# calculus

Most popular questions-
## Calculus

A stone is dropped from the upper observation deck of a tower, 200 m above the ground. (Assume g = 9.8 m/s^2.) a)Find the distance (in meters) of the stone above ground level at time t. b)With what velocity does it strike the ground? (Round your answer to

*asked by John on November 13, 2011* -
## calculus

a boat leaves a dock at 2:00 pm and travels due south at a speed of 20 km/h. Another boat has been heading due east at 15 km/h and reaches the same dock at 3:00 pm. at what time were the two boats closest together

*asked by LALA on November 14, 2011* -
## Calculus

If the volume of a cube is increasing at 24 in^3/min and the surface area of the cube is increasing at 12 in^2/min, what is the length of each edge of the cube? I know that dV/dt=24 and ds/ds=12. I also know that Volume=s^3 and Surface Area=6*s^2, but what

*asked by Anna on December 7, 2010* -
## Calculus

Suppose that p(x) is the density function for heights of American men, in inches, and suppose that p(69)=0.22. Think carefully about what the meaning of this mathematical statement is. (a) Approximately what percent of American men are between 68.7 and

*asked by Cesar on October 27, 2011* -
## Calculus

A car traveling at 42 ft/sec decelerates at a constant 7 feet per second squared. How many feet does the car travel before coming to a complete stop?

*asked by Izzy on April 26, 2012* -
## calculus

A potter forms a piece of clay into a right circular cylinder. As she rolls it, the height h of the cylinder increases and the radius r decreases. Assume that no clay is lost in the process. Suppose the height of the cylinder is increasing by 0.5

*asked by mike on March 31, 2013* -
## Calculus

The radius of a circle is increasing. At a certain instant, the rate of increase in the area of the circle is numerically equal to twice the rate of increase in its circumference. What is the radius of the circle at that instant? A. 1/2 B. 1 C. Sqrt 2 D. 2

*asked by Anonymous on October 26, 2014* -
## calculus

3. For what value of k will x+k/x have a relative maximum at x = -2? A. -4 B. -2 C. 2 D. 4 E. None of these

*asked by Taeyeon on February 26, 2012* -
## calculus

4. When the area in square units of an expanding circle is increasing twice as fast as its radius in linear units, the radius is A. 1/4pi B.1/4 C.1/pi D. 1 E.pi

*asked by Taeyeon on February 26, 2012* -
## 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

*asked by Gary on May 8, 2015* -
## calculus

Consider a window the shape of which is a rectangle of height h surmounted by a triangle having a height T that is 1.1 times the width w of the rectangle If the cross-sectional area is A, determine the dimensions of the window which minimize the perimeter.

*asked by sam on April 1, 2013* -
## calculus

1. If 3x^2+2xy+y2=2 then the value of dy/dx x = 1 is A. -2 B. 0 C. 2 D. 4 E. not defined

*asked by Taeyeon on February 26, 2012* -
## Calculus

A baseball team plays in a stadium that holds 53,000 spectators. With ticket prices at $10, the average attendance had been 49,000. When ticket prices were lowered to $8, the average attendance rose to 51,000. (a) Find the demand function (price p as a

*asked by Anonymous on July 15, 2012* -
## Calculus

A parcel delivery service will deliver a package only if the length plus the girth (distance around, taken perpendicular to the length) does not exceed 100 inches. Find the maximum volume of a rectangular box with square ends that satisfies the delivery

*asked by Anonymous on November 1, 2011* -
## Calculus

An airplane flys at a constant altitude of 2 miles and a constant speed of 600 miles per hour on a straight course that will take it directly over a kangaroo on the ground. How fast is the angle of elevation of the kangaroo's line of sight increasing when

*asked by Hailey on October 7, 2014* -
## Calculus

Find a cubic function f(x) = ax^3 + bx^2 + cx + d that has a local maximum value of 3 at x = −2 and a local minimum value of 0 at x = 1.

*asked by Benjamin on November 12, 2012* -
## calculus

2. The rate of change in the number of bacteria in a culture is proportional to the number present. In a certain laboratory experiment, a culture has 10,000 bacterial initially, 20,000 bacteria at time t1 minutes, and 100,000 bacteria at (t1 + 10) minutes.

