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3 years ago

F(x) = 5x2 - X+ 3 Please help

Mathematics

1 answer:

muminat3 years ago

5 0

Answer:

Step-by-step explanation:

Do you know how to use the quadratic formula?

$x = \frac{-b +/- \sqrt{b^2 - 4*a*c} }{2*a}$

a = 5

b = -1

c = 3

$x = \frac{1 +/- \sqrt{1 - 4*1*3} }{2}\\x= \frac{1 +\sqrt{-11} }{2}\\x = \frac{1 +/- i\sqrt{11} }{2}$

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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.

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It was $30.60 for each centerpieces

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Answer:

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Step-by-step explanation:

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bob and mark talk about their families. bob says he has 3 kids, the product of their ages is 72. Mark points out that there is s

Sonbull [250]

Given:
3 kids
72 is the product of their ages.
There is a youngest child.

This means that all three are of different ages. We need to factor 72 into 3 integers.
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36 ÷ 2 = 18
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