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3 years ago

How many different four-person relay team can recover from a student

1 answer:

3 0

Well, You have 4 students and 8 other students. If theres 8 people, this means theres 8 combinations possible. This means you do 8x4 and you get 32.

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which of the functions have a range of real numbers greater than or equal to 1 or less than or equal to-1

lilavasa [31]

The question is incomplete. Here is the complete question:

Which of the functions have a range of all real numbers greater than or equal to 1 or less than or equal to -1? check all that apply.

A. $y=\sec x$

B. $y= \tan x$

C. $y= \cot x$

D. $y= \csc x$

Answer:

A. $y=\sec x$

D. $y=\csc x$

Step-by-step explanation:

Given:

The range is greater than or equal to 1 or less than or equal to -1.

The given choices are:

Choice A: $y=\sec x$

We know that, the $\sec x=\frac{1}{\cos x}$

The range of $\cos x$ is from -1 to 1 given as [-1, 1]. So,

$|\cos x|\leq 1\\\textrm{Taking reciprocal, the inequality sign changes}\\\frac{1}{|\cos x|}\geq 1\\|\sec x|\geq 1$

Therefore, on removing the absolute sign, we rewrite the secant function as:

$\sec x\leq -1\ or\ \sec x\geq 1\\$

Therefore, the range of $y=\sec x$ is all real numbers greater than or equal to 1 or less than or equal to-1.

Choice B: $y= \tan x$

We know that, the range of tangent function is all real numbers. So, choice B is incorrect.

Choice C: $y= \cot x$

We know that, the range of cotangent function is all real numbers. So, choice C is incorrect.

Choice D: $y=\csc x$

We know that, the $\csc x=\frac{1}{\sin x}$

The range of $\sin x$ is from -1 to 1 given as [-1, 1]. So,

$|\sin x|\leq 1\\\textrm{Taking reciprocal, the inequality sign changes}\\\frac{1}{|\sin x|}\geq 1\\|\csc x|\geq 1$

Therefore, on removing the absolute sign, we rewrite the cosecant function as:

$\csc x\leq -1\ or\ \csc x\geq 1\\$

Therefore, the range of $y=\csc x$ is all real numbers greater than or equal to 1 or less than or equal to-1.

6 0

3 years ago

The prism shown has a volume of 300 m3. A prism has a length of 7.5 meters, width of w, and height of 5 meters. What is the widt

Shalnov [3]

Answer:

Step-by-step explanation:

7.5*5=37.5

200/37.5=6

3 0

3 years ago

Read 2 more answers

You buy a house for $230,000. It appreciates at a rate

Xelga [282]

Answer:

1,232,142

Step-by-step explanation:

bro just use a calculator

3 0

3 years ago

What is the value of y in the solution to the following system of equations? 5x − 3y = −11 2x − 6y = −14 −1 0 1 2

Alekssandra [29.7K]

5x - 3y = -11 (×2)
2x - 6y = -14 (x5)

10x - 6y = -22
10x - 30y = -70
---------------------- -
24y = 48
y = 2

5 0

3 years ago

PLEASE HELP ME WITH THIS!!!!!!!!

vlabodo [156]

Answer:

(9.5, 0) is in quadrant I. (-4, 7) is in quadrant II. (-1, -8) is in quadrant III.

Step-by-step explanation:

The negative signs say everything (quite literally). If there are no negative signs, it is in quadrant I. If there is one in the x-axis (the first number in an ordered pair), it is in quadrant II. If there are 2 negative signs, it is in quadrant III, and if there is one in the y-axis (the second number in an ordered pair), it is in quadrant IV.

4 0

3 years ago