Answer:
V = 63π / 200 m^3
Step-by-step explanation:
Given:
- The function y = f(x) is revolved around the x-axis over the interval [1,6] to form a spherical surface:
y = √(42*x - x^2)
- The surface is coated with paint with uniform layer thickness t = 1.5 mm
Find:
The volume of paint needed
Solution:
- Let f be a non-negative function with a continuous first derivative on the interval [1,6]. The Area of surface generated when y = f(x) is revolved around x-axis over the interval [1,6] is:
- The derivative of the function f'(x) is as follows:
- The square of derivative of f(x) is:
- Now use the surface area formula:
- The Volume of the pain coating is:
V = S*t
V = 210*π*3/2000
V = 63π / 200 m^3
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Answer:
Equation of line : y - y1 = m(x - x1)
where x and y are are the point in form
(x , y)
where m is the slope.
Calculate slope using points:
Sub points into slope point formula:
sub 1 point for x and y:
solve for c:
5 = 1 + c
c = 4
sub c back into equation :
7 everytime you look at it the answer disappears merry Christmas everyone