*asked by naseba on March 30, 2012* -
## Calculus

Gloria would like to construct a box with volume of exactly 45ft^3 using only metal and wood. The metal costs $15/ft^2 and the wood costs $6/ft^2. If the wood is to go on the sides, the metal is to go on the top and bottom, and if the length of the base is

*asked by Dave on November 4, 2015* -
## calculus

The function f is continuous on the closed interval [0,2] and has values that are given in the table below x = 0| 1 | 2 ____________ f(x) = 1| k | 2 The equation f(x) = 1/2 must have at least two solutions in the interval [0,2] if K = ? The answer is 0,

*asked by Joan on April 20, 2011* -
## calculus

Find the dimensions of the rectangle with area 256 square inches that has minimum perimeter, and then find the minimum perimeter. Dimensions: Minimum Perimeter:

*asked by casidhe on April 20, 2012* -
## Calculus

A particle moves along the x-axis with velocity v(t) = sin(2t), with t measured in seconds and v(t) measured in feet per second. Find the total distance travelled by the particle from t = 0 to t = π seconds. Do I have to take the integral of the equation

*asked by Henry on February 21, 2016* -
## Calculus

A ball is shot straight up into the air with initial velocity of 47 ft/sec. Assuming that the air resistance can be ignored, how high does it go?

*asked by Anonymous on February 2, 2011* -
## Calculus

A piece of wire 40cm long is cut into two pieces. One piece is bent into the shape of a square and the other is bent into the shape of a circle. How should the wire be cut so that the total area enclosed is a) a maximum? /b) a minimum? Perimeter of square

*asked by sh on January 20, 2010* -
## calculus

In the space below, provide the smaller of the two positive integers that add to 40 and have the largest possible product

*asked by emma on April 22, 2015* -
## Calculus

I really need help with this problem an automobile accelerates from rest at 1 + 3(square root)t mph/sec for 9 seconds. How far does it travel in those nine seconds? I have found that the velocity, after nine seconds, is 63 I have figuredout the answer but

*asked by James on April 1, 2007* -
## Calculus

A small resort is situated on an island that lies exactly 6 miles from P, the nearest point to the island along a perfectly straight shoreline. 10 miles down the shoreline from P is the closest source of fresh water. If it costs 1.4 times as much money to

*asked by Anonymous on April 26, 2012* -
## Calculus

Given the table below for selected values of f(x), use 6 right rectangles to estimate the value of the integral from 1 to 10 of f(x)dx. Table: 1 3 4 6 7 9 10 4 8 6 10 10 12 16 The only problem I'm having with this is figuring out the values of f(2.5),

*asked by Kait on April 4, 2018* -
## 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

*asked by Tom on May 27, 2015* -
## calculus

Let f be a differentiable function such that f(3) = 2 and f'(3) = 5. If the tangent line to the graph of f at x = 3 is used to find an approximation to a zero of f, that approximation is? So confused

*asked by Matt on April 21, 2011* -
## Calculus

Suppose the integral from 2 to 8 of g of x, dx equals 5, and the integral from 6 to 8 of g of x, dx equals negative 3, find the value of the integral from 2 to 6 of 2 times g of x, dx . 8 MY ANSWER 12 16 4

*asked by Lilly on March 15, 2016* -
## calculus

If an arrow is shot upward on Mars with a speed of 52 m/s, its height in meters t seconds later is given by y = 52t − 1.86t2. (Round your answers to two decimal places.) What is the average speed over the given time intervals? (i) [1, 2] (ii) [1, 1.5]

*asked by John on January 31, 2018* -
## Calculus

An equation of the line tangent to the graph of y=(2x+3)/(3x-2) at the point (1,5) is...do I take the derivative of y=(2x+3)/(3x-2) to find the slope and then plug that into y-5=m(x-1)?

*asked by Anonymous on November 18, 2007* -
## Calculus

If an arrow is shot upward on Mars with a speed of 54 m/s, its height in meters t seconds later is given by y = 54t − 1.86t2 (i) [1, 2](ii) [1, 1.5] (iii) [1, 1.1] (iv) [1, 1.01] (v) [1, 1.001] (b) Estimate the speed when t = 1.

