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July 29, 2014

July 29, 2014

**Recent Homework Questions About Calculus**

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**calculus**

Suppose f (1) = 2, f ΄(1) = 3, g(1) = 5, and g΄(1) = -4. Evaluate (f g)΄v at x = 1. Answer -12 7 10 23
*Thursday, February 6, 2014 at 1:14pm*

**calculus**

If limit as delta x approaches 0 of tan(0+Δx)-tan(0)/Δx =1 which of the following is false: d/dx [tanx]=1 the slope of y = tan(x) at x = 0 is 1 y = tan(x) is continuous at x = 0 y = tan(x) is differentiable at x = 0
*Thursday, February 6, 2014 at 12:56pm*

**calculus**

Suppose h(x) = f (g(x)) and the graphs of f and g are shown below. Describe the continuity of h at x = 0. how would you do this if you were given two graphs: F--- discontinuity at -2,0; point at -1,1; and point at 0,0 (to make a parabola) then discontinuity at 0,-1; and then ...
*Thursday, February 6, 2014 at 12:49pm*

**Math (pre calculus)**

please simplify (1/1+x+h) - (1 /1+x ) divided by h
*Thursday, February 6, 2014 at 1:49am*

**pre calculus **

Simplify the rational expression 3 (1 + x)^1/3 - x (1 + x)^-2/3 divided by (1 + x)^2/3
*Thursday, February 6, 2014 at 1:44am*

**Math (pre calculus)**

State whether the given equation is true for all values of the variables (disregard any value that makes a denominator zero) equation one (2/ 4 + x) = (1/2) + (2/x) equation two (1 + x + x^2 / x) = (1/x) + 1 + x
*Thursday, February 6, 2014 at 1:41am*

**Calculus**

A trough is 15 ft long and 4 ft across the top, as shown in the figure. Its ends are isosceles triangles with height 3 ft. Water runs into the trough at the rate of 2.5 ft^3/min. How fast is the water level rising when it is 2 ft deep?
*Thursday, February 6, 2014 at 1:02am*

**Pre-Calculus**

A certain sum of money is invested in a business. in each year this investment earns 1 1/2 times as much as in the preceding year. If the investment earned a total of $29,250.00 in four years, how much did it earn in the fourth year?
*Wednesday, February 5, 2014 at 7:22pm*

**calculus**

Which of the following best describes the limit as x approaches 4 of the quotient of 2 times x divided by the quantity negative 2 plus square root of x ? It exists and equals 4 It fails to exist because it is unbounded. It fails to exist because its one-sided limits are not ...
*Wednesday, February 5, 2014 at 6:58pm*

**calculus**

It is known that x 2 + 4x ≤ f(x) ≤ -x 2 -4x the interval [-4, 0]. Use the Squeeze Theorem to evaluate the limit as x approaches negative 2 of f of x. -4 0 4 Squeeze Theorem does not apply
*Wednesday, February 5, 2014 at 6:58pm*

**calculus**

Suppose f of x equals 3 times x minus k when x is less than 5 and equals 1 plus k times x when x is greater than or equal to 5.Find the value of k that would make f continuous at x = 5. -3 0 7/3 no such k will make f continuous
*Wednesday, February 5, 2014 at 6:57pm*

**calculus**

At a constant temperature, the pressure, P, and volume, V, of a trapped gas have the relationship P equals the quotient of k divided by V , where k is some positive constant. What occurs if the volume is compressed such that V → 0+? The pressure increases without bound. ...
*Wednesday, February 5, 2014 at 6:56pm*

**Calculus 2**

Find Mx, My, and (x, y) for the laminas of uniform density ρ bounded by the graphs of the equations. y=sqrt(x)+4 y=(1/2)x+4 The I keep getting 20/3 for Mx but webassign acts like it is wrong.
*Wednesday, February 5, 2014 at 1:51pm*

**calculus**

At midnight, ship B was 90 km due south of ship A. Ship A sailed east at 15 km/hr and ship B sailed north at 20 km/hr. At what time were they closest together?
*Wednesday, February 5, 2014 at 10:38am*

