All categories

2 years ago

Convert 8.132132132 ... to a rational expression in the form of a over b , where b ≠ 0.

Mathematics

1 answer:

bezimeni [28]2 years ago

5 0

Let x = 8.132132132...

Then 1000x = 8132.132132132...

Subtract x from 1000x to eliminate the fractional part:

1000x - x = 8132.132132132... - 8.132132132...

999x = 8132 - 8 = 8124

x = 8124/999 = 2708/333

You might be interested in

What is the value of x in the equation x – y = 30, when y = 15?

vovikov84 [41]

X should be 45
45-15=30

6 0

3 years ago

Read 2 more answers

Convert the Cartesian equation (x 2 + y 2)2 = 4(x 2 - y 2) to a polar equation.

SashulF [63]

ANSWER

${r}^{2} = 4 \cos2\theta$

EXPLANATION

The Cartesian equation is

${( {x}^{2} + {y}^{2} )}^{2} = 4( {x}^{2} - {y}^{2} )$

We substitute

$x = r \cos( \theta)$

$y = r \sin( \theta)$

and

${x}^{2} + {y}^{2} = {r}^{2}$

This implies that

${( {r}^{2} )}^{2} = 4(( { r \cos\theta) }^{2} - {(r \sin\theta) }^{2} )$

Let us evaluate the exponents to get:

${r}^{4} = 4({ {r}^{2} \cos^{2}\theta } - {r}^{2} \sin^{2}\theta)$

Factor the RHS to get:

${r}^{4} = 4{r}^{2} ({ \cos^{2}\theta } - \sin^{2}\theta)$

Divide through by r²

${r}^{2} = 4 ({ \cos^{2}\theta } - \sin^{2}\theta)$

Apply the double angle identity

$\cos^{2}\theta -\sin^{2}\theta= \cos(2 \theta)$

The polar equation then becomes:

${r}^{2} = 4 \cos2\theta$

7 0

3 years ago

I need help on this can some one explain it and answer please!!!!

Alex_Xolod [135]

Answer:

4(a). C= 3 + 1.5x

b. 'x' stands for the number of times the cup is refilled.

c. 3 + 1.5 (5)= $10.50

d. My answer to part (c) makes sense because the price of the cup is $3, and I have to pay $1.50 for each additional refill, in accordance to the formula I wrote.

Step-by-step explanation:

The original price of the cup is 3 dollars, but with each refill you get, you have to pay $1.50.

6 0

1 year ago

THIS IS WORTH 74 points

Debora [2.8K]

Answer:

Your answer is 163⁄200Step-by-step explanation:

7 0

2 years ago

You are working at a clothing store where your weekly

Leviafan [203]

Answer:

n=900

Step-by-step explanation:

the equation is:

197=125+0.08n

72=0.08n

n=900

8 0

2 years ago