*asked by Hector on July 12, 2017* -
## Calculus

Squares with sides of length x are cut out of each corner of a rectangular piece of cardboard measuring 3 ft by 4 ft. The resulting piece of cardboard is then folded into a box without a lid. Find the volume of the largest box that can be formed in this

*asked by Michelle on November 5, 2015* -
## calculus

2. Consider the function f defined by f(x)=(e^X)cosx with domain[0,2pie] . a. Find the absolute maximum and minimum values of f(x) b. Find the intervals on which f is increasing. c. Find the x-coordinate of each point of inflection of the graph of f.

*asked by Yoona on January 2, 2012* -
## calculus

a particle moves along the y axis so that its position at any time t, for 0 is less than or equal to t which is less than or equal to 5, is given by y(t)=t^4-18t^2. in which intervals is the particle speeding up?

*asked by kriti on January 18, 2011* -
## Calculus

A man of height 1.7 meters walks away from a 5-meter lamppost at a speed of 1.6 m/s. Find the rate at which his shadow is increasing in length. (Round your answer to three decimal places.) This problem is absolutely killing me I see a lot of examples like

*asked by Jake on October 7, 2015* -
## Calculus

Find a formula for the fourth degree polynomial p(x) whose graph is symmetric about the y-axis (meaning it has no odd powers of x), and which has a y-intercept of 10, and global maxima at (3,253) and (−3,253).

*asked by Dana on April 7, 2013* -
## Calculus

You are given a piece of sheet metal that is twice as long as it is wide an has an area of 800m^2. Find the dimensions of the rectangular box that would contain a max volume if it were constructed from this piece of metal by cutting out squares of equal

*asked by Marie on March 26, 2014* -
## Calculus

Find the linearization L(x) of y=e^(7x)ln(x) at a=1. L(x)=

*asked by Reonea on October 30, 2011* -
## Calculus

for the function F(t)=ln(t^2), let f(t)=F'(t). Write the integral from a to b of f(t) dt and evaluate it with the fundamental theorem of calculus. the integral from 1 to 3 ___ dt= __

*asked by bob on November 30, 2011* -
## Calculus

Pumping stations deliver gasoline at the rate modeled by the function D, given by D(t)= 6t/(1+2t) with t measure in hours and and R(t) measured in gallons per hour. How much oil will the pumping stations deliver during the 3-hour period from t = 0 to t =

*asked by Henry on February 21, 2016* -
## Calculus

A rectangular recreational field needs to be built outside of a gymnasium. Three walls of fencing are needed and the fourth wall is to be a wall of the gymnasium itself. The ideal area for such a field is exactly 250000ft2. In order to minimize costs, it

*asked by Erik on November 4, 2015* -
## Calculus

Set up, but do not evaluate, the integral which gives the volume when the region bounded by the curves y = Ln(x), y = 1, and x = 1 is revolved around the line y = −3.

*asked by Michael on March 7, 2019* -
## Calculus

he 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'(8). Give units in your answer. b. What is the meaning of

*asked by Student on December 8, 2017* -
## Calculus

The function f is continuous on the interval [3, 13] with selected values of x and f(x) given in the table below. Use the data in the table to approximate f '(3.5) x 3 4 7 10 13 f(x) 2 8 10 12 22

*asked by Jim on April 6, 2018* -
## calculus

If f is the focal length of a convex lens and an object is placed at a distance p from the lens, then its image will be at a distance q from the lens, where f, p, and q are related by the lens equation 1/f = 1/p + 1/q What is the rate of change of p with

*asked by Sam on May 6, 2011* -
## Calculus

The top and bottom margins of a poster are 2 cm and the side margins are each 4 cm. If the area of printed material on the poster is fixed at 386 square centimeters, find the dimensions of the poster with the smallest area.

*asked by Nathan on November 18, 2013* -
## CALCULUS

Sketch the region enclosed by the given curves. y = 4/X y = 16x, y = 1X/16 x > 0 and the area between the curves

*asked by LAUERN PLEASE HELP on April 12, 2014* -
## calculus

A rectangular beam is cut from a cylindrical log of radius 25 cm. The strength of a beam of width w and height h is proportional to wh2. (See Figure 4.70.) Find the width and height of the beam of maximum strength.

