Answer:
Step-by-step explanation:
First of all, let's draw the two curves. First one (red) is a classic parabola, second (blue) is a similar curve with a tigher form. Imagine is made with paint so it's not high quality. The intersection between the two curves are easily found by solving a system of equations and are (0;0) and (1;1). At this point, the volume comes from the rotation of the shaded area, and can be obtained as difference from the rotation of the blue curve minus the red curve.
Remembering that the volume of the solid of revolution bound between 
is given by ![\pi \int_a^b [f(x)]^2dx](https://tex.z-dn.net/?f=%5Cpi%20%5Cint_a%5Eb%20%5Bf%28x%29%5D%5E2dx)
, in our case the volume is given by the expression
![\pi [\int_0^1 (\sqrt[4]{x})^2-(x^2)^2 dx] = \pi[\int_0^1 \sqrt{x}-x^4 dx] = \pi[\frac23x^\frac32 -\frac15 x^5 ] _0^1 = \pi (\frac23 -\frac15) = \frac7{15}\pi](https://tex.z-dn.net/?f=%5Cpi%20%5B%5Cint_0%5E1%20%28%5Csqrt%5B4%5D%7Bx%7D%29%5E2-%28x%5E2%29%5E2%20dx%5D%20%3D%20%5Cpi%5B%5Cint_0%5E1%20%5Csqrt%7Bx%7D-x%5E4%20dx%5D%20%20%3D%20%5Cpi%5B%5Cfrac23x%5E%5Cfrac32%20-%5Cfrac15%20x%5E5%20%5D%20_0%5E1%20%3D%20%5Cpi%20%28%5Cfrac23%20-%5Cfrac15%29%20%3D%20%5Cfrac7%7B15%7D%5Cpi)
Seven hundred and thirteen thousand, two hundred and ninety eight
9. Area of a triangle is proportional to height. If the height increases by a factor of 4, then ...
The area will increase by a factor of 4. . . . . (2nd selection)
10. The base lengths and height are needed:
• 5 mm
• 8 mm
• 10 mm
Well, you have to be given an interval. That is not an interval.
You should be given something like
If you add those fractions up you'll just get a point on the number line.
Find the LCD for all of them which is 9/6 - 4/6 + 3/6 = 8/6 = 2/3
You'll end up with a point on 2/3
