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2 years ago

For the following exercises, graph the given functions by hand. 48. f(x) = | 2x − 4 | − 3

Mathematics

1 answer:

oksian1 [2.3K]2 years ago

4 0

A horizontal translation of the function by 4 units and a vertical translation down by 3 units

<h3>Graph of modulus function</h3>

The parent function of the given function is g(x) = |x|. The resulting function (x) = | 2x − 4 | − 3 shows the following translations

A vertical stretch of the graph by 2 units

A horizontal translation of the function by 4 units and a vertical translation down by 3 units

Learn more on translation here: brainly.com/question/12861087

#SPJ1

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tester [92]

Answer:

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Step-by-step explanation:

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densk [106]

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3 years ago

Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in t

Tresset [83]

Answer: The volume of largest rectangular box is 4.5 units.

Step-by-step explanation:

Since we have given that

Volume = $xyz$

with subject to $x+2y+3z=9$

So, let $z=\dfrac{9-x-2y}{3}$

So, Volume becomes,

$V=xyz\\\\V=xy(\dfrac{9-x-2y}{3})\\\\V=\dfrac{9xy-x^2y-2xy^2}{3}$

Partially derivative wrt x and y we get that

$9-2x-2y=0\implies 2x+2y=9\\\\and\\\\9-x-4y=0\implies x+4y=9$

By solving these two equations, we get that

$x=3,y=\dfrac{3}{2}$

So, $z=\dfrac{9-x-2y}{3}=\dfrac{9-3-3}{3}=\dfrac{3}{3}=1$

So, Volume of largest rectangular box would be

$xyz=3\times \dfrac{3}{2}\times 1=\dfrac{9}{2}=4.5$

Hence, the volume of largest rectangular box is 4.5 units.

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4 years ago

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3 years ago

For the following exercises, graph the given functions by hand. 48. f(x) = | 2x − 4 | − 3

For the following exercises, graph the given functions by hand. 48. f(x) = | 2x − 4 | − 3