*asked by Maria on November 1, 2011* -
## Calculus

f(x) and g(x) are a differentiable function for all reals and h(x) = g[f(2x)]. The table below gives selected values for f(x), g(x), f '(x), and g '(x). Find the value of h '(1). (4 points) x 1 2 3 4 5 6 f(x) 0 3 2 1 2 0 g(x) 1 3 2 6 5 0 f '(x) 3 2 1 4 0 2

*asked by Henry on February 21, 2016* -
## Calculus

Graph the curve. Find the exact length of the curve. x = 2et cos(t), y = 2et sin(t), 0 ≤ t ≤ π

*asked by Kaitlyn on January 19, 2016* -
## calculus

A woman 5.5 ft tall walks at a rate of 6 ft/sec toward a streetlight that is 22 ft above the ground. At what rate is the length of her shadow changing when she is 15 ft from the base of the light?

*asked by Anonymous on March 2, 2008* -
## Calculus

f is a continuous function with a domain [−3, 9] such that f of x equals 3 for x between negative 3 and 0 including negative 3, equals negative 1 times x plus 3 for x between 0 and 6 inclusive, and equals negative 3 for x greater than 6 and less than or

*asked by Ke$ha on May 12, 2017* -
## Calculus

Suppose f(pi/3) = 3 and f '(pi/3) = −7, and let g(x) = f(x) sin x and h(x) = (cos x)/f(x). Find the following. a. g'(pi/3) b. h'(pi/3)

*asked by Christina on November 7, 2011* -
## 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

*asked by Rasheda on January 29, 2014* -
## Calculus

f is a continuous function with a domain [−3, 9] such that f(x)= 3 , -3 ≤ x < 0 -x+3 , 0 ≤ x ≤ 6 -3 , 6 < x ≤ 9 and let g(x)= ∫ f(t) dt where a=-2 b=x On what interval is g increasing? Justify your answer. For 0 ≤ x ≤ 6, express g(x) in

*asked by Skyler on February 24, 2016* -
## Calculus

The graph of f ′(x) is continuous and decreasing with an x-intercept at x = 0. Which of the following statements is false? (4 points) The graph of f has an inflection point at x = 0. The graph of f has a relative maximum at x = 0. The graph of f is

*asked by Henry on February 20, 2016* -
## Calculus

A man 2m tall walks away from a lamppost whose light is 5m above the ground. If he walks at a speed of 1.5m/s, at what rate is his shadow growing when he is 10m from the lamppost? I tried to draw a diagram, but I don't understand where the 5m is, the

*asked by sh on December 1, 2009* -
## calculus

You are designing a rectangular poster to contain 256 in^2 of printing with a 3-in. margin at the top and bottom and a 2-in. margin at each side. What overall dimensions will minimize the amount of paper used?

*asked by Anonymous on March 2, 2008* -
## Calculus

Consider the curve defined by y + cosy = x +1 for 0 =< y =< 2pi.... a. Find dy/dx in terms of y. *I got 1/(y-siny) but I feel like that's wrong. b. Write an equation for each vertical tangent to the curve. c. find d^2y/dx^2 in terms of y. d. Sketch a graph

*asked by Penny on January 24, 2012* -
## Calculus

Suppose that p(x) is the density function for heights of American men, in inches, and suppose that p(69)=0.22. Think carefully about what the meaning of this mathematical statement is. (a) Approximately what percent of American men are between 68.7 and

*asked by Cesar on October 28, 2011* -
## Calculus

By recognizing each series below as a Taylor series evaluated at a particular value of x, find the sum of each convergent series. A) 1+5 + (5^2)/(2!)+(5^3)/(3!)+(5^4)/(4!)+...+ (5^k)/(k!)+...= B)

*asked by Cole on June 18, 2013* -
## calculus

A conical water tank with vertex down has a radius of 12 feet at the top and is 23 feet high. If water flows into the tank at a rate of 20 {\rm ft}^3{\rm /min}, how fast is the depth of the water increasing when the water is 17 feet deep?

*asked by Mike on November 30, 2012* -
## calculus

A sample of a radioactive substance decayed to 94.5% of its original amount after a year. (Round your answers to two decimal places.) (a) What is the half-life of the substance? (b) How long would it take the sample to decay to 65% of its original amount?

*asked by kela on November 9, 2012* -
## Calculus

For a cylinder with a surface area of 90, what is the maximum volume that it can have? Round your answer to the nearest 4 decimal places. The volume of a cylinder is πr^2*h and the surface area is 2πrh+2πr^2.

