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babymother [125]
2 years ago
9

Can someone give me the steps to solving this?

Mathematics
1 answer:
DerKrebs [107]2 years ago
4 0

Answer:

\tan \theta  = \dfrac{8}{15}

Step by step explanation:

\text{Given that,}\\\\~~~~~~~\sin \theta = \dfrac{8}{17}\\\\\implies \sin^2 \theta = \dfrac{64}{289}\\\\\implies 1-\cos^2 \theta = \dfrac{64}{289}\\\\\implies \cos^2 \theta = 1-\dfrac{64}{289}\\\\\implies \cos^2 \theta = \dfrac{225}{289}\\\\\implies \cos \theta =\pm\sqrt{\dfrac{225}{289}}\\\\\implies \cos \theta = \pm\dfrac{15}{17}

\text{In quadrant I, all ratios are positive, so,}~ \cos \theta = \dfrac{15}{17}\\\\\text{Now,}\\\\\tan \theta  = \dfrac{\sin \theta }{\cos \theta}\\\\\\~~~~~~~~=\dfrac{\tfrac{8}{17}}{\tfrac{15}{17}}\\\\\\~~~~~~~~=\dfrac{8}{17} \times \dfrac{17}{15}\\\\\\~~~~~~~=\dfrac{8}{15}

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<h3>What would be the value of $150 after eight years if you earn 12 % interest per year? A. $371.39 B. $415.96 C. $465.88 </h3>

<em>The compound interest is applied, that is to say, each year the interest produced is accumulated to the outstanding capital and the interest of the next period is calculated on the new outstanding capital.</em>

The formula for calculating compound interest is:

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