**calculus**

At midnight, ship B was 90 km due south of ship A. Ship A sailed east at 15 km/hr and ship B sailed north at 20 km/hr. At what time were they closest together?
*Wednesday, February 5, 2014 at 10:35am*

**Calculus**

I'd really like some help in solving an integral. ʃ 1/ √x (1-3√x) In numerator: 1 In denominator: the square root of x times 1 minus 3 times the square root of x The answer given is -2/3 ln l1-3√xl + C but I don't know how to get there.
*Wednesday, February 5, 2014 at 12:05am*

**CALCULUS 2**

Use calculus to find the volume of the following solid S: The base of S is an elliptical region with boundary curve 9x^2+4y^2=36. Cross-sections perpendicular to the x-axis are isosceles right triangles with hypotenuse in the base.
*Tuesday, February 4, 2014 at 10:47pm*

**Calculus**

A steady wind blows a kite due west. The kite's height above ground from horizontal position x = 0 to x = 60 ft is given by the following. y= 155-(1/40)(x-50)^2 Find the distance traveled by the kite.
*Tuesday, February 4, 2014 at 10:27pm*

**Calculus**

A steady wind blows a kite due west. The kite's height above ground from horizontal position x = 0 to x = 60 ft is given by the following. y= 155-(1/40)(x-50)^2
*Tuesday, February 4, 2014 at 10:09pm*

**Calculus**

Use Simpson's Rule with n = 10 to estimate the arc length of the curve. y = tan x, 0 < x < π/9
*Tuesday, February 4, 2014 at 10:08pm*

**calculus**

Use the principles of translating and reflecting to graph the function f(x)=(x-5)^3 +2
*Tuesday, February 4, 2014 at 1:27am*

**pre calculus**

determine the order of magnitude for the following: 1. a $1 bill and a dime 2. two products scored a PH level of 6.1 and 4.o I can't figure out #1… but I did get #2 to be 10^2.1 Please help with #1 and check to see I did #2 right?
*Monday, February 3, 2014 at 4:25pm*

**calculus**

y= -5x + 4 OVER 10 - 5x find the asymptotes of the function
*Monday, February 3, 2014 at 1:37am*

**Calculus II**

Solve the initial value problem using Taylor Series and the following conditions: y'(t) = y(t) + 2t y(0) = A
*Sunday, February 2, 2014 at 11:01pm*

**CALCULUS PLEASE HELP!!!**

SHOW WORK PLEASE!!! The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 2 sin πt + 3 cos πt, where t is measured in seconds. (Round your answers to two decimal places.) (a) Find the ...
*Sunday, February 2, 2014 at 8:12pm*

**calculus**

In a lab experiment 8 grams of acid were produced in 28 minutes and 17 grams in 47 minutes. Let g be the number of grams and m be the number of minutes. Find a linear equation that you could use to calculate g for any number of minutes.
*Sunday, February 2, 2014 at 3:28am*

**Calculus & Vectors**

A search and rescue aircraft, travelling at a speed of 240 km/h starts out at a heading of N 20 degrees West. After travelling for 1h and 15 min, it turns to a heading of N 80 degrees E and continues for another two hours before returning to base. Find the total distance the ...
*Saturday, February 1, 2014 at 6:10pm*

**calculus**

The rabbit population on a small island is observed to be given by the function P(t)=120t−0.4t4+700 where t is the time (in months) since observations of the island began.
*Saturday, February 1, 2014 at 5:28pm*

**CALCULUS**

Find a formula for the inverse of the function. y=x^2-x, x>=(greater than or equal to) 1/2 Please give me a step by step explanation. I think my algebra is wrong... Ty
*Saturday, February 1, 2014 at 9:16am*

**calculus**

Four out of five days were used to create a problem, how many days will it take to solve it?
*Saturday, February 1, 2014 at 8:21am*

**calculus**

Four out of five days were used to create a problem, how many day will it take to solve it?
*Saturday, February 1, 2014 at 8:21am*

**integral calculus**

Evaluate the limit limit gose from x to 4 (x/x-4)integral from x to 4
*Friday, January 31, 2014 at 10:04pm*

