SparklingWater2

A

t=-(16/2$\cdot$(-16))=$\boxed{\frac12}$

B

h(t)=-16(1/2)^2+16(1/2)+96=$\boxed{100}$

C

h=-16(0)^2+16(0)+96=$\boxed{96}$

(not sure about C, I'm kinda bad at functions)

1. The part cut off of the frustum will be 2/5 of the original cone, so the smaller cone is$\frac{2h\pi r^2}{15}$ of the original cone, so the smaller cone's height is $^3\sqrt{\frac25}$, so the height is $\boxed{\frac{^3\sqrt5-^3\sqrt2}{^3\sqrt5}}$ of the original cone.

we can use pythagorean theorum: 10^2-2^2=h^2=96

h=$\sqrt96$=$\boxed{4\sqrt6}$

$\boxed{f(x)=x^2+2}$

A=1000(1+0.0125/4)^(18x4)=~$\boxed{2446}$

Because CPQ=QDC=90 and PC=CD=2, we know that PQ=QD. and for the exact same reasons,PQ=QA, or QD=QA. if we mark a point E bisecting CD, we can find AD by pythagorean theorum in triangle BCE:$\sqrt{9-1}=\sqrt{8}=2\sqrt2$, and AD/2=AQ=QD=PQ, so we have

PQ=$\frac{2\sqrt2}2=\boxed{\sqrt2}$  

the area of the black shaded region is:$\pi+25\pi-9\pi=17\pi$

the area of the white shaded region is:$9\pi-\pi+49\pi-25\pi=32\pi$

therefore, the ratio of the black area to white area is $\boxed{\frac{17}{32}}$

the diameter of the circle will be the diagonal of the square, which is 12$\sqrt2$, and the area of the circle is $\pi$(d/2)$^2$=$K\pi$=72$\pi$, so therefore, the value of $K=\boxed{72}$

We can start by looking at the angles, and we see that each interior angle is 120$^\circ$. this means that  we can find so 30-60-90 triangles.

we can start by looking at the top half(notice we are cutting the hexagon from one of its diagonals), and if we draw two straight lines as heights, we can two 30-60-90 triangles on the side, and we get 1/2 as the base of the triangle. we can do the same for the other triagle, which also has a base of 1/2, and the length between these two triangles is 1, so 1/2+1/2+1=2, which is the length of one diagonal.

there are 6 diagonals in total, so 2 $\cdot$ 2 $\cdot$ 2 $\cdot$ 2$\cdot$ 2 $\cdot$ 2 = 2$^6$=$\boxed{64}$

the degree with an arc is marked (3x)$^\circ$, and we know that a striaght line consists of 180 degrees in total, so 180-82.5=3x+2x=97.5

5x = 97.5

x = 19.5

3x = 19.5 $\cdot$ 3 = $\boxed{58.5^\circ}$