Popular questions
  1. 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
  2. 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
  3. 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
  4. 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
  5. 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
  6. 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
  7. Calculus

    A rectangular tank with a square base, an open top, and a volume of 864 ft^3 is to be constructed of the sheet steel. Find the dimensions of the tank that minimize the surface area

    asked by Ashlyn on April 22, 2018
  8. 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
  9. 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
  10. 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
  11. 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
  12. 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
  13. 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
  14. Calculus

    An equation of the line tangent to the graph of y=(2x+3)/(3x-2) at the point (1,5) 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
  15. 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
  16. 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
  17. 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
  18. Calculus

    Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis. x = 7y^2, y ≥ 0, x = 7; about y = 2

    asked by sp on January 30, 2018
  19. 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
  20. 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
  21. Calculus

    A ball is thrown straight down from the top of a 220-foot building with an initial velocity of -22 feet per second. What is its velocity after 3 seconds? What is its velocity after falling 108 feet?

    asked by Susana on October 3, 2011
  22. calculus

    The sides and diagonal of the rectangle above are strictly increasing with time. At the instant when x=4 and y=3, dx/dt=dz/dt and dy/dt=k(dz/dt). What is the value of k at that instant. solved for z with pythagorean theorem and stuck at that step. z=5

    asked by Repost on April 27, 2011
  23. 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
  24. 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
  25. 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
  26. 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
  27. 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
  28. 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
  29. 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
  30. calculus

    For which of the following mixtures will Ag2SO4(s) precipitate? 150.0 mL of 0.10 M Na2SO4(aq) and 5.0 mL of 0.20 M AgNO3(aq) 150.0 mL of 0.10 M Na2SO4(aq) and 5.0 mL of 0.30 M AgNO3(aq) 150.0 mL of 0.10 M Na2SO4(aq) and 5.0 mL of 0.40 M AgNO3(aq) 150.0 mL

    asked by chris12 on November 20, 2016
  31. Calculus

    The velocity function (in meters per second) is given for a particle moving along a line. v(t) = 3t − 7, 0 ≤ t ≤ 3 (a) Find the displacement. -7.5 m (b) Find the distance traveled by the particle during the given time interval.

    asked by Anonymous on May 10, 2018
  32. Calculus

    A cylinder is inscribed in a right circular cone of height 5.5 and radius (at the base) equal to 2 . A) What are the dimensions of such a cylinder which has maximum volume? B) What is the radius? C) What is the height?

    asked by Michaela on April 27, 2013
  33. 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
  34. 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
  35. 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
  36. 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

    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
  38. 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
  39. 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
  40. 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
  41. Calculus

    Suppose that 5 J of work is needed to stretch a spring from its natural length of 28 cm to a length of 36 cm. (a) How much work is needed to stretch the spring from 32 cm to 34 cm? (Round your answer to two decimal places.) (b) How far beyond its natural

    asked by Kaitlyn on January 23, 2016
  42. 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
  43. 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
  44. Calculus

    A rectangular field is to be enclosed by a fence and divided into three lots by fences parallel to one of the sides. Find the dimensions of the largest field that can be enclosed with 800 feet of fencing. Help me please!!!!!!!!!!! THANK YOU

    asked by Lex on October 18, 2014
  45. 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
  46. calculus

    A street light is at the top of a 15 foot tall pole. A 6 foot tall woman walks away from the pole with a speed of 7 ft/sec along a straight path. How fast is the tip of her shadow moving (away from the woman) when she is 50 feet from the base of the pole?

    asked by M on October 24, 2018
  47. Calculus

    A spinner is used for which it is equally probable that the pointer will land on any one of six regions. Three of the regions are colored red , two are colored green, and one in colored yellow. If the pointer is spun twice, find the probability it will

    asked by John on December 10, 2007
  48. 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
  49. Calculus