*asked by John on November 4, 2015* -
## calculus

Estimate the area under the curve f(x) = x2 from x = 1 to x = 5 by using four inscribed (under the curve) rectangles. Answer to the nearest integer.

*asked by rae on February 9, 2018* -
## Calculus

Find constants a and b in the function ax^b/ln(x) such that f(1/5)=1 and there is a local min at x=1/5

*asked by Tanner on October 20, 2015* -
## Calculus

4. Find the area of the largest rectangle (with sides parallel to the coordinate axes) that can be inscribed in the region enclosed by the graphs of f(x) = 18 – x^2 and g(x) = 2x^2 – 9.

*asked by Anonymous on January 16, 2012* -
## calculus

the edge of a cube is increasing at the rate of .05 centimeters per second. in terms of the side of the cube s, what is the rate of change of the volume of the cube, in cm^3/sec

*asked by crystal on February 10, 2011* -
## calculus

By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made. If the cardboard is 14 in. long and 6 in. wide, find the dimensions of the box that will yield the maximum

*asked by eve on March 16, 2013* -
## Calculus

A sphere with radius 1m has temperature 15 degrees C. It lies inside a con- centric sphere with radius 2m and temperature 25 degrees C: The temperature T(r) at a distance r from the common centre of the spheres satisfi es the di fferential equation:

*asked by Maria on August 8, 2011* -
## calculus

If 800 feet of fencing is used to enclose a rectangular plot of land that borders a river, what is the maximum area that can be enclosed? Answer to the nearest square foot without commas. For example, if the answer is 1,000, write 1000.

*asked by emma on April 22, 2015* -
## Calculus

A person whose height is 6 feet is walking away from the base of a streetlight along a straight path at 4 feet per second. If the height of the streetlight is 15 feet, what is the rate at which the person's shadow is lengthening?

*asked by Anonymous on October 27, 2014* -
## Calculus

A graphic designer is asked to create a movie poster with a 128 in^2 photo surrounded by a 4 in border at the top and bottoms and a 2 in border on each side. What overall dimensions for the poster should the designer choose to use the least amount of

*asked by Anonymous on October 21, 2015* -
## calculus

The area A = πr2 of a circular puddle changes with the radius. At what rate does the area change with respect to the radius when r = 5ft?

*asked by Anonymous on December 17, 2014* -
## Calculus

A particle moves along a line so that at any time t its position is given by x(t)=2(pi)t+cos(2(pi)t). Determine the particle's maximum velocity.

*asked by MEG on November 15, 2010* -
## Calculus

Oil is leaking out of a ruptured tanker at a rate of r = 19e^(2t) gallons per hour. Write a definite integral that represents the total quantity of oil which leaks out of the tanker in the first 3 hours. Using your formula answer the following questions:

*asked by Lena on November 14, 2010* -
## calculus

Find an interval of length 0.1 in [1, 2] containing a root of the equation. (Enter your answer using interval notation.) x7 + 7x − 10 = 0

*asked by patel on September 22, 2012* -
## 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

*asked by Tom on May 15, 2015* -
## calculus

If f(x) = 3 cos^2(x) − 6 sin(x) 0 ≤ x ≤ 2π Find the intervals of increase and decrease, the intervals of concave up and concave down, local maximum values, local minimum values, and inflection point

*asked by SIRI on October 17, 2014* -
## Calculus

1) A particle is moving along the x-axis so that its position at t ≥ 0 is given by s(t) = (t)In(2t). Find the acceleration of the particle when the velocity is first zero. 2) The driver of a car traveling at 50 ft/sec suddenly applies the brakes. The

*asked by James on October 2, 2017* -
## calculus

Find the distance, in feet, a particle travels in its first 4 seconds of travel, if it moves according to the velocity equation v(t)= −t2 + 4 (in feet/sec).

