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Advocard [28]
3 years ago
9

How do you solve tan(sin^-1 x/2)? (show steps)

Mathematics
1 answer:
andrew11 [14]3 years ago
4 0

First: Equations are solved. \tan\left(\sin^{-1}\dfrac x2\right) is an expression, and expressions can be simplified.

Now suppose y=\sin^{-1}\dfrac x2. Imagine a right triangle with one angle (not the one opposite the hypotenuse, of course) labeled y. This relation suggests that

\sin y=\dfrac x2

and under the hood, we're assuming that -\dfrac\pi2, because otherwise we wouldn't be able to properly alternate from x to y so seamlessly.

Now,

\tan\left(\sin^{-1}\dfrac x2\right)=\tan y

so the given expression is the same as the tangent of that same angle y.

If \sin y=\dfrac x2, then in the triangle, the leg opposite the angle y occurs with the length of the hypotenuse in a ratio of x to 2. By the Pythagorean theorem, the remaining side - call it z - satisifies

z^2+x^2=2^2\implies z=\sqrt{4-x^2}

and we have

\tan y=\dfrac xz=\dfrac x{\sqrt{4-x^2}}

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Answer:

The number of  Diplo pops  D = 18

The number of sneakers   S = 12

Step-by-step expla nation:

Given:

Cost of one Diplo pops = $.50

Cost of one sneakers  = $.60

Total number of candies purchased = 30 pieces

cost of the number of candies purchased = $16.80

To Find:

Number of each type of candies = ?

Solution:

Let

The number of  Diplo pops be D

The number of sneakers be  S

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S+D = 30

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S(0.50) + D(0.60) = 16.80----------------(2)

Substituting (1) in (2)

(30 - D)(0.50) + D(0.60) = 16.80

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15 + 0.10D =  16.80

0.10D = 16.80 - 15

0.10D = 1.80

D = \frac{1.80}{0.10}

D = 18

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Point Y is the midpoint of segment XZ. If XY = 2(3x +1) and YZ = 5x + 22, find the value of x.
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<h3>Point Y is the midpoint of segment XZ. Then value of x is 20</h3>

<em><u>Solution:</u></em>

Given that,

<em><u>Point Y is the midpoint of segment XZ</u></em>

XY = 2(3x +1)

YZ = 5x + 22

To find: Value of x

Since, Point Y is the midpoint of segment XZ,

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XY = YZ

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