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3 years ago

PLEASE HELP!!

Mathematics

1 answer:

Tanya [424]3 years ago

3 0

Answer:

First blank: [-π/2 , π/2]

Second blank: [-π/2 , π/2]

Step-by-step explanation:

The conditions for inverse function to exist is that the function should be one to one function.

A function for which every element of the range of the function corresponds to exactly one element of the domain.

The function can be tested by the vertical line test.

For the given function f(x) = sin x is not one to one function.

so, the domain of the function f(x)=sin x restricted so that its inverse function exists

The domain will be the range provided that when we apply the vertical line test will intersects at only one point

So, the domain will be [-π/2 , π/2]

And this means f(x) = sin⁻¹ x are on the interval [-π/2 , π/2]

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Name an angle bisector shown in the figure. DE AB GB CF

expeople1 [14]

Answer:

Step-by-step explanation:

we know that

An angle bisector is a line that divide an angle into two equal angles.

In this problem

$m\angle ACF=m\angle FCD$ ---> given problem

$m\angle ACD=m\angle ACF+m\angle FCD$ ---> by addition angle postulate

CF is an angle bisector of angle $m\angle ACD$

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3 years ago

To create a giant gemstone, sara first made two identical square pyramids that each had a base area of 100 square inches. Then s

inysia [295]

Answer:

8 inches.

Step-by-step explanation:

From the statement we have that they first made two identical square pyramids, each with a base area of 100 square inches.

Ab = s ^ 2 = 100

Therefore each side would be:

s = (100) ^ (1/2)

s = 10

So, side of the square base = 10 inches

Then they tell us that they glued the bases of the pyramids together to form the precious stone. The surface area of the gemstone is 520 square inches, so for a single pyramid it would be:

Ap = 520/2 = 260

For an area of the square pyramid we have the following equation:

Ap = 2 * x * s + s ^ 2

Where x is the height of each triangular surface and s is the side of the square base

Replacing we have:

260 = 2 * x * 10 + 10 ^ 2

20 * x + 100 = 260

20 * x = 160

x = 160/20

x = 8

Therefore, the value of x is 8 inches.

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3 years ago

0.0002 in scientific notation

Westkost [7]

Answer:

2 * 10 ^-4

Step-by-step explanation:

We need the first number to be between 1 and less than 10

.0002

2 * 10 ^ exponent

We move the decimal 4 places to the right. Since we move it to the right the exponent is negative and is the number of places we moved the decimal

2 * 10 ^-4

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3 years ago

11. Find the area of each figure. Show all your calculations a. 3 cm 13 cm

Firlakuza [10]

Answer:

$39$

Step-by-step explanation:

$A=lw$

Area = length * width

$A = 3 * 13$

$A=39$

Hope this helps

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3 years ago

Simplify (3-4i)(5+2i)

Andre45 [30]

Foil
15+6i-20i-8i^2
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15+8+6i-20i
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3 years ago