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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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Identify the line with an undefined slope
Fudgin [204]

Answer:

d. vertical line

Step-by-step explanation:

A line with an undefined slope is a vertical line

Slope is the change in y over the change in x

When the slope is undefined, it means that the x does not change, which is a vertical line

8 0
2 years ago
Read 2 more answers
Can someone help me with this?
nadya68 [22]

Answer:

C

Step-by-step explanation:

It is not E becuase SQRT(97) is less than SQRT(100), SQRT(100) is 10,

SQRT(81) is 9 SO SQRT(97) is between 9 and 10, C.

Hope it helps :)

4 0
3 years ago
Read 2 more answers
The area of the conference table in Mr. Nathan’s office must be no more than 175 ft2. If the length of the table is 18 ft more t
valentina_108 [34]
The answer is  0 < x <span>≤ 7 
</span>
First, we know that width =  x
Which means that length = x +18

So, the possible equation for the Table's area is

X (X + 18)  ≤ 175

X^2 + 18x - 175  <span>≤ </span>0

Next, we need to calculate is by using complete square method
x^2 + 18x + 81 <span>≤ 175 + 81

(x + 9)^2 </span><span>≤ 256

|x + 9| </span><span>≤ sqrt(256)

|x + 9| </span><span>≤ +-16

-16 </span>≤ x + 9 <span>≤ 16

</span>-16 - 9 ≤ x <span>≤ 16 - 9

</span>-25 ≤ x <span>≤ 7

Since the width couldn't be negative, we can change -25 with 0,

so it become
</span> 0 < x ≤ 7 
7 0
3 years ago
Simplify the expression (k2)4
lilavasa [31]

4 times 2= 8. so, 4times k2 = k8. To understand this better, imagine that k equaled 2. That would make the expression above = (2x2)4, which would equal 16. However, since we don't know the value of k, we have to use the numbers that we already have, It would be like solving the expression: (2x2)4 without multiplying the first 2. It would then be 2x8. So, we just simplified it, we didn't solve it.

6 0
3 years ago
A young couple purchases their first new home in 2011 for​ $95,000. They sell it to move into a bigger home in 2018 for​ $105,00
mart [117]

Given:

The value of home in 2011 is $95,000.

The value of home in 2018 is $105,000.

To find:

The exponential model for the value of the home.

Solution:

The general exponential model is

y=ab^x       ...(i)

where, a is initial value and b is growth factor.

Let 2011 is initial year and x be the number of years after 2011.

So, initial value of home is 95,000, i.e., a=95,000.

Put a=95000 in (i).

y=95000b^x       ...(ii)

The value of home in 2018 is $105,000. It means the value of y is 105000 at x=7.

105000=95000b^7

\dfrac{105000}{95000}=b^7

\dfrac{21}{19}=b^7

Taking 7th root on both sides, we get

\left(\dfrac{21}{19}\right)^{\frac{1}{7}}=b

Put b=\left(\dfrac{21}{19}\right)^{\frac{1}{7}} in (ii).

y=95000\left(\left(\dfrac{21}{19}\right)^{\frac{1}{7}}\right)^x

y=95000\left(\dfrac{21}{19}\right)^{\frac{x}{7}}

Therefore, the required exponential model for the value of home is y=95000\left(\dfrac{21}{19}\right)^{\frac{x}{7}}, where x is the number of years after 2011.

5 0
3 years ago
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