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Svetach [21]
3 years ago
10

Describe the turn of a circle

Mathematics
1 answer:
Vaselesa [24]3 years ago
4 0
It rotates 360 degrees and 180 half way in a circular motion
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Which describes how square S could be transformed to square S prime in two steps? Assume that the center of dilation is the orig
gayaneshka [121]

Answer:

The correct option is;

A dilation by a scale factor of Two-fifths and then a translation of 3 units up

Step-by-step explanation:

Given that the coordinates of the vertices of square S are

(0, 0), (5, 0), (5, -5), (0, -5)

Given that the coordinates of the vertices of square S' are

(0, 1), (0, 3), (2, 3), (2, 1)

We have;

Length of side, s, for square S is s = √((y₂ - y₁)² + (x₂ - x₁)²)

Where;

(x₁, y₁) and (x₂, y₂) are the coordinates of two consecutive vertices

When (x₁, y₁) = (0, 0) and (x₂, y₂) = (5, 0), we have;

s = √((y₂ - y₁)² + (x₂ - x₁)²) = s₁ = √((0 - 0)² + (5 - 0)²) = √(5)² = 5

For square S', where (x₁, y₁) = (0, 1) and (x₂, y₂) = (0, 3)

Length of side, s₂, for square S' is s₂ = √((3 - 1)² + (0 - 0)²) = √(2)² = 2

Therefore;

The transformation of square S to S' involves a dilation of s₂/s₁ = 2/5

The after the dilation (about the origin),  the coordinates of S becomes;

(0, 0) transformed to (remains at) (0, 0) ....center of dilation

(5, 0) transformed to (5×2/5, 0) = (2, 0)

(5, -5) transformed to (2, -2)

(0, -5) transformed to (0, -2)

Comparison of (0, 0), (2, 0), (2, -2), (0, -2) and (0, 1), (0, 3), (2, 3), (2, 1) shows that the orientation is the same;

For (0, 0), (2, 0), (2, -2), (0, -2) we have;

(0, 0), (2, 0) the same y-values, (∴parallel to the x-axis)

(2, -2), (0, -2) the same y-values, (∴parallel to the x-axis)

For (0, 1), (0, 3), (2, 3), (2, 1) we have;

(0, 3), (2, 3) the same y-values, (∴parallel to the x-axis)

(0, 1), (2, 1) the same y-values, (∴parallel to the x-axis)

Therefore, the lowermost point closest to the y-axis in (0, 0), (2, 0), (2, -2), (0, -2) which is (0, -2) is translated to the lowermost point closest to the y-axis in (0, 1), (0, 3), (2, 3), (2, 1) which is (0, 1)

That is (0, -2) is translated to (0, 1) which shows that the translation is T((0 - 0), (1 - (-2)) = T(0, 3) or 3 units up

The correct option is therefore a dilation by a scale factor of Two-fifths and then a translation of 3 units up.

7 1
3 years ago
What is the area of the figure? <br><br>A. 617.5 m^2<br>B. 824 m^2<br>C. 759 m^2<br>713.5 m^2
Flura [38]
Hey !!

Check the attachment.

Hence, On proper calculations ,
We get our answer as D) 713.5 m^2


Hope it helps you :)

8 0
3 years ago
Identify the variation as direct, inverse, joint or combined. y = cx²
viva [34]

Answer:

combined variation          

Step-by-step explanation:

we have

y=cx^{2}

we know that

a)<u> in the interval </u>----> (0,∞)

If the value of x increase the value of y increase

so

Is a direct variation

b) <u>in the interval -</u>---> (-∞,0)

If the value of x increase the value of y decrease

so

Is a inverse variation

therefore

Is a combined variation


4 0
3 years ago
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Find the surface area for the given cylinder with the radius 6 and the height 24
Basile [38]
1130.97 is the surface area of the cylinder
6 0
3 years ago
Read 2 more answers
Which table represents a linear function?
kolezko [41]

Answer:

last one

Step-by-step explanation:

5 0
3 years ago
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