A solar oven is to be made from an open box with reflective sides. Each box is made from a 30-in. by 24-in. rectangular sheet of aluminium with square of length x (in inches) removed from each corner. Then the flaps are folder up to form an open box. a. Show that the volume of the box is given by V x = 4 x 3 − 108 x 2 + 720 x for 0 < x < 12. b. Graph the function from part (a) and a “maximumâ€� feature on a graphing utility to approximate the length of the sides of the squares that should be removed to maximize the volume. Round to the nearest tenth of an inch. c. Approximate the maximum volume. Round to the nearest cubic inch.
A solar oven is to be made from an open box with reflective sides. Each box is made from a 30-in. by 24-in. rectangular sheet of aluminium with square of length x (in inches) removed from each corner. Then the flaps are folder up to form an open box. a. Show that the volume of the box is given by V x = 4 x 3 − 108 x 2 + 720 x for 0 < x < 12. b. Graph the function from part (a) and a “maximumâ€� feature on a graphing utility to approximate the length of the sides of the squares that should be removed to maximize the volume. Round to the nearest tenth of an inch. c. Approximate the maximum volume. Round to the nearest cubic inch.
Solution Summary: The author illustrates how a solar oven has to be made from an open box with reflective sides. The volume of the box is given by cvolume=lengthtimes width
A solar oven is to be made from an open box with reflective sides. Each box is made from a 30-in. by 24-in. rectangular sheet of aluminium with square of length x (in inches) removed from each corner. Then the flaps are folder up to form an open box.
a. Show that the volume of the box is given by
V
x
=
4
x
3
−
108
x
2
+
720
x
for
0
<
x
<
12.
b. Graph the function from part (a) and a “maximum� feature on a graphing utility to approximate the length of the sides of the squares that should be removed to maximize the volume. Round to the nearest tenth of an inch.
c. Approximate the maximum volume. Round to the nearest cubic inch.
8. For x>_1, the continuous function g is decreasing and positive. A portion of the graph of g is shown above. For n>_1, the nth term of the series summation from n=1 to infinity a_n is defined by a_n=g(n). If intergral 1 to infinity g(x)dx converges to 8, which of the following could be true? A) summation n=1 to infinity a_n = 6. B) summation n=1 to infinity a_n =8. C) summation n=1 to infinity a_n = 10. D) summation n=1 to infinity a_n diverges.
PLEASE SHOW ME THE RIGHT ANSWER/SOLUTION
SHOW ME ALL THE NEDDED STEP
13: If the perimeter of a square is shrinking at a rate of 8 inches per second, find the rate at which its area is changing when its area is 25 square inches.
DO NOT GIVE THE WRONG ANSWER
SHOW ME ALL THE NEEDED STEPS
11: A rectangle has a base that is growing at a rate of 3 inches per second and a height that is shrinking at a rate of one inch per second. When the base is 12 inches and the height is 5 inches, at what rate is the area of the rectangle changing?
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Interpreting Graphs of Quadratic Equations (GMAT/GRE/CAT/Bank PO/SSC CGL) | Don't Memorise; Author: Don't Memorise;https://www.youtube.com/watch?v=BHgewRcuoRM;License: Standard YouTube License, CC-BY
Solve a Trig Equation in Quadratic Form Using the Quadratic Formula (Cosine, 4 Solutions); Author: Mathispower4u;https://www.youtube.com/watch?v=N6jw_i74AVQ;License: Standard YouTube License, CC-BY