3 years ago

Solve for x. Round to the nearest tenth, if necessary.

Mathematics

1 answer:

Illusion [34]3 years ago

7 0

Cos(o)= ads
CoS61X
5.5=* (Cos (60)
11.344
-
X= 5.5

COSC61)
The answer is in the picture

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The sum of 30 times (1/3)^(n-1) from 1 to infinity

sergeinik [125]

Let

$S_n=\displaystyle1+\frac13+\frac1{3^2}+\cdots+\frac1{3^n}$

Then

$\dfrac13S_n=\displaystyle\frac13+\frac1{3^2}+\frac1{3^3}+\cdots+\frac1{3^{n+1}}$

and

$S_n-\dfrac13S_n=\dfrac23S_n=1-\dfrac1{3^{n+1}}\implies S_n=\dfrac32-\dfrac1{2\cdot3^n}$

and as $n\to\infty$ , we end up with

$\displaystyle\lim_{n\to\infty}S_n=\lim_{n\to\infty}\sum_{i=1}^{n+1}\frac1{3^{i-1}}=\lim_{n\to\infty}\left(\frac32-\frac1{2\cdot3^n}\right)=\frac32$

So we have

$\displaystyle\sum_{n=1}^\infty30\left(\frac13\right)^{n-1}=30\cdot\frac32=45$

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3 years ago

You want to replace the countertops in the kitchen. one counter measures 24inches by 6 feet. the other is 30 inches by 4 feet.

V125BC [204]

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3 years ago

What percent of 2/3 is 1/6? HELP!!!!! :(

KiRa [710]

Answer:

Look at the pictures

Step-by-step explanation:

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3 years ago

Help please I'm lost

yarga [219]

36 1/2 to 37.

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those would be the ones I'd click

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3 years ago

Brian deposited $4000 into an account with 5.4% interest, compounded monthly. Assuming that no withdrawals are made, how much wi

Yanka [14]

The future value of the amount deposited will be given by:
FV=p(1+r/100n)^nt

where:
FV=future value
p=principle
r=rate
n=terms
t=time
thus substituting our values in the formula we get:
FV=4000(1+5.4/1200)^(6×12)
FV=$5,526.57

Answer: $5,526.57

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4 years ago