**Calculus**

Let f be the function given by f(x)= 2x/(sqrt(x^2 +x +1)) c. Write an equation for each horizontal asymptote of the graph of f. d. Find the range of f. Use f'(x) to justify your answer.
*Friday, January 31, 2014 at 5:26pm*

**Calculus**

Find the distance between the given parallel planes. 4z = 4y − 4x, 6z = 3 − 6x + 6y
*Friday, January 31, 2014 at 3:15pm*

**Calculus**

Find the distance between the given parallel planes. 5x−4y+z=10, 10x−8y+2z=3
*Friday, January 31, 2014 at 3:14pm*

**Calculus**

Find the distance from the point to the given plane. (−3,8,7), x−2y−4z=8
*Friday, January 31, 2014 at 3:13pm*

**Calculus**

Find the distance from the point to the given plane. (1,−5,9), 3x+2y+6z=5
*Friday, January 31, 2014 at 3:12pm*

**Calculus**

Find parametric equations for the line through the point (0,2,2)that is parallel to the plane x+y+z = 2 and perpendicular to the line x=1+t, y=2−t, z=2t. (Use the parameter t.) (x(t), y(t), z(t)) =
*Friday, January 31, 2014 at 3:11pm*

**Calculus**

Where does the line through (1,0,1) and (3,−2,5)intersect the plane x+y+z=10? (x, y, z) =________?
*Friday, January 31, 2014 at 3:09pm*

**Calculus**

Find the point at which the line intersects the given plane. x = 1 + 4t, y = 4t, z = 2−3t ; x + 2y − z + 1 = 0 (x, y, z) = _____________?
*Friday, January 31, 2014 at 3:07pm*

**Calculus**

Find the point at which the line intersects the given plane. x = 4 − t, y = 5 + t, z = 2t; x − y + 3z = 3 (x, y, z) =____________?
*Friday, January 31, 2014 at 3:05pm*

**Calculus**

Find an equation of the plane. The plane that passes through the point (−1, 2, 1)and contains the line of intersection of the planes x + y − z = 4 and 4x − y + 5z = 4
*Friday, January 31, 2014 at 3:04pm*

**Calculus**

Find an equation of the plane. The plane that passes through (8, 0, −2)and contains the line x = 6 − 2t, y = 3 + 5t, z = 3 + 2t
*Friday, January 31, 2014 at 2:57pm*

**CALCULUS**

Starting with the graph of f(x)=5x, write the equation of the graph that results from reflecting f(x) about the line y =4. y=_______? Thank you!
*Friday, January 31, 2014 at 12:27am*

**Calculus**

Let g and h be any two twice-differentiable functions that are defined for all real numbers and that satisfy the following properties for all x: I) (g(x))^2 + (h(x))^2=1 ii) g'(x)= (h(x))^2 iii) h(x)>0 iv) g(0)=0 a)Justify that h'(x)=-g(x)h(x) for all x b) Justify ...
*Thursday, January 30, 2014 at 2:44pm*

**Calculus II**

Find an equation of the set of all points equidistant from the points A(−2, 6, 3) and B(5, 3, −3)
*Thursday, January 30, 2014 at 11:33am*

**Physics**

Problem 1 (80 points) Consider a spring of equilibrium length L, lying horizontally in a frictionless trough. The spring has cross sectional area S perpendicular to its length. The trough constrains the motion of the spring so that any wave propagating along the spring is a ...
*Wednesday, January 29, 2014 at 11:24pm*

**Pre-Calculus**

Find dy/dx if y= x^6[(x^2-9)^8]? So the answer is supposed to be 2x^5[(x^2-9)^7](11x^2-27), but I don't understand how to get it. Do you use product rule, chain rule or both? thanks
*Wednesday, January 29, 2014 at 9:44pm*

**Calculus**

A superball is tossed vertically 40 feet and rebounds on each bounce 3/5 of the height from which it fell. How far will it travel before coming to rest?
*Wednesday, January 29, 2014 at 8:14pm*

