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2 years ago

What is 0.7 written as a fraction?

Mathematics

2 answers:

alexgriva [62]2 years ago

7 0

7/10 is the fraction for 0.7

Elis [28]2 years ago

3 0

The decimal 0.7 written as a fraction is 7/10

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If sinA=√3-1/2√2,then prove that cos2A=√3/2 prove that

Ivan

Answer:

$\boxed{\sf cos2A =\dfrac{\sqrt3}{2}}$

Step-by-step explanation:

Here we are given that the value of sinA is √3-1/2√2 , and we need to prove that the value of cos2A is √3/2 .

Given :-

• $\sf\implies sinA =\dfrac{\sqrt3-1}{2\sqrt2}$

To Prove :-

• $\sf\implies cos2A =\dfrac{\sqrt3}{2}$

Proof :-

We know that ,

$\sf\implies cos2A = 1 - 2sin^2A$

Therefore , here substituting the value of sinA , we have ,

$\sf\implies cos2A = 1 - 2\bigg( \dfrac{\sqrt3-1}{2\sqrt2}\bigg)^2$

Simplify the whole square ,

$\sf\implies cos2A = 1 -2\times \dfrac{ 3 +1-2\sqrt3}{8}$

Add the numbers in numerator ,

$\sf\implies cos2A = 1-2\times \dfrac{4-2\sqrt3}{8}$

Multiply it by 2 ,

$\sf\implies cos2A = 1 - \dfrac{ 4-2\sqrt3}{4}$

Take out 2 common from the numerator ,

$\sf\implies cos2A = 1-\dfrac{2(2-\sqrt3)}{4}$

Simplify ,

$\sf\implies cos2A = 1 -\dfrac{ 2-\sqrt3}{2}$

Subtract the numbers ,

$\sf\implies cos2A = \dfrac{ 2-2+\sqrt3}{2}$

Simplify,

$\sf\implies \boxed{\pink{\sf cos2A =\dfrac{\sqrt3}{2}} }$

Hence Proved !

8 0

3 years ago

1 Point The circle below is centered at (-3, 2) and has a radius of 3. What is its equation?

arlik [135]

Answer:

(x + 3)^2 + (y - 2)^2 = 9

Step-by-step explanation:

Equation for a circle: (x – h)^2 + (y – k)^2 = r^2

Step 1: Determine what h, k, and r are

h is the x value of the point: -3

k is the y value of the point: 2

r is the radius of the circle: 3

Step 2: Plug in and solve

(x – h)^2 + (y – k)^2 = r^2

(x – (-3))^2 + (y – (2))^2 = (3)^2

(x + 3)^2 + (y - 2)^2 = 9

Answer: (x + 3)^2 + (y - 2)^2 = 9

8 0

3 years ago

Part B The mass of an average grain of rock salt is about 40 times the mass of an average grain of table salt. If you multiply t

yawa3891 [41]

Answer:

0.012

Step-by-step explanation:

We know the standard notation of table salt is 0.003, so we simply multiply 40 by this.

answer - 0.0003 X 40 = 0.012

3 0

1 year ago

Emily reads a story book. o the first day, she reads 1/9 of the whole book, and on the second day, she reads 24 pages. The ratio

Marina86 [1]

There are 270 pages in this book.

Given that,

Emily reads a storybook the first day,

She reads 1/9 of the whole book, and on the second day, she reads 24 pages.

The ratio of the number of pages read to the remaining pages in the two days is 1:4.

We have to find

How many pages are there in this book?

According to the question,

Let, P is the number of pages,

The first day Emily reads p/9 pages of the whole book,

And the second day she read 24 pages.

The ratio of the number of pages read to the remaining pages in the two days = 1;4 = p/5.

Therefore,

The number of pages reads first day + the number of pages read the second day = The ratio of the number of pages read to the remaining pages in the two days

$\rm \dfrac{p}{9} + 24 = \dfrac{p}{5}\\\\ \dfrac{p}{5} - \dfrac{p}{9} = 24\\\\\dfrac{p \times 9 - p\times 5}{45} = 24\\\\ \dfrac{9p-5p}{45} = 24\\\\\dfrac{4p}{45} = 24\\\\4p = 24\times 45\\\\4p = 1080\\\\p = \dfrac{1080}{4}\\\\p = 270 \ pages$