Math questions

[smeag]

Cindy deposits 17,850 into an account that pays 6.55 % interest, compounded quarterly. How long will she have to wait for he money to double?

Find the exact value of cot x if cos x = 8/17

a plane left crosbyton and flew 300 miles at a bearing of 52 and landed in paden. from paden, the plane flew 500 miles at a bearing of 106 and landed in hissop. how far is crosbyton from hissop?

if cos x = -4/5 and pi<x<3pi/2, then tan2x =
(everywhere I used x is theta)

simplify the expression: (tan(pi/2 - x))/ cosx

if sin x = -3/5 and cos y = -8/17, with x and y both in quadrantIII, find the value of cos(x + y)

if U = <-3,-6> and V= <2,4>, then 3U + 4V =

Thx for helping

[nsguy1350]

Interest is of the form [unparseable or potentially dangerous latex formula], where A is the money, P is the initial money, r is the interest, in decimal non-percent form, t is the time (in years), and q is the amount of times per year.

A = P if t = 0, always. Therefore, always set P to the initial value. When the money doubles, you get A = 2P, and dividing by P on both sides, you get [unparseable or potentially dangerous latex formula]. Taking the natural logarithm of both sides and bringing down the 4t, [unparseable or potentially dangerous latex formula]. Solve for t. I don't feel like getting my calculator, so I'll leave that up to you :D

If cos x = 8/17, then sin x either equals -15/17 or 15/17, depending on the Quadrant (I or IV). Set up a triangle on a coordinate system to see this. I can't tell you the exact value because I don't know if it should be positive or negative. Does it specify?

If crosbyton is the origin, bishop has coordinates [unparseable or potentially dangerous latex formula]. You can see this with trigonometry. The catch is to see the word "bearing", which means add 90 degrees. That's how pilots talk (or maybe something besides pilots, I don't really know.)

I don't know what you mean in that statement about theta. Anyways, cos x = -4/5. Because of the domain restriction, sin has to be negative, so -4/5. [unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula].
Therefore, [unparseable or potentially dangerous latex formula].

[unparseable or potentially dangerous latex formula].
[unparseable or potentially dangerous latex formula]. I'm guessing that's your final answer.

[unparseable or potentially dangerous latex formula]. Remembering the quadrant, you should be able to work from there.

k<x,y> = <kx,ky>. Distribute the coefficient.
3U + 4V = 3<-3,-6> + 4<2,4> = <-9,-18> + <8,16> = <-1,-2>.

If anything I said is wrong or isn't on the answer key, I probably made a mental mistake or a typo. Tell me if you catch something.

[smeag]

[nsguy1350]

Could you clarify? I still am not understanding what you mean. The picture is the LaTeX I typed about the tan(2x) problem, which is the problem in question, but I don't see how sin^2 or cos^2 relates.