**Calculus**

A particle starts at the point (5,0) at t=0 and moves along the x-axis in such a way that at time t>0 its velocity v(t) is given by v(t)= t/(1+t^2). a). Determine the maximum velocity of the particle. Justify your answer. b). Determine the position of the particle at t=6. c...
*Wednesday, January 29, 2014 at 4:38pm*

**Calculus**

write in parametric form the equation of the line that joins (1,-2) and (3,0)
*Wednesday, January 29, 2014 at 4:14pm*

**Physics**

Problem 1 (80 points) Consider a spring of equilibrium length L, lying horizontally in a frictionless trough. The spring has cross sectional area S perpendicular to its length. The trough constrains the motion of the spring so that any wave propagating along the spring is a ...
*Wednesday, January 29, 2014 at 3:50pm*

**Calculus **

Consider the solid obtained by rotating the region bounded by the following curves about the line x=1. y=x,y=0,x=4,x=6 Find the volume So it would be pi (integral from 3 to 6) of ((1-y)^2 -(1-0)^2) right? so then you integrate it and get pi(Y^3/3-y^2) from 3 to 6. ?
*Wednesday, January 29, 2014 at 3:15pm*

**calculus**

i am on "rolles and the mean value theorem" and was just wondering, when i am doing rolles, do i really need to find the exact value of x where f'(c) = 0? for example: f(x) = (x+4)^2 (x-3) on [-4,3] i get to: 3x^2+10x-8=7 then i dont know if i then need to find ...
*Tuesday, January 28, 2014 at 11:51pm*

**Calculus**

Find the critical numbers of the function. h(t) = t3/4 − 5t1/4
*Tuesday, January 28, 2014 at 10:25pm*

**Calculus**

A poster is to have an area of 160 in2 with 1 inch margins at the bottom and sides and a 7 inch margin at the top. What dimensions will give the largest printed area? (Give your answers correct to one decimal place.)
*Tuesday, January 28, 2014 at 10:25pm*

**Calculus**

Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = (x2 - 1)3 [-1, 6]
*Tuesday, January 28, 2014 at 10:24pm*

**Calculus**

Find the absolute minimum and absolute maximum values of f on the interval below. f(x) = x4 - 8x2 + 6 [-3, 4]
*Tuesday, January 28, 2014 at 10:23pm*

**Calculus**

Find two numbers whose difference is 132 and whose product is a minimum.
*Tuesday, January 28, 2014 at 10:04pm*

**Calculus**

A box with a square base and open top must have a volume of 4,000 cm3. Find the dimensions of the box that minimize the amount of material used.
*Tuesday, January 28, 2014 at 10:03pm*

**Calculus**

A poster is to have an area of 160 in2 with 1 inch margins at the bottom and sides and a 7 inch margin at the top. What dimensions will give the largest printed area? (Give your answers correct to one decimal place.)
*Tuesday, January 28, 2014 at 10:02pm*

**pre-calculus**

The suggested retail price for a new car is p dollars. The dealership advertises a 10% discount and a factory rebate of $1500. Write a function S in terms of p, representing the cost of the car after receiving the dealership discount.
*Tuesday, January 28, 2014 at 8:15pm*

**calculus**

If the nth partial sum of an is sn=(3n-2)/(n+1) what is an when x>1? and what is the sum of an?
*Tuesday, January 28, 2014 at 1:06am*

**Calculus**

write and row reduce the augmented matrix to find the general solution. x + y - z = 7 2x - y - 5z = 2 -5x + 4y + 14z = 1 3x - y - 7z = 5
*Monday, January 27, 2014 at 6:51pm*

**Calculus HELP!!**

6 2 6 Let u = 4 , v = 2 , w = 2 5 3 1 Show that 2u - 3v - w = 0. Use that fact to find x1 and x2 that satisfy the equation 6 2 6 4 2 {x1} = 2 5 3 {x2} 1
*Monday, January 27, 2014 at 4:54pm*

**Calculus**

the legs of a right triangle have lengths a and b satisfying a + b =10. which values of a and b maximize the area of the triangle?
*Monday, January 27, 2014 at 1:19pm*

