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2 years ago

How to solve this question

Mathematics

1 answer:

erica [24]2 years ago

3 0

Multiplication property; distribution property of an exponent. Multiply exponents together, then distribute the ¨( )¨

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Find sin2x, cos2x, and tan2x if sinx=-15/17 and x terminates in quadrant III

vodka [1.7K]

Given:

$\sin x=-\dfrac{15}{17}$

x lies in the III quadrant.

To find:

The values of $\sin 2x, \cos 2x, \tan 2x$ .

Solution:

It is given that x lies in the III quadrant. It means only tan and cot are positive and others are negative.

We know that,

$\sin^2 x+\cos^2 x=1$

$(-\dfrac{15}{17})^2+\cos^2 x=1$

$\cos^2 x=1-\dfrac{225}{289}$

$\cos x=\pm\sqrt{\dfrac{289-225}{289}}$

x lies in the III quadrant. So,

$\cos x=-\sqrt{\dfrac{64}{289}}$

$\cos x=-\dfrac{8}{17}$

Now,

$\sin 2x=2\sin x\cos x$

$\sin 2x=2\times (-\dfrac{15}{17})\times (-\dfrac{8}{17})$

$\sin 2x=-\dfrac{240}{289}$

And,

$\cos 2x=1-2\sin^2x$

$\cos 2x=1-2(-\dfrac{15}{17})^2$

$\cos 2x=1-2(\dfrac{225}{289})$

$\cos 2x=\dfrac{289-450}{289}$

$\cos 2x=-\dfrac{161}{289}$

We know that,

$\tan 2x=\dfrac{\sin 2x}{\cos 2x}$

$\tan 2x=\dfrac{-\dfrac{240}{289}}{-\dfrac{161}{289}}$

$\tan 2x=\dfrac{240}{161}$

Therefore, the required values are $\sin 2x=-\dfrac{240}{289},\cos 2x=-\dfrac{161}{289},\tan 2x=\dfrac{240}{161}$ .

7 0

2 years ago

What is 28:36 in simplest form

xeze [42]

It would be 7:9 because if you divide each side by 4 then you can get it in simplest form

6 0

3 years ago

Read 2 more answers

Fill in the blank _+8=+6 And chose the property of addition you send

Paha777 [63]

Answer:

-2

Step-by-step explanation:

Just use 6-8 and you will get - 2

Check again with - 2+8 you will get positive 6

4 0

2 years ago

5x + 3 - 2x = 12 + 7x - 2 solution ??? SOMEONE HELPPP PLEASE !!

tensa zangetsu [6.8K]

Answer:

x = -7/4

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtract Property of Equality

Algebra I

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

5x + 3 - 2x = 12 + 7x - 2

Step 2: Solve for x

Combine like terms: 3x + 3 = 7x + 10
[SPE] Subtract 3x on both sides: 3 = 4x + 10
[SPE] Subtract 10 on both sides: -7 = 4x
[DPE] Divide 4 on both sides: -7/4 = x
Rewrite: x = -7/4

Step 3: Check

Plug in x into the original equation to verify it's a solution.

Substitute in x: 5(-7/4) + 3 - 2(-7/4) = 12 + 7(-7/4) - 2
Multiply: -35/4 + 3 + 7/2 = 12 - 49/4 - 2
Add: -23/4 + 7/2 = 12 - 49/4 - 2
Add: -9/4 = 12 - 49/4 - 2
Subtract: -9/4 = -1/4 - 2
Subtract: -9/4 = -9/4

Here we see that -9/4 does indeed equal -9/4.

∴ x = -7/4 is the solution to the equation.

8 0

2 years ago

Write an arithmetic expression that calculates the average of 18 and 46. you may already know that: the average of two numbers i

Masteriza [31]

In this question , we have to write an arithmetic expression that calculates the average of 18 and 46.

TO find the average, we have to add the numbers and divide by 2.

So here we have to add 18 and 46 and divide by 2, that is

$d = \frac{18+46}{2} = \frac{64}{2}$

And that's the required algebraic expression .

8 0

3 years ago