Answer:
y = -
Step-by-step explanation:
Given
The denominator of the expression cannot be zero as this would make it undefined. Equating the denominator to zero and solving gives the value that y cannot be, that is
4y + 2 = 0 ( subtract 2 from both sides )
4y = - 2 ( divide both sides by 4 )
y = = -
← excluded value
Answer:
V = 2000r³/3
Step-by-step explanation:
We know that the base is a circular disk, so it creates a circle on the xy plane. It would be in the form x² + y² = r². In other words x² + y² = (5r)². Let's isolate y in this equation now:
x² + y² = (5r)²,
x² + y² = 25r²,
y² = 25r² - x²,
y = √25r² - x² ---- (1)
Now remember that parallel cross sections perpendicular to the base are squares. Therefore Area = length^2. The length will then be = 2√25r² - x² --- (2). Now we can evaluate the integral from -5r to 5r, of [ 2√25r² - x² ]² dx.
As you can see, your exact solution would be, V = 2000r³/3. Hope that helps!