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3 years ago

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At age 35 you start saving for retirement. If your investment plan pays an APR of 6% and you want to have $1.5 million when you

retire in 30 years, how much should you deposit monthly? Assume an ordinary annuity.

1 answer:

Alisiya [41]3 years ago

8 0

<span>I would suggest you deposit $1,493.26 monthly</span>

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I have to use trigonometric identities to solve. But I’m having trouble finding the values of cos A and sin B. Can anyone help m

katrin [286]

let's notice something, angles α and β are both in the I Quadrant, and on the first quadrant the x-coordinate/cosine and y-coordinate/sine are both positive.

$\bf \textit{Sum and Difference Identities} \\\\ cos(\alpha - \beta)= cos(\alpha)cos(\beta) + sin(\alpha)sin(\beta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin(\alpha)=\cfrac{\stackrel{opposite}{15}}{\stackrel{hypotenuse}{17}}\impliedby \textit{let's find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}$

$\bf \pm\sqrt{17^2-15^2}=a\implies \pm\sqrt{64}=a\implies \pm 8 = a\implies \stackrel{I~Quadrant}{\boxed{+8=a}} \\\\[-0.35em] ~\dotfill\\\\ cos(\beta)=\cfrac{\stackrel{adjacent}{3}}{\stackrel{hypotenuse}{5}}\impliedby \textit{let's find the \underline{opposite side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}$

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$\bf cos(\alpha - \beta)=\stackrel{cos(\alpha)}{\left( \cfrac{8}{17} \right)}\stackrel{cos(\beta)}{\left( \cfrac{3}{5} \right)}+\stackrel{sin(\alpha)}{\left( \cfrac{15}{17} \right)}\stackrel{sin(\beta)}{\left( \cfrac{4}{5} \right)}\implies cos(\alpha - \beta)=\cfrac{24}{85}+\cfrac{60}{85} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill cos(\alpha - \beta)=\cfrac{84}{85}~\hfill$

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3 years ago

A player shoots a basketball from a height of 6 feet. The equation, h = -16t 2 + 25t + 6, gives the height, h , of the basketbal

spin [16.1K]

175t because the motion times the width gives you 175t

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3 years ago

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The following two right triangles are similar.If side PQ = 42, side LM = 28, and side QR = 24, what is the length of side MN?

Phantasy [73]

Answer:

a. 16

Step-by-step explanation:

Find the scale:

42 ÷ 28 = 1.5

Use this scale for QR to find MN:

24 ÷ 1.5 = 16

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2 years ago

It's the computer seice can u help me

Dmitrij [34]

Answer:

I can help you, just tell me what it is.

Step-by-step explanation:

Step 1: Tell me the problem

Step 2: Wait for a response.

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2 years ago

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8. Solve x/10 = –7. A. x = –0.7 B. x= –17 C. x = –70 D. x = 3

ANEK [815]

For this problem, I believe you would just have to plug in for x.

For example, -17 divided by 10 and so on.

The answer should be C, -70. -70 divided by 10 equals -7.

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3 years ago