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3 years ago

What is the area of this composite shape?

Mathematics

1 answer:

Varvara68 [4.7K]3 years ago

6 0

<h3>Answer: 51 square inches</h3>

=======================================================

Explanation:

There are a few ways to do this. One way is to divide the figure as shown in the diagram below. I divided it into a rectangle and a triangle. Find the area of the rectangle and triangle, then add up those areas to get the final answer.

A = area of rectangle

A = length*width

A = 7*6

A = 42

B = area of triangle

B = 0.5*base*height

B = 0.5*(6-3)*(13-7)

B = 0.5*3*6

B = 1.5*6

B = 9

C = total area

C = A+B

C = 42+9

C = 51 square inches

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Answer:

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x = 17.40 seconds

Step-by-step explanation:

Given the expression

$f\left(x\right)\:=-16x^2+272x+110$

Here:

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y represents the height of the rocket

We know that when the rocket will hit the ground, the height will get y = 0

i.e.

$0\:=-16x^2+272x+110$

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$-16x^2+272x+110=0$

subtract 110 from both sides

$-16x^2+272x+110-110=0-110$

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$\frac{-16x^2+272x}{-16}=\frac{-110}{-16}$

$x^2-17x=\frac{55}{8}$

$\mathrm{Add\:}\left(-\frac{17}{2}\right)^2\mathrm{\:to\:both\:sides}$

$x^2-17x+\left(-\frac{17}{2}\right)^2=\frac{55}{8}+\left(-\frac{17}{2}\right)^2$

$x^2-17x+\left(-\frac{17}{2}\right)^2=\frac{633}{8}$

$\left(x-\frac{17}{2}\right)^2=\frac{633}{8}$

$\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}$

solving

$x-\frac{17}{2}=\sqrt{\frac{633}{8}}$

$x=\frac{\sqrt{1266}}{4}+\frac{17}{2}$

x = 17.40 seconds

also solving

$x-\frac{17}{2}=-\sqrt{\frac{633}{8}}$

$x=-\frac{\sqrt{1266}}{4}+\frac{17}{2}$

x = -0.40 seconds

As time can not be negative.

Thus, the value of x = 17.40 seconds

Therefore, the time that the rocket will hit the ground will be:

x = 17.40 seconds

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