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andrezito [222]
3 years ago
12

Question 6 (2 points)

Mathematics
1 answer:
nirvana33 [79]3 years ago
6 0

Answer:

Step-by-step explanation:

Ratio = 3 : 2

Length =3x

Width = 2x

Perimeter = 50 inches

2*(length + width ) = 50

2* (3x + 2x ) = 50

       2* 5x    = 50

               10x = 50

                  x = 50/10

x = 5

Length = 3*5 = 15 inches

Width = 2*5   =  10 inches

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Answer:

Step-by-step explanation:

1. r=3

To convert from polar coordinates (r,θ) to rectangular coordinates (x,y), we use the following equations

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Sinθ=y/r

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Then we have

r=3,

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All points with r = 3 are at

distance 3 from the origin, so r = 3 describes the circle of radius 3, with center at the origin (0,0).

Option C

2. r=2sinθ

When r=2sinθ

To convert from polar coordinates (r,θ) to rectangular coordinates (x,y), we use the following equations

x=rCosθ

Cosθ=x/r

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Also, r²=x²+y²

Now, apply the given information

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Cross multiply

r²=2y

x²+y²=2y

x²+y²-2y =0

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It is a circle with center (0,1) and radius 1.

Because the sine is periodic, we know that we will get the entire curve for values of θ in [0, 2π). As θ runs from 0 to π/2, r increases

from 0 to 2. Then as θ continues to π, r decreases again to 0. When θ runs from π to

2π, r is negative, and it is not hard to see that the first part of the curve is simply traced

out again, so in fact we get the whole curve for values of θ in [0, π). Thus, check attachment for curve, Now, this suggests that the curve could possibly be a circle,

and if it is, it would have to be the circle x² + (y − 1)² = 1. Having made this guess, we can easily check it. First we substitute for x and y to get (r cos θ)² + (r sin θ − 1)² = 1;

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Option E

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y=r√2 /2

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x²+y²= r²

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x²+y²= 0

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Option D

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Here the distance from the origin

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The correct option is B

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(x-1)² + y² -1 =0

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It is a circle with center (1,0) and radius 1.

A circle of radius 1 with center on the y-axis

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