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3 years ago

Find the product. Write your answer in exponential form. 5^7•5^-9•5^-5

Mathematics

1 answer:

MissTica3 years ago

4 0

5^7 = 5 × 5 × 5 × 5 × 5 × 5 × 5 = 78,125

5^-9 = 5 ÷ 5 ÷ 5 ÷ 5 ÷ 5 ÷ 5 ÷ 5 ÷ 5 ÷ 5 = 0.000000512

5^-5 = 5 ÷ 5 ÷ 5 ÷ 5 ÷ 5 = 0.00032

78,125 × 0.000000512 × 0.00032 = 0.0000128‬

Answer: 0.0000128‬ or 1.28 x 10^-5

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3 years ago

The area of triangle ABC is 3√2 square inches. Find the measure of the acute angle, A, if b = 9 meters and c = 2 meters.

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Step-by-step explanation:

Please find the attachment.

We have been given that area of triangle ABC is 3√2 square inches.

$\text{Area}=\frac{1}{2}\text{Base}\times \text{height}$

We know that area of triangle an be found using trigonometry as:

$\text{Area}=\frac{1}{2}\times c\times h$

$\text{sin}(A)=\frac{h}{9}\\h=9\cdot \text{sin}(A)$

$3\sqrt{2}=\frac{1}{2}\times 2\times 9\cdot \text{sin}(A)$

$3\sqrt{2}=9\cdot \text{sin}(A)$

$9\cdot \text{sin}(A)=3\sqrt{2}$

$\text{sin}(A)=\frac{3\sqrt{2}}{9}$

$\text{sin}(A)=\frac{\sqrt{2}}{3}$

Now, we will use inverse sine to find the value of angle A as:

$A=\text{sin}^{-1}(\frac{\sqrt{2}}{3})$

$A=28.1255057^{\circ}$

$A\approx 28^{\circ}$

Therefore, the measure of angle A is approximately 28 degrees.

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