    The population of a region is growing exponentially. There were 40 million people in 1980 (when t=0) and 50 million people in 1990. Find an exponential model for the population (in millions of people) at any time t, in years after 1980. P(t)= Predicted

    asked by Z32 on October 6, 2009
  50. Calculus

    The graph of f ′(x), the derivative of x, is continuous for all x and consists of five line segments as shown below. Given f (0) = 6, find the absolute maximum value of f (x) over the interval [0, 3]. a) 0 b) 8 c) 10 d) 16

    asked by Alice on April 11, 2019
  51. 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
  52. 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
  53. Calculus

    A 0.2 ml dose of a drug is injected into a patient steadily for 0.75 seconds. At the end of this time, the quantity, Q, of the drug in the body starts to decay exponentially at a continuous rate of 0.2 percent per second. Using formulas, express Q as a

    asked by Abigail on February 6, 2011
  54. 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
  55. 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
  56. Calculus

    The equation of motion of a particle is s = t3 − 12t, where s is in meters and t is in seconds. For the velocity function, I got v(t)=3t^2-12 and for acceleration, a(t)=6t. The final question is: Find the acceleration when the velocity is 0. How do I do

    asked by Kelly on September 29, 2015

    Rate of Change You are given the dollar value of a product in 2008 and the rate at which the value of the product is expected to change the nest 5 years. write a linear equation that gives the dollar value V of the product in terms of the yeart.(let t= 0

    asked by kim on September 26, 2009
  58. calculus

    A man launches his boat from point A on a bank of a straight river, 3 km wide, and wants to reach point B, 2 km downstream on the opposite bank, as quickly as possible. He could row his boat directly across the river to point C and then run to B, or he

    asked by Avilene on December 4, 2009
  59. Calculus

    A box (with no top) is to be constructed from a piece of cardboard of sides A and B by cutting out squares of length h from the corners and folding up the sides. Find the value of h that maximizes the volume of the box if A = 7 and B = 12

    asked by Jackie on October 26, 2019
  60. Calculus

    If f(x)=sqrt (x^2-4) and g(x)=3x-2, then the derivative of f(g(x)) at x=3 is A. 7/sqrt 5 B. 14/sqrt 5 C. 18/sqrt 5 D. 15/sqrt 21 E. 30/sqrt 21

    asked by Anonymous on October 27, 2014
  61. calculus

    1. Let f be the function that is defined for all real numbers x and that has the following properties. (i) f''(x)=24x-18 (ii) f'(1)=-6 (iii) f'(2)=0 a. Find each x such that the line tangent to the graph of f at (x, f (x)) is horizontal b. Write an

    asked by Yoona on February 13, 2012
  62. calculus

    If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate at which the diameter decreases when the diameter is 9 cm. (Give your answer correct to 4 decimal places.)

    asked by nate on November 29, 2011
  63. 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
  64. Calculus

    A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. An industrial tank of this shape must have a volume of 1600 cubic feet. The hemispherical ends cost twice as much per square foot of surface area as the sides. Find

    asked by Emily on November 3, 2016
  65. Calculus

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

    asked by Reonea on October 30, 2011
  66. Calculus

    Consider all right circular cylinders for which the sum of the height and circumference is 30 centimeters. What is the radius of one with maximum volume. Work: V=(pi)r^2(h) h= V/(pi)(r^2) 2(pi)r + h=30 V=(pi)r^2(h) V'=2(pi)(r)h+2pi(r^2)=0

    asked by Anonymous on June 4, 2008
  67. 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
  68. Calculus

    A jogger runs around a circular track of radius 65 ft. Let (x,y) be her coordinates, where the origin is the center of the track. When the jogger's coordinates are (39, 52), her x -coordinate is changing at a rate of 15ft/s. Find (dy/dx)

    asked by Anonymous on March 6, 2013
  69. Calculus

    A rancher plans to make four identical and adjacent rectangular pens against a barn, each with an area of 100m^2. what are the dimensions of each pen that minimize the amount of fence that must be used?

    asked by Anonymous on October 25, 2011
  70. 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
  71. 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
  72. 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
  73. Calculus

