Answer:
r=8
Step-by-step explanation:
Given formula:
r = C / 2π
It is given that C = 16π
hence
r = 16π / 2π = 8
a) The first integral corresponds to the area under y = f(x) on the interval [0, 3], which is a right triangle with base 3 and height 5, hence the integral is

b) The integral is zero since the areas under the curve over [3, 4] and [4, 5] are equal but opposite in sign. In other words, on the interval [3, 5], f(x) is symmetric and odd about x = 4, so

c) The integral over [5, 9] is the negative of the area of a rectangle with length 9 - 5 = 4 and height 5, so

Then by linearity, we have

Answer:
468
Step-by-step explanation:
Y = x - 9 meets the y-axis at (0,-9)
y = -2x - 3 meets the y-axis at (0,-3)
This is because for every linear equation, there is a formula corresponding to it as y=mx + c, where (0,c) is where it meets the y-axis. As we assign the value of 0 to x, only c will be left to equal y, being the intercept.
Answer:

Step-by-step explanation:
#We use the base diagonal and the height diagonal to calculate the beam's height:

#The volume of the beam can then be calculated as:

Hence, the beam's volume is 