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2 years ago

What's 86/8 in a mixed number

Mathematics

1 answer:

dsp732 years ago

3 0

Answer:

10 6/8 or 10 3/4

Step-by-step explanation:

Calculate out how many times the denominator goes into the numerator. To do that, divide 86 by 8 and keep only what is to the left of the decimal point:

86 / 8 = 10.7500 = 10

Multiply the answer from Step 1 by the denominator and deduct that from the original numerator.

86 - (8 x 10) = 6

Keep the original denominator and use the answers from Step 1 and Step 2 to get this:

10 6/8

Minimize the fraction part from Step 3 by dividing the numerator and denominator by 2, which is the greatest common factor, to get the final answer. 86/8 as a Mixed Number is:

10 3/4

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<h3>Answer: Choice B $\frac{\sqrt{15}}{4}$ </h3>

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Work Shown:

Angle theta is between 0 and pi/2, so this angle is in quadrant Q1.

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$\sin \theta = \frac{1}{4}\\\\\sin^2 \theta = \left(\frac{1}{4}\right)^2\\\\\sin^2 \theta = \frac{1}{16}$

Then use the pythagorean trig identity to get

$\sin^2 \theta + \cos^2 \theta = 1\\\\\cos^2 \theta = 1-\sin^2 \theta\\\\\cos \theta = \sqrt{1-\sin^2 \theta} \ \ \ \text{cosine is positive in Q1}\\\\\cos \theta = \sqrt{1-\frac{1}{16}}\\\\\cos \theta = \sqrt{\frac{16}{16}-\frac{1}{16}}\\\\\cos \theta = \sqrt{\frac{16-1}{16}}\\\\\cos \theta = \sqrt{\frac{15}{16}}\\\\\cos \theta = \frac{\sqrt{15}}{\sqrt{16}}\\\\\cos \theta = \frac{\sqrt{15}}{4}\\\\$

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