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Nonamiya [84]
3 years ago
8

Graph y=sin^-1 (1/4 x) on the interval -5≤x≤5.

Mathematics
1 answer:
GaryK [48]3 years ago
4 0

Answer:

D

Step-by-step explanation:

The arcsine (\sin^{-1}) function of x is defined as the inverse sine function of x when -1≤x≤1.

So, when

-4\le x\le 4,

we have that

-1\le \dfrac{1}{4}x\le 1.

This gives us the domain -4\le x\le 4 of the function y=\sin^{-1}\left(\dfrac{1}{4}x\right).

The range of the function y=\sin^{-1}x is -\dfrac{\pi }{2}\le x\le \dfrac{\pi }{2}, so the range of the function y=\sin^{-1}\left(\dfrac{1}{4}x\right) is the same (options A and C are false).

When x=-4,

y=\sin^{-1}\left(\dfrac{1}{4}\cdot (-4)\right)=\sin^{-1}(-1)=-\dfrac{\pi}{2}.

So, option B is false and option D is true.

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Bobby bought two shares of stock, which he sold for $96 each. If he had a profit of 20 percent on the sale of one of the shares
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Answer:

The correct option is c) a loss of $8.

Step-by-step explanation:

Consider the provided information.

If the selling price of two item is same and one item sold at a profit of x % and other at a loss of x % in that case total sale result loss:

To calculate the loss use the formula: Loss\ \%=(\frac{x}{10})^2\ \%

It is given that he had a profit of 20 percent on the sale of one of the shares but a loss of 20 percent on the sale of the other share, where the selling price is $96 each.

That means the total sale result will be a loss.

Now use the above formula by substitute x=20.

Loss\ \%=(\frac{20}{10})^2\ \%\\\\Loss\ \%=4\ \%

It is given that the sales price is $96 of each that means total sales price is:

$96+$96=$192

Let the cost price of the shares were x.

According to question: x-4% of x = 192

x-\frac{4}{100}\times x = 192\\\\x-0.04x = 192\\\\0.96x = 192\\x = 200

Hence, the cost price of the shares was 200.

Loss = Cost price -Sales price

Loss = $200 - $192

Loss = $8

Hence, the correct option is c) a loss of $8.

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Step-by-step explanation:

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OverLord2011 [107]
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One angle of a right triangle measures 8°. What is the measure of the other acute angle?
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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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