1. The graph of a function y = √16-(x-5)2 + 3 is given below: Approximate the area under the graph from [0,8] using 4 evenly spaced trapezoids. 4 2. A square-base pyramid has base length x ft and height h. a. Write down an expression for the surface area of the pyramid. b. The surface area of the pyramid is 20 ft². Find an expression for h in terms of x. c. Find an expression for the volume of the pyramid, V(x), in terms of x. d. i. Find V'(x) ii. Hence, find the value of x which maximizes the volume of the pyramid.
1. The graph of a function y = √16-(x-5)2 + 3 is given below: Approximate the area under the graph from [0,8] using 4 evenly spaced trapezoids. 4 2. A square-base pyramid has base length x ft and height h. a. Write down an expression for the surface area of the pyramid. b. The surface area of the pyramid is 20 ft². Find an expression for h in terms of x. c. Find an expression for the volume of the pyramid, V(x), in terms of x. d. i. Find V'(x) ii. Hence, find the value of x which maximizes the volume of the pyramid.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![1. The graph of a function y = √16-(x-5)2 + 3 is given below:
Approximate the area under the graph from [0,8] using
4 evenly spaced trapezoids.
4
2. A square-base pyramid has base length x ft and height h.
a. Write down an expression for the surface area of the pyramid.
b. The surface area of the pyramid is 20 ft². Find an expression for h in terms of x.
c. Find an expression for the volume of the pyramid, V(x), in terms of x.
d.
i. Find V'(x)
ii. Hence, find the value of x which maximizes the volume of the pyramid.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8889c1d4-3af3-47cf-9a25-085e8413ba6a%2F1f098139-64da-4ee3-9092-7c0a7a8d170c%2Fj6yax7g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. The graph of a function y = √16-(x-5)2 + 3 is given below:
Approximate the area under the graph from [0,8] using
4 evenly spaced trapezoids.
4
2. A square-base pyramid has base length x ft and height h.
a. Write down an expression for the surface area of the pyramid.
b. The surface area of the pyramid is 20 ft². Find an expression for h in terms of x.
c. Find an expression for the volume of the pyramid, V(x), in terms of x.
d.
i. Find V'(x)
ii. Hence, find the value of x which maximizes the volume of the pyramid.
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