Find the simplified form of the expression. Given your answer in scientific notation (8 x 10^4)(9 x 10^8)

1 answer:

6 0

$(8 \times {10}^{4} )(9 \times {10}^{8} ) \\ = 8 \times 9 \times {10}^{4} \times {10}^{8 } \\ = 72 \times {10}^{4 + 8} \\ = 7.2 \times 10 \times {10}^{12} \\ = 7.2 \times {10}^{13}$

This is the answer with step by step explanation

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Find the volume of a regular hexahedron if one of the diagonals of its faces is 8 root 2 inches.

Naily [24]

The answer is 114sqrt{6} in³

A regular hexahedron is actually a cube.

Diagonal of a cube D is a hypotenuse of a right triangle which other two legs are face diagonal (f) and length of a side (a):
D² = f² + a²

Face diagonal is a hypotenuse of a right triangle which sides are a and a:
f² = a² + a² =2a²

D² = f² + a²
f² = 2a²

D² = 2a² + a² = 3a²
D = √3a² = √3 * √a² = √3 * a = a√3

Volume of a cube with side a is: V = a³
D = a√3
⇒ a = D/√3

V = a³ = (D/√3)³

We have:
D = 8√2 in

$V= (\frac{D}{ \sqrt{3} } )^{3} =( \frac{8 \sqrt{2} }{ \sqrt{3} } )^{3}=( \frac{8 \sqrt{2} * \sqrt{3} }{ \sqrt{3}* \sqrt{3}} )^{3} =( \frac{8 \sqrt{2*3} }{ \sqrt{3*3}} )^{3} =( \frac{8 \sqrt{6} }{ \sqrt{3^{2} }} )^{3} =( \frac{8 \sqrt{6} }{ 3} )^{3} = \\ \\ = \frac{ 8^{3} *( \sqrt{6} )^{3}}{3^{3}} = \frac{512* \sqrt{6 ^{2} }* \sqrt{6} }{27} = \frac{512*6* \sqrt{6} }{27} = 114sqrt{6}$

8 0

3 years ago

Which of the following numbers is not an integer? A -32 B 80 C 5.81 D 0 O<br>

larisa [96]

5.81

option C

hope it helps...!!!

3 0

2 years ago

Read 2 more answers

Which fraction is equal to 0.8? Express your answer in simplest form. A. 3/5 B. 4/5 C. 1/8 D. 5/8

Murrr4er [49]