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2 years ago

5

If (8^2)p = 8^4, what is the value of p?

1 answer:

den301095 [7]2 years ago

3 0

The answer is 2.
Explantation:
First, we simplify it to 64^p = 4096.
Then, take the log of both sides:
p = log (4096) / log (64)
p = 2

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A box with no top is to be constructed from a piece of cardboard whose length measures 5 in. more than its width. The box is to

ddd [48]

Answer:

$9\text{ inch, }14\text{ inch, }2\text{ inch}$

Step-by-step explanation:

GIVEN: A box with no top is to be constructed from a piece of cardboard whose length measures $5\text{ inch}$ more than its width. The box is to be formed by cutting squares that measure $2\text{ inch}$ on each side from the four corners and then folding up the sides.

TO FIND: If the volume of the box will be $100\text{ inch}^3$ , what are the dimensions of the piece of cardboard.

SOLUTION:

Let the width of cardboard be $x$

length of cardboard $=x+5\text{ inch}$

As box is formed by cutting $2\text{ inch }$ squares from corners of cardboard

length of cardboard $=x+5-4=x+1\text{ inch}$

width of cardboard $=x-4\text{ inch}$

height of cardboard $=2\text{ inch}$

volume of cardboard $=\text{length}\times\text{width}\times\text{height}$

$=2(x+1)(x-4)$

$x^2-3x-54=0$

solving we get

$x=9,-6$

width of cardboard $=9\text{ inch}$

length of cardboard $=x+5=14\text{ inch}$

height of cardboard $=2\text{ inch}$

8 0

2 years ago

Please help me, im struggling

Molodets [167]

<u>Part 1</u>

<u /> $f(a)=4-7a+16a^2$

<u>Part 2</u>

<u /> $f(a+h)=4-7(a+h)+16(a+h)^2\\\\=4-7(a+h)+16(a^2 +2ah+h^2)\\\\=4-7a-7h+16a^2 +32ah+16h^2$

<u>Part 3</u>

<u /> $\frac{f(a+h)-f(a)}{h}=\frac{(4-7a-7h+16a^2 +32ah+16h^2-(4-7a+16a^2)}{h}\\\\=\frac{-7h+32ah+16h^2}{h}\\\\=32a+16h-7$

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1 year ago

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