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DIA [1.3K]
3 years ago
13

The figures below are based on semicircles and squares. Find the perimeter and the area of each shape. Give your answer as a com

pletely simplified exact value in terms of π (no approximations).

Mathematics
1 answer:
irina1246 [14]3 years ago
8 0

Answer:

Part 1) The area of the figure is A=48\ cm^2

Part 2) The perimeter of the figure is P=4(2+3\pi)\ cm

Step-by-step explanation:

Part 1) Find the area of the figure

we know that

The area of the figure is equal to the area of three squares

so

A=3[4^2]=48\ cm^2

Part 2) Find the perimeter of the figure

we know that

The perimeter of the figure is equal to two times the length side of the square, plus the circumference of six semicircles ( or the circumference of three circles)

Remember that

The circumference of a circle is equal to

C=\pi D

where

D is the diameter of the circle

In this problem

D=4\ cm

so

P=2(4)+3[\pi(4)]=(8+12\pi)\ cm

simplify

P=4(2+3\pi)\ cm

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4 0
3 years ago
Ax +by = 16
Talja [164]

Answer:

  • The system has infinitely many solutions when a = 3/4 and b = 1/2

<h3>Given </h3>

System of linear equations

  • ax +by = 16
  • 3x+2y=64

<h3>To find </h3>

  • Values of a and b that leads to infinitely many solutions

<h3>Solution</h3>

The linear system of equations has infinitely many solutions when lines overlap, so both have same slope and y-intercept.

We can solve it in two different ways

1. Note that when the first equation is multiplied by 4, it has same value of constant as the second equation, which is 64.

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When compared it gives us:

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2. Convert both equations from standard to slope-intercept form and compare:

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  • by = -ax + 16
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Work out values of a and b:

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3 0
1 year ago
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