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3 years ago

Evaluate fog and gof if f(x)=5x-8 and g(x)= x^3

Mathematics

1 answer:

DerKrebs [107]3 years ago

3 0

Answer:

see explanation

Step-by-step explanation:

note that f ○ g = f(g(x))

To evaluate substitute x = x³ into f(x)

f(g(x)) = f(x³) = 5x³ - 8

In the same way

g ○ f = g(f(x))

To evaluate substitute x = 5x - 8 into g(x)

g(f(x)) = g(5x - 8) = (5x - 8)³

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A metal washer is made by cutting out a circle 13.2 mm in diameter from a larger circle. To the nearest tenth, what is the area

Lana71 [14]

The area of the washer will be the area of the smaller circle SUBTRACTED from the area of the larger circle.

Area of a circle = pi * r^2 where r is your radius (which is half the diameter).
Larger circle area = pi *(diameter/2) ^2.
Smaller circle area = pi * (13.2/2)^2 = pi * 6.6^2 = 136.8484....

So...the area of the washer = larger circle area - 136.4848...

5 0

3 years ago

Calculate the total area of the shaded region.

LUCKY_DIMON [66]

so hmmm seemingly the graphs meet at -2 and +2 and 0, let's check

$\stackrel{f(x)}{2x^3-x^2-5x}~~ = ~~\stackrel{g(x)}{-x^2+3x}\implies 2x^3-5x=3x\implies 2x^3-8x=0 \\\\\\ 2x(x^2-4)=0\implies x^2=4\implies x=\pm\sqrt{4}\implies x= \begin{cases} 0\\ \pm 2 \end{cases}$

so f(x) = g(x) at those points, so let's take the integral of the top - bottom functions for both intervals, namely f(x) - g(x) from -2 to 0 and g(x) - f(x) from 0 to +2.

$\stackrel{f(x)}{2x^3-x^2-5x}~~ - ~~[\stackrel{g(x)}{-x^2+3x}]\implies 2x^3-x^2-5x+x^2-3x \\\\\\ 2x^3-8x\implies 2(x^3-4x)\implies \displaystyle 2\int\limits_{-2}^{0} (x^3-4x)dx \implies 2\left[ \cfrac{x^4}{4}-2x^2 \right]_{-2}^{0}\implies \boxed{8} \\\\[-0.35em] ~\dotfill$

$\stackrel{g(x)}{-x^2+3x}~~ - ~~[\stackrel{f(x)}{2x^3-x^2-5x}]\implies -x^2+3x-2x^3+x^2+5x \\\\\\ -2x^3+8x\implies 2(-x^3+4x) \\\\\\ \displaystyle 2\int\limits_{0}^{2} (-x^3+4x)dx \implies 2\left[ -\cfrac{x^4}{4}+2x^2 \right]_{0}^{2}\implies \boxed{8} ~\hfill \boxed{\stackrel{\textit{total area}}{8~~ + ~~8~~ = ~~16}}$

7 0

2 years ago

Andrea has 18 yards of fabric. How many 4-inch pieces can she cut from her original piece?

Mrac [35]

Answer:

162 pieces

Step-by-step explanation:

Andrea has 18 yards

How many 4 inch pieces can she get?

Convert

1 yard = 3 feet

18 yards = 54 feet

1 foot = 12 inches

54 feet = 648 inches

Divide

648 inches ÷ 4 inches = 162 pieces

Hope this helps :)

6 0

3 years ago

Read 2 more answers

A woman has 7 keys. only one of them will open her door. when seh arrives at the door there is no sufficient light for her to fi

Gala2k [10]

Since she has seven key the probability that the first one will open the door is
$\frac{1}{7}$
if it takes three attempts to open the door,the probability is
$\frac{1}{3}$
if the three attempts would not work
then the probability that the fourth attempt will open the door is
$\frac{1}{4}$
hope this helps

7 0

3 years ago

What is the scale factor use to create this dilation?

andrezito [222]

Given Info: "The dashed triangle is the image of the solid triangle"

So the "before" is the large solid triangle and the "after" is the smaller dashed triangle.

The horizontal side of the solid triangle is 15 units. The corresponding side for the dashed triangle is 3 units. Dividing the two values gives: 3/15 = 1/5 = 0.2

Make this value negative. The reason why is due to the fact that we have a sort of reflection going on as we're scaling down the figure.

So the final answer is -0.2

3 0

3 years ago