fairway with an initial speed of 55m/s at an initial angle of 25 degrees. (Assume the tee from which the ball is hit is of negligible height). a). how far does the ball travel horizontally b). when does the ball land? c). what is the max...
*Tuesday, February 17, 2015 by Mark*

**calculus**

An artificially created lake is bordered on one side by a straight dam. The shape of the lake surface is that of a region in the xy-plane bounded by the graphs of 2y=16-x^2 and x+2y=4. Find the area of the surface of the lake.
*Tuesday, February 17, 2015 by Akki*

**Calculus**

Calculate the area of the bounded region between the curves y^2=x and 3y = -3y + 9 ?
*Tuesday, February 17, 2015 by Akki*

**Calculus**

Find an equation of a line tangent to y = 2sin x whose slope is a maximum value in the interval (0, 2π]
*Tuesday, February 17, 2015 by Sara*

**calculus**

s= [b]*[d]+64t-16t^2 what is the greatest height above the ground the rock will go
*Monday, February 16, 2015 by steve*

**calculus**

hi! just needed help on an FRQ for ap calculus ab. let me know if you have any questions for me. I'm just really confused as far as what I am meant to do. If you could walk me through it that would be amazing. THANKS!! A population is modeled by a function P that satisfies...
*Monday, February 16, 2015 by phoebe*

**Pre calculus**

A tugboat is traveling at 30 miles per hour at a compass heading of 38 degrees. The current is from the direction of 125 degrees moving at 7 mph. Find the resultant speed and the direction of the boat. I understand the concept and that I must use the law of cosines. I got 30^2...
*Monday, February 16, 2015 by Hanna*

**Pre-calculus **

Let z and w be complex numbers such that |2z-2|=25, |z+2w|=5, and |z+w|=2. Find |z|. I first squared both equations and expressed the square of the magnitudes in terms of the complex numbers and its conjugates. Next, I summed the equations together and attempted to solve for |...
*Monday, February 16, 2015 by majorbill*

**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*