Question

Question #1)

Answer 1

Answer with explanation:

1.

The Identity Wrote by Jeremy

   $\sqrt{9}=9^{\frac{1}{2}}$

To prove this identity , his work is as follows

 $\sqrt{9}=3\\\\=3^1\\\\=3^{ \frac{1}{2}+\frac{1}{2}}\\\\=3^{ \frac{1}{2}} \times 3^{ \frac{1}{2}}\\\\=(3\times 3)^{ \frac{1}{2}}\\\\=9^{ \frac{1}{2}}$

Used the following law of indices

$1.\rightarrow x^{a+b}=x^a\times x^b\\\\2.\rightarrow x^a \times y^a=(x y)^a$

Option C

    $\rightarrow 3^{ \frac{1}{2}} \times 3^{ \frac{1}{2}}= (3\times 3)^{ \frac{1}{2}}$

2.

Height of stick after x seconds is given by

   f(x)=625 -16 x²

Replacing , f(x) by , y in the above equation

 y= 625 -16 x²

16 x²= - (y-625)

→when x=0, y=625

Coordinates of vertex = (0, 625)

⇒Maximum of the function is given by , when time , x=0,

Maximum height = 625

Following are  the correct interpretations of the coordinates of the point at the maximum of the function f(x).

B: The time when the stick is at its highest point.

C: The height of the stick when it is dropped from Miami Tower.

E: The distance of the stick from Miami Tower when it hits the ground.

Answer 2

1. From Jeremy's work:
√9
=3^(1/2)×3^(1/2)
multiplying number with the same powers is the same as multiplying the number first then raising it to the power.
=(3×3)^(1/2)
from above we conclude that the answer is:
C: 3^1/2 x 3^1/2= (3x3)^1/2

2. Given that the height of the stick at time t seconds after it was dropped is given by the function:
f(x)=625-16x²
At the maximum point f'(x)=0
thus
f'(x)=-32x=0
thus at maximum point x=0, y=625. The coordinates is (0,625), this represents the distance of the stick from Miami Tower when it hits the ground.

Answer: E