The sum of two numbers is 32. The larger is 3 less than 6 times the smaller. What is the larger number?

Mathematics

1 answer:

Mama L [17]3 years ago

5 0

Answer:

Step-by-step explanation:

32=3x-4+x

32=4x-4

+4 +4

36=4x

/4 /4

9=x

Larger #= 3x-4

Larger #= 3(9)-4

Larger #= 27-4

larger #= 23

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Simplify x = cos[2 arcsin(3/5)].<br><br> -7/25<br> 7/25<br> 4/5

Marina CMI [18]

Answer:

7/25

Step-by-step explanation:

Let $\theta= \arcsin(\frac{3}{5})$ so we have $x=\cos(2\theta)$

As $\cos(2\theta)=\cos^2\theta-\sin^2\theta$ , we'll have $\cos[2\arcsin(\frac{3}{5})]=\bigr[\cos(\arcsin(\frac{3}{5}))\bigr]^2-\bigr[(\sin(\arcsin(\frac{3}{5}))\bigr]^2$

To determine $\cos(\arcsin(\frac{3}{5}))$ , construct a right triangle with an opposite side of 3 and a hypotenuse of 5. This is because since $\theta=\arcsin(\frac{3}{5})$ , then $\sin\theta=\frac{3}{5}=\frac{\text{Opposite}}{\text{Hypotenuse}}$ . If you recognize the Pythagorean Triple 3-4-5, you can figure out that the adjacent side is 4, and thus, $\cos\theta=\frac{4}{5}=\frac{\text{Adjacent}}{\text{Hypotenuse}}$ . This means that $\cos(\arcsin(\frac{3}{5}))=\frac{4}{5}$ .