*asked by Anonymous on June 15, 2015* -
## Calculus

An OPEN box has a square base and a volume of 108 cubic inches and is constructed from a tin sheet. Find the dimensions of the box, assuming a minimum amount of material is used in it's construction. HINT: the goal is to minimize the surface are of the

*asked by Jennifer on May 14, 2013* -
## Calculus

An energy drink container in the shape of a right circular cylinder must have a volume of 12 fluid ounces (1 fluid ounce is approximately 1.80469 cubic inches). The cost per square inch of constructing the top and bottom is twice the cost of constructing

*asked by Katie on April 10, 2016* -
## Calculus

The base of a solid in the xy-plane is the circle x^2+y^2 = 16. Cross sections of the solid perpendicular to the y-axis are semicircles. What is the volume, in cubic units, of the solid? a. 128π/3 b. 512π/3 c. 32π/3 d. 2π/3

*asked by Louis on March 21, 2017* -
## calculus

a particle moves along the curve xy=10. if x=2 and dy/dt=3, what is the value of dx/dt. i'm guessing this is something to do with parametric equations. if x is 2, then y=5. but how do i get dx/dt. you have to differentiate the equation with respect to t so

*asked by Anonymous on April 21, 2007* -
## calculus

The point P(4, −2)lies on the curve y = 2/(3 − x). (a) If Q is the point(x, 2/(3 − x)),use your calculator to find the slope mPQ of the secant line PQ (correct to six decimal places) for the following values of x. 1) 3.9 mPQ= 2) 3.99 mPQ= 3)3.999

*asked by student on August 28, 2012* -
## Calculus

Sorry this is really long. Just wondering how I would do each of these A particle is moving with velocity v(t) = t^2 – 9t + 18 with distance, s measured in meters, left or right of zero, and t measured in seconds, with t between 0 and 8 seconds

*asked by John on February 14, 2016* -
## Calculus

Given a right circular cone, you put an upside-down cone inside it so that its vertex is at the center of the base of the larger cone, and its base is parallel to the base of the larger cone. If you choose the upside-down cone to have the largest possible

*asked by Mishaka on December 16, 2011* -
## Calculus

The line that is normal to the curve x^2=2xy-3y^2=0 at(1,1) intersects the curve at what other point? Please help. Thanks in advance. We have x2=2xy - 3y2 = 0 Are there supposed to be 2 equal signs in this expression or is it x2 + 2xy - 3y2 = 0 ? I'll

*asked by Jen on October 15, 2006* -
## Calculus

Water leaks from a tank at the rate of r(t) gallons per hour. The rate decreased as time passed, and values of the rate at two-hour time intervals are shown in the table below. The total amount of water that leaked out is evaluated by a Riemann sum. Find

*asked by Tim on April 8, 2018* -
## Calculus

For which pair of functions f(x) and g(x) below will the lim f(x)/g(x)equal 0 x-infinity f(x) e^x; g(x) = x^3 f(x) x^5; g(x) = e^x f(x) x^3; g(x) = ln(x) f(x) x^negative 2; g(x) = e^negative x

*asked by Gary on March 10, 2015* -
## calculus

Consider the given function and the given interval. f(x) = 4 sin x − 2 sin 2x, [0, π] (a) Find the average value fave of f on the given interval. fave = (b) Find c such that fave = f(c). (Round your answers to three decimal places.) c = (smaller value)

*asked by James on February 11, 2013* -
## Calculus

A particle moves along the x-axis with position function s(t) = e^cos(x). How many times in the interval [0, 2π] is the velocity equal to 0? 1< My answer 2 3 More than 3 I don't really get this question will someone please explain it to me?

*asked by Someone on January 11, 2017* -
## Calculus

A particle moves along line segments from the origin to the points (3, 0, 0), (3, 3, 1), (0, 3, 1), and back to the origin under the influence of the force field F(x, y, z) = z2i + 5xyj + 4y2k. I have tried multiple times to solve this problem but the

*asked by Jessica on December 8, 2014* -
## Calculus

It took 1800 J of work to stretch a spring from its natural length of 2m to a length of 5m. Find the spring's force constant. Please help. Thanks in advance.

*asked by JEUCD 37 on March 8, 2012* -
## calculus

5. Let f be the function given by f(x) = x3- 7x + 6. a. Find the zeros of f b. Write an equation of the line tangent to the graph of f at x = -1 c. Find the x coordinate of the point where the tangent line is parallel to the secant line on the interval [1,

*asked by Yoona on November 7, 2011* -
## 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?

*asked by joe9 on May 4, 2015* -
## Calculus

If an arrow is shot upward on Mars with a speed of 52 m/s, its height in meters t seconds later is given by y = 52t − 1.86t2. (Round your answers to two decimal places.) What is the average speed over the given time intervals? (i) [1, 2] (ii) [1, 1.5]

*asked by Nick on January 31, 2018*

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