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3 years ago

Rewrite the expression as an algebraic expression in x. tan(sin−1(x))

1 answer:

7 0

Let $tan^{-1} x=\alpha$
Then it can be shown by using a right-angled triangle and the rule of Pythagoras that $\alpha= tan^{-1} \frac{x}{ \sqrt{1-x^{2}} }$
Therefore
$tan(sin ^{-1} (x))=\frac{x}{ \sqrt{1-x^{2}} }$

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Jack is in a helicopter and looking down at two friends’ homes. The angle of depression to the first home is 72°. The angle of d

alexandr402 [8]

The distance between the helicopter and the first home is 369. 87 m

<h3>How to solve the distance using the angle of depression?</h3>

The distance between the helicopter and the first home can be found using sine law,

Hence,

180 - 72 - 49 = 59 degrees.

Therefore,

420 / sin 59 = A / sin 49°

where

A = distance form the first home to the helicopter.

cross multiply

420 sin 49 = A sin 59°

A = 420 sin 49 / sin 59

A = 316.978023694 / 0.8571673007

A = 369.869339199

A = 369. 87 m

Therefore, the distance between the helicopter and the first home is 369. 87 m

learn more on angle of depression here: brainly.com/question/1976859

#SPJ1

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2 years ago

F:[1/2,infinity)—>[3/4,infinity) <br> f(x)=x^2-x+1 <br> find the inverse of f(x);please explain

dexar [7]

Answer:

$f^{-1}(x)=\frac{1}{2}+\sqrt{x-\frac{3}{4}}$

Step-by-step explanation:

y=x^2-x+1

We want to solve for x.

I'm going to use completing the square.

Subtract 1 on both sides:

y-1=x^2-x

Add (-1/2)^2 on both sides:

y-1+(-1/2)^2=x^2-x+(-1/2)^2

This allows me to write the right hand side as a square.

y-1+1/4=(x-1/2)^2

y-3/4=(x-1/2)^2

Now remember we are solving for x so now we square root both sides:

$\pm \sqrt{y-3/4}=x-1/2$

The problem said the domain was 1/2 to infinity and the range was 3/4 to infinity.

This is only the right side of the parabola because of the domain restriction. We want x-1/2 to be positive.

That is we want:

$\sqrt{y-3/4}=x-1/2$

Add 1/2 on both sides:

$1/2+\sqrt{y-3/4}=x$

The last step is to switch x and y:

$1/2+\sqrt{x-3/4}=y$

$y=1/2+\sqrt{x-3/4}$

$f^{-1}(x)=1/2+\sqrt{x-3/4}$

8 0

2 years ago

What is the value of A when we rewrite 1.44^1.2x as A^x

Lina20 [59]

Answer:

a = 0.64

Step-by-step explanation:

hope that helped

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2 years ago

Can some show the work for this problem.

Nostrana [21]

What problem is there to show work for?

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2 years ago

Please help me with this.<br>Evaluate 8r - rs when r=6 and s=5

kondaur [170]

The answer of the equation is 18.

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2 years ago

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