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4 years ago

What is the domain of validity for csc theta = 1 / sin theta?

1 answer:

4 0

$De finition\ of\ csc\theta=\frac{1}{sin\theta}\\-----------------------\\therefore\ csc\theta=\frac{1}{sin\theta}\to\frac{1}{sin\theta}=\frac{1}{sin\theta}\\\\the\ denominator\ must\ be\ different\ from\ zero,\ therefore\\\\sin\theta\neq0\iff\theta\neq k\pi\ where\ k\in\mathbb{Z}\\\\Answer:\boxed{D}$

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If 36 is 90% of a value, what is that value?

laila [671]

You know 36 is 90% of a value, so it will equal 90/100.
Multiply 90/100 types x (value). Easiest way is to simplify 90/100 = 9/10.
x = 36 / 9/10
x = 360 / 9
x = 40
Therefore, the value would be 40.

4 0

3 years ago

Read 2 more answers

What is the solution to ln (x2 - 16) = 0?

bogdanovich [222]

ANSWER

$x = \pm \sqrt{17}$
EXPLANATION

The given equation is

$ln( {x}^{2} - 16) = 0$

Take antilogarithm of both sides to base e.

${e}^{ ln( {x}^{2} - 16) } = {e}^{0}$

This will simplify to

${x}^{2} - 16 = 1$

Group like terms to obtain,

${x}^{2} = 1 + 16$

${x}^{2} = 17$

Take square root of both sides to get,

$x = \pm \sqrt{17}$

6 0

3 years ago

Read 2 more answers

Kevin reads 5 pages in 15 minutes at this rate how many pages will he read in 45 minutes

Aleksandr-060686 [28]

Answer:

15 pages

Step-by-step explanation:

45/15=3

3x5=15

4 0

3 years ago

The value of y is directly proportional to the value of x. When x=3.5, the value of y is 14. What is the value of y when x = 28?

inna [77]

Answer:

x = 7

Step-by-step explanation:

y = 14

14 x 2 = 28

Therefore:

3.5 x 2 = 7

7 0

3 years ago

Katie blows up a balloon and ties it so there is a fixed amount of air in the balloon.

kifflom [539]

Answer:

According to Charles' Law the order of arrangement of the location where the balloon has the smallest size to the location where the balloon has the largest size is given as follows;

A freezer < A cold refrigerator < A normal room temperature classroom < A warm cupboard

Step-by-step explanation:

The parameter of the balloon Katie blows are;

The amount of air in the balloon = Fixed (constant)

The initial size of the balloon = The length of the measured string

The locations in which the balloon can be placed = A freezer, a warm cupboard, a cold refrigerator, a normal temperature classroom

The size of the balloon is given by the volume of the balloon

according to Charles' Law, the volume of a given mass of gas is directly proportional to its temperature

Mathematically, Charles law can be expressed as follows;

V ∝ T

Therefore, as the temperature to which the balloon is subjected decreases, the volume decreases

The locations arranged in order of increasing temperature is given as follows;

Freezer < Cold refrigerator < Normal temperature classroom < Warm cupboard

Given that Katie blow's the balloon in a normal temperature classroom, according to Charles Law, we have;

The temperature of the air in the balloon decreases largely in a freezer, therefore, the size of the balloon largely decreases

The temperature of the air in the balloon increases in a warm cupboard, therefore, the size of the balloon increases

The temperature of the air in the balloon decreases slightly in a cold refrigerator, therefore, the size of the balloon decreases

The temperature of the air in the balloon remains the in a normal temperature classroom, therefore, the size of the balloon remains the same

The size of the balloon reduces the most in a freezer

The size of the balloon increases in a warm cupboard

The size of the balloon decreases slightly in a cold refrigerator

The size of the balloon remains the same in a normal temperature classroom.

8 0

3 years ago