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)
The given fraction is:
We cannot take anything common from the numerator but from the denominator we can take out 2 as common because 2 is a factor of both the terms i.e. 2y and 10.
2y + 10 can be written as 2y +2(5) which can further be written as 2(y+5)
So, our fraction now becomes:
y+5 occurs in both the numerator and denominator and thus be cancelled out leaving behind:
Therefore, the given fraction in lowest term is equal to 1/2. So option B is the correct answer
Answer:
Step-by-step explanation:
Part 1:y=426x+4298
y=223x+6129
Part 2: x=9.020 (x is the number of months and y is the miles)
Part 3: y=8140.394, or 8,140 since it's rounding to the nearest mile
The increase is D: 50% because the 1 in the parentheses stands for the 20 that was already there, with the .5 being the amount that’s actually being increased. 0.5 translates to 50%, so the answer is D.
Answer:
4
Step-by-step explanation:
