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3 years ago

Find the absolute maximum value for the function f(x) = x^2 − 4, on the interval [–3, 0) U (0, 2].

Mathematics

1 answer:

Andreyy893 years ago

5 0

Answer:

Step-by-step explanation:

The function $y=x^2 -4$ is

decreasing for all $x\in [-3,0);$
is increasing for all $x\in (0,2]$

(see attached diagram for details).

The maximum value of the function is at endpoints -3 or 2. find y(-3) and y(2):

$y(-3)=(-3)^2-4=9-4=5\\ \\y(2)=4^2-4=0$

So, the maximum value is 5.

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Four less than three times a number is three more than two times the number. What is the number?

MAXImum [283]

Hello!

Say that n is the number. There are two parts to this statement. The first part is "four less than three times a number", and the second is "is three more than two times the number. An expression fitting the first part will go on the left side of the equation, and the second part will go on the right.

Look at the first part. "Four less than three times a number". The first thing being done here is the three times a number. This would be 3n, as it is 3 times n. Now, there is the four less part. You would therefore have to subtract 4 from 3n, to get 3n - 4.

Now the second part. "Is three more than two times the number". The first thing being done here is the two times the number. That would be 2n. The next is "is three more than". If the other side is three more than 2n, then you must add 3 to 2n to make them equivalent. Therefore, it would be 2n + 3.

Now, set them equal to each other, and solve.

3n - 4 = 2n + 3

3n - 2n = 3 + 4

n = 7

Therefore, your number is 7.

Hope this helps!

5 0

3 years ago

Which angles are coterminal with −6π5 ? Select each correct answer. 14π/5 −16π/5 −π/5 −11π/5

wariber [46]

ANSWER

$- \frac{16 \pi}{5} \: and \: \frac{14\pi}{5}$

EXPLANATION

Coterminal angles are angles in standard position that have the same terminal side.

To find an angle in standard position that is coterminal with

$- \frac{6 \pi}{5}$

We add or subtract multiples of
$2 \pi$

The first addition gives,

$- \frac{6 \pi}{5} + 2 \pi = \frac{4 \pi}{5}$

We add the second multiple to get,

$- \frac{6 \pi}{5} +2( 2 \pi )= \frac{14 \pi}{5}$

Since this is the maximum value among the options, we end the addition here.

Let us now subtract the first multiple to get,

$- \frac{6 \pi}{5} - 2 \pi = - \frac{16 \pi}{5}$

We end the subtraction here because this is the least value among the options.

Therefore the angles that are coterminal with
$- \frac{6 \pi}{5}$
are

$- \frac{16 \pi}{5} \: and \: \frac{14\pi}{5}$

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3 years ago

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What is the equation of the line that passes through (5,-2) and (-3, 4)?

natali 33 [55]

3x-4y-7= 0 is the answer

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3 years ago

Frances wants to paint rectangular wall that has a width of 8 feet and a height of 9 ft.She has a quart of paint that will cover

VladimirAG [237]

The area of the wall is 72 feet squared.

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Overall, divorce rates have declined in the last 20 years, but among middle-aged couples, the rates are rising. Do an internet s

denpristay [2]

Answer:

The current divorce rate is about 7% based on the survey.

Step-by-step explanation:

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3 years ago