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storchak [24]
3 years ago
7

Antonio uses dish soap in his recipe for giant bubbles. he compares the prices of two brands of soap. which brand is the better

buy
Brand A: 32 fl oz ( 2.56 )
Brand B: 48 fl oz ( $4.80 )
Mathematics
1 answer:
schepotkina [342]3 years ago
6 0

Answer:$2.36

Step-by-step explanation:

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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
If a set of school supplies cost $6.70, how much change do you get from $10.00?
aivan3 [116]
6.70-10.00=3.30
So you get $3.30 as change
5 0
3 years ago
Read 2 more answers
Help me please im not good a this
Ghella [55]
0,-5 i hope this is can sorry if its wrong
3 0
3 years ago
Please help me with this problem please!!!!!!!!!!!!!!
777dan777 [17]

Answer:

Brain

Step-by-step explanation:

7 0
2 years ago
Which is the graph of x – y = 1?
Jet001 [13]

Answer:

its the second graph

Step-by-step explanation:

you could use this website to find out graph

desmos calculator

5 0
3 years ago
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