    A searchlight rotates at a rate of 2 revolutions per minute. The beam hits a wall located 8 miles away and produces a dot of light that moves horizontally along the wall. How fast (in miles per hour) is this dot moving when the angle between the beam and

    asked by Reonea on October 30, 2011
  74. 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
  75. calculus

    3. The radius r of a sphere is increasing at a constant rate of 0.04 centimeters per second. (Note: The volume of a sphere with radius r is v=4/3pir^3 ). a. At the time when the radius of the sphere is 10 cm, what is the rate of increase of its volume? b.

    asked by Yoona on January 3, 2012
  76. 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
  77. 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
  78. 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
  79. calculus

    A searchlight rotates at a rate of 3 revolutions per minute. The beam hits a wall located 7 miles away and produces a dot of light that moves horizontally along the wall. How fast (in miles per hour) is this dot moving when the angle \theta between the

    asked by MEMO on March 7, 2014
  80. Calculus

    Two ships leave the same port at noon. Ship A sails north at 22 mph, and ship B sails east at 12 mph. How fast is the distance between them changing at 1 p.m.? (Round your answer to one decimal place.)

    asked by Ali on October 10, 2012
  81. 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
  82. calculus

    Triangle ABC is given where m∠A=33°, a = 15 in., and the height, h, is 9 in. How many distinct triangles can be made with the given measurements? Explain your answer

    asked by rosie on March 13, 2019
  83. 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
  84. Calculus

    A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing $60/ft and on the other three sides by a metal fence costing $50/ft. If the area of the garden is 102 square feet, find the dimensions of the garden that

    asked by Sarah on April 9, 2016
  85. Calculus

    A man standing 9 feet from the base of a lamppost casts a shadow 6 feet long. If the man is 6 feet tall and walks away from the lamppost at a speed of 30 feet per minute, at what rate, in feet per minute, will his shadow lengthen?

    asked by Mike Nguyen on September 25, 2014
  86. calculus

    A 5.5 foot tall woman walks at 6ft/s torward a street light that is 16.5 ft above the ground. what is the rate of change of the length of her shadow when she is 14ft from the street light? At what rate is the tip of her shadow moving? How do I get the

    asked by Anon on April 14, 2016
  87. calculus

    In the early 1960s, radioactive strontium-90 was released during atmospheric testing of nuclear weapons and got into the bones of people alive at the time. If the half-life of strontium-90 is 27 years, what fraction of the strontium-90 absorbed in 1962

    asked by jessica on July 3, 2012
  88. 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
  89. 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
  90. 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
  91. 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
  92. Calculus

    A sporting goods store sells 100 pool tables per year. It costs $20 to store one pool table for a year, based on the average inventory on hand. It costs $40 for each delivery of pool tables. How many times per year and in what lot size should the store

    asked by Casey on March 3, 2012
  93. 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
  94. calculus

    A long rectangular sheet of metal, 12 inches wide, is to be made into a rain gutter by turning up two sides so that they are perpendicular to the sheet. How many inches should be turned up to give the gutter its greatest capacity?

    asked by MEG on November 15, 2010
  95. 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
  96. 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

    asked by Mwe on February 7, 2015
  97. 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 Harry on April 4, 2018
  98. calculus

    Use Newton's method to approximate a root of the equation 3sin(x)=x as follows. Let x1=1 be the initial approximation. The second approximation x2 is and the third approximation x3 is

    asked by kwack on September 7, 2010
  99. Calculus

    A rectangle has width w inches and height h, where the width is twice the height. Both w and h are functions of time,t, measured in seconds. If A represents the area of the rectangle, what is the rate of change of A with respect to t at the instant where

    asked by Anonymous on December 2, 2019
  100. Calculus

    A ball is dropped from a height of 10 feet and bounces. Each bounce is ¨ú of the height of the bounce before. Thus, after the ball hits the floor for the first time, the ball rises to a height of 10(¨ú ) = 7.5 feet, and after it hits the second floor

    asked by Sandy on April 15, 2009