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$\frac{20b}{{\left(4b^3\right)}^3}$

1. A body falls from rest against resistance proportional to the square root of the speed at any instant. If the body attains speed V1 and V2 feet per second, after 1 and 2 seconds in motion, respectively, find an expression for the limiting velocity.

Probability of geometric mean being higher than 1/6
If we choose 2 numbers from [0,2], independent from each other,what is the probability of their geometric mean being higher than 1/6?

Find the number of element in the power set of the set {x,(y,z)}

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$2+\cos <!--\; \; -->(2x)=3\cos <!--\; \; -->(x)$
Find all values of X in the interval $[0,2\mathrm{\pi <!--\; \pi \; -->}]$ that satisfythe equation

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For each of the following differential equations, determine the general or particular solution: ${\displaystyle 2x{y}^{\prime }+y=y^2\log x}$

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Refer to Given in Number 18. What is the probability, that a randomly selected student did not participate in any club?

10. What is the axis of symmetry for the parabola:
$y=-<!--\; -\; -->2(x-<!--\; -\; -->3)(x-<!--\; -\; -->7)$
A) x=-2
B) x=-3
C) x=3
D) x=5
11. Find the equation of a parabola in vertex form that passes through the point (7, 11) with vertex (5,-1)
(A) $y=3(x-<!--\; -\; -->5{)}^2-<!--\; -\; -->1$
(B) $y=\frac{1}{12}(x+5{)}^2-<!--\; -\; -->1$
(C) $y=-<!--\; -\; -->3(x-<!--\; -\; -->7{)}^2+11$
(D) $y=\frac{1}{12}(x+7{)}^2+11$

How does $7\log <!--\; \; -->(8x)=7\ln <!--\; \; -->8x$
I was working on some math homework with a program called scientific notebook. I was check that
I was writing something correctly.
The original equation is $(\log <!--\; \; -->(x^4)+\log <!--\; \; -->(x^5))/\log <!--\; \; -->(8x)=7$
I then converted it to $\log <!--\; \; -->(x^{(4+5)})=7\log <!--\; \; -->(8x)$
I was expecting to get $\log <!--\; \; -->((8x{)}^7)$ when I entered the $7\log <!--\; \; -->(8x)$ into the program to evaluate. Can someone please explain this to me?

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If ${\displaystyle \frac{{\cos }^4\alpha }{x}+\frac{{\sin }^4\alpha }{y}=\frac{1}{x+y}}$, prove that ${\displaystyle \frac{dy}{dx}={\tan }^2\alpha }$

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