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Tamiku [17]
3 years ago
11

How much money should be invested in an account that earns 8% interest compounded quarterly to yield $10,000 in 4 years? (Round

your answer to the nearest cent.)
Mathematics
1 answer:
sweet [91]3 years ago
4 0

Answer:

757,576cents

Step-by-step explanation:

Given

Amount = $10000

Time = 4years

Rate = 8%

n = 1/4 year (compounded quarterly

Using the formula to get the principal

A = P(1+r/n)^nt

10000 = P(1+0.08/0.25)^4(1/4)

10000 = P(1+0.32)

10000= 1.32P

P = 10000/1.32

P = 7575.76

Hence he suppose to invest $7575.76 which is equivalent to 7575.76×100 cents i.e 757,576cents

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Please help!! In radians, what is the period of the function y = .5cos5x
Levart [38]

Answer:

(2pi)/5

Step-by-step explanation:

The cosine function cos(x) has a period of 2*pi.

If we change the argument of the cosine, the new argument will have a period of 2*pi. If the new argument is 5x, we have that the period will be:

5x = 2*pi

x = 2*pi/5

The period of this function will be (2pi)/5, because for every (2pi)/5 change in the value of x, the function will have the same value. The value of 5 multiplying the cosine does not interfere in the period.

5 0
3 years ago
Verify the identity (tan x + 1)^2 + (tan x-1)^2= 2 sec^2 x
Elina [12.6K]

(\tan x+1)^2+(\tan x-1)^2=2\sec^2x\\\\\text{use}\ \tan x=\dfrac{\sin x}{\cos x}\\\\L_s=\left(\dfrac{\sin x}{\cos x}+\dfrac{\cos x}{\cos x}\right)^2+\left(\dfrac{\sin x}{\cos x}-\dfrac{\cos x}{\cos x}\right)^2\\\\=\left(\dfrac{\sin x+\cos x}{\cos x}\right)^2+\left(\dfrac{\sin x-\cos x}{\cos x}\right)^2\\\\=\dfrac{(\sin x+\cos x)^2}{\cos^2x}+\dfrac{(\sin x-\cos x)^2}{\cos^2x}\\\\\text{use}\ (a\pm b)^2=a^2\pm2ab+b^2

=\dfrac{\sin^2x+2\sin x\cos x+\cos^2}{\cos^2x}+\dfrac{\sin^2x-2\sin x\cos x+\cos^2}{\cos^2x}\\\\=\dfrac{\sin^2x+2\sin x\cos x+\cos^2+\sin^2x-2\sin x\cos x+\cos^2}{\cos^2x}\\\\=\dfrac{2\sin^2x+2\cos^2x}{\cos^2x}=\dfrac{2(\sin^2x+\cos^2x)}{\cos^2x}\\\\\text{use}\ \sin^2x+\cos^2x=1\\\\=\dfrac{2(1)}{\cos^2x}=2\cdot\dfrac{1}{\cos^2x}=2\left(\dfrac{1}{\cos x}\right)^2\\\\\text{use}\ \sec x=\dfrac{1}{\cos x}\\\\=2(\sec^2x)=2\sec^2x=R_s\\\\L_s=R_s\Rightarrow The\ identity

4 0
3 years ago
Mark has 312 books in his bookcases. He has 11 times as many fiction as nonfiction books. How many fiction books does Mark have?
larisa [96]
11x represents the fiction
X represents the nonfiction book

11x+x=312
12x=312
Divide both by 12
X=26

To find the fiction you have to do 11 times 26

11•26=286

To check the answer you add 286 and 26

If it adds up to 312 the answer is correct
6 0
3 years ago
What is 98/128 in simplest form
weeeeeb [17]
49/64 you divide the numerator and denominator by 2 hope this helped
6 0
3 years ago
Read 2 more answers
What is the correct answer..
solong [7]

Answer:

64 feet

Step-by-step explanation:

To find the height of the kite we use sin trigonometric ratio.

Let the height of the kite from the ground be x feet.

\therefore \: \sin 40 \degree =  \frac{x}{100}  \\  \\  \therefore \: 0.6427876097=  \frac{x}{100}  \\  \\ \therefore \: 0.6427876097 \times 100= x \\  \\  \therefore \:x = 64.29  \\  \\  \therefore \:x = 64 \: feet

3 0
3 years ago
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