**Calculus**

integrate (pi&0) sin t/(2-cost) dt
*Monday, January 27, 2014 at 9:42am*

**Calculus**

integrate (pi/6 & 0) (1-cos3t)(sin3t)dt
*Monday, January 27, 2014 at 9:23am*

**Calculus**

write and row reduce the augmented matrix to find the general solution: 2x - z = 2 6x + 5y + 3z = 7 2x - y = 4
*Sunday, January 26, 2014 at 4:36pm*

**Calculus**

write and row reduce the augmented matrix to find the general solution: x - 2y + 13 = 0 y - 4x = 17
*Sunday, January 26, 2014 at 4:34pm*

**Geometry/Algebra/Calculus**

Why isn't the surface area of a sphere with radius r the following: 2*pi * (pi*r) That comes from the following flow of logic: Doesn't it makes sense to think of the surface area of the sphere with radius r as the the circumference of the semi-circle with radius r, pi*...
*Sunday, January 26, 2014 at 1:46am*

**calculus**

"superman is in level flight 6 miles above ground. his flight plan takes him directly over whs high school. how fast is he flying when the distance between him and the whs high school is exactly 10 miles and the rate is increasing 40mph?" i keep getting: r = 10 r'...
*Saturday, January 25, 2014 at 10:34pm*

**calculus**

"superman is in level flight 6 miles above ground. his flight plan takes him directly over whs high school. how fast is he flying when the distance between him and the whs high school is exactly 10 miles and the rate is increasing 40mph?" i keep getting: r = 10 r'...
*Saturday, January 25, 2014 at 9:18pm*

**Calculus 1**

Find all the points on the ellipse 3x^2-xy+y^2=64 that lie on the line y=3x
*Saturday, January 25, 2014 at 6:38pm*

**Calculus**

The figure shows graphs of the marginal revenue function R ' and the marginal cost function C ' for a manufacturer. (Recall from Section 4.7 that R(x) and C(x) represent the revenue and cost when x units are manufactured. Assume that R and C are measured in thousands ...
*Saturday, January 25, 2014 at 6:28pm*

**Calculus**

a)Find the number a such that the line x = a bisects the area under the curve y= 1/x^2, 1<x<3. a=3/2 b)Find the number b such that the line y = b bisects the area in part (a) b=?
*Saturday, January 25, 2014 at 6:21pm*

**Calculus**

Sketch the region and find its area. S = {(x,y) | x > -6, 0 < y < e-x/2}
*Saturday, January 25, 2014 at 12:46pm*

**Calculus**

Graph the integrands and use areas to evaluate integrals (integrate(3&-3)) root(9-x^2) dx
*Friday, January 24, 2014 at 10:34pm*

**Calculus**

integrate (t(root t)+t(root t))/t^2 dt
*Friday, January 24, 2014 at 10:26pm*

**Calculus 1**

On the graph of f(x) = 8*sin(3pi*x), points P and Q are at consecutive lowest and highest points with P occurring before Q. Find the slope of the line which passes through P and Q. Slope = ? I have tried 48/pi and it didn't work
*Thursday, January 23, 2014 at 9:38pm*

**pre-calculus**

A company plans to manufacture a container having the shape of a right circular cylinder, open at the top, and having a capacity of 24pi cubic inches. If the cost of the material for the bottom is $.30 per square inch and that for the curved sides is $.10 per square inch, ...
*Thursday, January 23, 2014 at 7:33pm*

**calculus**

Suppose that the sales at Borders bookstores went from 68 million dollars in 1990 to 427 million dollars in 1995 . Find an exponential function to model the sales (in millions of dollars) as a function of years,t, since 1990.
*Thursday, January 23, 2014 at 1:37am*

**Calculus and vectors**

A cylindrical tank is to have a capacity of 1000 m³. It is to fit into a foundry that is 12 m wide with a height of 11 m. The base of the tank will cost half as much as the top. The metal for the side of the tank will cost four fifths as much as the top. An equation that ...
*Wednesday, January 22, 2014 at 10:16pm*

