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Strike441 [17]
3 years ago
14

Use set builder notation to represent the following sets

Mathematics
1 answer:
Romashka-Z-Leto [24]3 years ago
7 0
3 is a set builder of -3,-2,-1,0,1,2
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I’m not sure how to do this
Brums [2.3K]

Answer: lim as x → -5 of f(x) and g(x) = 300

               Domain of f(x) and g(x) is All Real Numbers

               f(-5) = 200

               g(-5) = 300

<u>Step-by-step explanation:</u>

The limit of f(x) as x approaches -5:

f(x) =\dfrac{4x^3+500}{x+5}\\\\\\.\qquad =\dfrac{4(x^3+125)}{x+5}\\\\\\.\qquad =\dfrac{4(x^3+5^3)}{x+5}\qquad \text{we can factor the cubic}\\\\\\.\qquad =\dfrac{4(x+5)(x^2-5x+25)}{x+5}\\\\\\.\qquad =4(x^2-5x+25)\\\\\\\text{as x approaches -5, f(x) = }4[(-5)^2-5(-5)+25]\\\\.\qquad \qquad \qquad \qquad \qquad =4(25 + 25 + 25)\\\\.\qquad \qquad \qquad \qquad \qquad =4(75)\\\\.\qquad \qquad \qquad \qquad \qquad =300

The limit of g(x) as x approaches -5:

g(x) = 4x² - 20x + 100

      = 4(-5)² - 20(-5) + 100

      = 100 + 100 + 100

      = 300

There is a restriction at x = -5 for f(x), however, that discontinuity has been filled with the 200 at x = -5. So the domain is ALL REAL NUMBERs.

There are no restrictions on x for g(x) so the domain is ALL REAL NUMBERs.

5 0
3 years ago
First come first served brainiest:)
inessss [21]

Anserve

Step-by-step explanation:

3 0
3 years ago
Suppose you have a pieceof material that is 17 feet long. you only need 5/8 of the total length. how many feet do you need
Ilya [14]
(5/8) * 17 feet = 10.625 feet
5 0
3 years ago
Help me now !!!!!<br> help i need help
iren2701 [21]

cylinder:

V = πr²h

V = 3.14(2)² * 3

V = 3.14(4) * 3

V = 3.14(12)

V = 37.7m³

rectangular prism:

V = lwh

V = (2.4)(9)(5)

V = 108m³

the entirety of the sculpture:

V = volume of cylinder + volume of rectangular prism

V = 37.7 + 108

<u>V = 145.7m³</u>

4 0
2 years ago
How many sides does this regular polygon have? <br>Pls help ​
galina1969 [7]

Answer:

9 sides

Step-by-step explanation:

7y + 2y = 180

9y = 180

y =20

so, 2y, the exterior angle is 2 x 20 = 40

Divide 360 by 40 = 9

3 0
3 years ago
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