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3 years ago

Evaluate the expression for the given values. (5 x - 4 y) 2 given x = 1 and y = -1.

Mathematics

1 answer:

Reika [66]3 years ago

3 0

$((5 \times 1) - (4 \times - 1) = \\ 5 - ( - 4) = \\ 5 + 4 = \\ 9$

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<img src="https://tex.z-dn.net/?f=cos%20%5B%20arctan%28%5Cfrac%7B12%7D%7B5%7D%29%20-%20arcsin%20%28%5Cfrac%7B-3%7D%7B5%7D%29%5D"

qwelly [4]

Answer: -16/65

Step-by-step explanation:

Drawing the right triangle (as attached) gives us that $\arctan \left(\frac{12}{5} \right)=\arcsin \left(\frac{12}{13} \right)$

Also, $-\arcsin \left(-\frac{3}{5} \right)=\arcsin \left(\frac{3}{5} \right)$

This means our original expression is equal to:

$\cos \left[\arcsin \left(\frac{12}{13} \right)+\arcsin \left(\frac{3}{5} \right) \right]$

Using the cosine addition formula, which states $\cos(a+b)=\cos a \cos b-\sin a \sin b$ , we get this itself is equal to:

$\cos \left(\arcsin \left(\frac{12}{13} \right) \right)\cos \left(\arcsin \left(\frac{3}{5} \right)\right)-\sin \left(\arcsin \left(\frac{12}{13} \right) \right)\sin \left(\arcsin \left(\frac{3}{5} \right)\right)$

Since $\sin^{2} \theta+\cos^{2} \theta=1$ , we know that:

$\sin^{2} \left(\arcsin \left(\frac{12}{13} \right)\right)+\cos^{2} \left(\arcsin \left(\frac{12}{13} \right)\right)=1\\\\\frac{144}{169} +\cos^{2} \left(\arcsin \left(\frac{12}{13} \right)\right)=1\\\\cos^{2} \left(\arcsin \left(\frac{12}{13} \right)\right)=\frac{25}{169}\\\\cos \left(\arcsin \left(\frac{12}{13} \right)\right)=\frac{5}{13}$

Similarly, cos(arcsin(3/5))=4/5.

This means the given expression is equal to:

$\left(\frac{5}{13} \right) \left(\frac{4}{5} \right)-\left(\frac{12}{13} \right) \left(\frac{3}{5} \right)\\\\\frac{20}{65}-\frac{36}{65}=\boxed{-\frac{16}{65}}$

3 0

2 years ago

PLEASE HELP ME!!!! In each diagram AB is tangent to C at B. Find the value of x.

klio [65]

Answer is 9

Step by step explanation
As CB is radius CB=3, CA=3+7=10
X^2=(7+3)^2-3^2=100-9=81
X=9

3 0

3 years ago

A.perform the indicated operation. 1.(6x-4)+(-2x+2) Solution and answer:

Anestetic [448]

Answer:

4x - 2

Step-by-step explanation:

(2(3x-2))+(-2(x-1))

2(3x-2)-2(x-1)

2(3x-2-(x-1))

2(3x-2-x+1)

2(2x-1)

4x-2

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4 years ago

A 30 inch tv has a screen that is 18 inches high. how wide is the screen

Bond [772]

Well from my calculations I got 24 inches.

8 0

3 years ago

Y=12x=25 help please

Harlamova29_29 [7]

Answer:

Simplifying

y = 12x + 25

Reorder the terms:

y = 25 + 12x

Solving

y = 25 + 12x

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Simplifying

y = 25 + 12x

Step-by-step explanation:

I tried

6 0

3 years ago