**calculus**

limit as n approaches infinity for the function ((-1)^n)((5n+7)/(6n+5))
*Wednesday, January 22, 2014 at 9:19pm*

**Calculus**

Find the limit. lim 5-x/(x^2-25) x-->5 Here is the work I have so far: lim 5-x/(x^2-25) = lim 5-x/(x-5)(x+5) x-->5 x-->5 lim (1/x+5) = lim 1/10 x-->5 x-->5 I just wanted to double check with someone and see if the answer is supposed to be positive or negative. ...
*Wednesday, January 22, 2014 at 1:20pm*

**Calculus**

Water is leaking out of a pool at a rate of 4 cubic inches per second, what is the rate of change of the height of the water at the instant the volume equals 20ft cubic feet
*Wednesday, January 22, 2014 at 12:25am*

**calculus**

what is the 2nd derivative of: 1-xy = x-y i get (-y-1)/(x-1) for the first the second i know is (-y-1)/(x-1)^2 but i keep getting (0)/(x-1)^2 please show me the steps i should be taking and if possible what i did wrong
*Monday, January 20, 2014 at 10:57pm*

**Calculus**

I've been having a hard time with these lately... could someone explain it to me? Find f '(a). f(x) = (3x^2 − 3x + 4)
*Monday, January 20, 2014 at 10:50pm*

**calculus **

Find the limit lim x→−∞ sqrt(4x^6 − x)/(x^3 + 6)
*Monday, January 20, 2014 at 7:07pm*

**Calculus, Limits**

Find the limit. lim t → ∞ (sqrt t + t^2)/(6t − t^2)
*Monday, January 20, 2014 at 7:04pm*

**calculus**

a rectangle is 10 inches by 6 inches whose sides are changing. write a formula for both the perimeter and how fast each is changing in terms of L and W how do i do this, an explanation instead of an answer would be most appreciated, thanks in advance.
*Monday, January 20, 2014 at 12:26am*

**Calculus**

What is the domain of f(x)= (x-3)/(x^2-9)? lim f(x) x->3
*Saturday, January 18, 2014 at 10:18pm*

**calculus**

i need to use implicit differentiation to find the derivative: yx+y = 8 i keep getting y'=-1-y. i already know the derivative of this, by using explicit by simplification: y(x+1)=8 y=(8)/(x+1) y'= -(8)/(x+1)^2 how do i go about doing this the right way?
*Friday, January 17, 2014 at 5:49pm*

**calculus**

at what point do the graph of the function f(x)=(x^2)+4x-1 have a horizontal tangent?
*Tuesday, January 14, 2014 at 3:04pm*

**Calculus**

lim x to 1 of (sin(1-cosx))/x
*Tuesday, January 14, 2014 at 1:34pm*

**Calculus**

For what value of a is f(x)=(x^2)-a x<3 f(x)=2ax x(> or =)3 continuous at every x?
*Monday, January 13, 2014 at 10:23pm*

**calculus**

a.Find the slope of the tangent line to the curve y=9-2x^2 at the point (2,1) b.Find an equation of this tangent line.
*Monday, January 13, 2014 at 4:39pm*

**calculus**

i need to find the derivative using chain rule: (x^2 + 2x - 6)^2 (1-x^3)^2 i got the answer from a site but the problem is i cannot get my work to match up with the answer, i dont know what im doing wrong. answer: 10x^9 + 36x^8 − 64x^7 − 182x^6 + 168x^5 + 80x^4 + ...
*Monday, January 13, 2014 at 3:00am*

**Integral Calculus**

A jeepney's velocity over time in ft/sec as it moves along the x-axis is governed by the function v(t)=3t^2-10t+15. If the jeep's position at t= 1 second is 8ft, what is the total displacement made by the jeepney from t=0 to t=5sec? please I need help, i just need the ...
*Sunday, January 12, 2014 at 7:01pm*

**pre-calculus**

Express the edge length of a cube as a function of the cube's diagonal length d. Then express the surface area and volume of the cube as a function of the diagonal length.
*Sunday, January 12, 2014 at 6:21pm*

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