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3 years ago

9.01 prove that the two circles are similar

Mathematics

1 answer:

il63 [147K]3 years ago

4 0

Answer:

see the procedure

Step-by-step explanation:

we know that

Figures can be proven similar if one, or more, similarity transformations (reflections, translations, rotations, dilations) can be found that map one figure onto another.

In this problem to prove circle C and circle A are similar, a translation and a scale factor (from a dilation) will be found to map one circle onto another.

we have that

Circle C is centered at (0,-1) and has a radius of 2 units

Circle A is centered at (3,4) and has a radius of 5 units

step 1

Move the center of the circle C onto the center of the circle A

the transformation has the following rule

(x,y)--------> (x+3,y+5)

(0,-1)------> (0+3,-1+5)-----> (3,4)

center circle C is now equal to center circle A

The circles are now concentric (they have the same center)

step 2

A dilation is needed to increase the size of circle C to coincide with circle A

scale factor=radius circle A/radius circle C-----> 5/2=2.5

radius circle C will be=2*scale factor-----> 2*2.5=5 units

radius circle C is now equal to radius circle A

therefore

A translation, followed by a dilation will map one circle onto the other, thus proving that the circles are similar

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valkas [14]

( - 14x^3)(y^3) + 4x^5y^6)/(2x^4y^5)

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3 years ago

Help please:Suppose that x and y inversely, and x=10 when y=8 write the function that models the inverse variation

jarptica [38.1K]

SOLUTION

From the question, we are told that y varies inversely as x

This is mathematically written as

$\begin{gathered} y\propto\frac{1}{x} \\ \propto\text{ is a sign of proportionality } \end{gathered}$

Now, we will remove the proportionality sign and replace it with equal to sign =

If we do this, we will intoduce a constant k

$\begin{gathered} y\propto\frac{1}{x} \\ y=k\times\frac{1}{x} \\ y=\frac{k}{x} \end{gathered}$

So we have the formula

$y=\frac{k}{x}$

We will substitute the values of x for 10 and y for 8 into the formula to get k, we have

$\begin{gathered} y=\frac{k}{x} \\ 8=\frac{k}{10} \\ k=8\times10 \\ k=80 \end{gathered}$

Now, we will substitute k for 80 back into the formula to get the inverse function, we have

$\begin{gathered} y=\frac{k}{x} \\ y=\frac{80}{x} \end{gathered}$

Hence the answer is option C

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1 year ago

PLEASE HELP me

prohojiy [21]

To find the average number of customers for dinner, use the simple ratio of 5 lunch customers for every 8 dinner customers.

Because there are 40 lunch customers, this is eight groups of five lunch customers. This means you will need 8 groups of 8 dinner customers to make it equivalent.

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3 years ago

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lana66690 [7]

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3 years ago

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son4ous [18]

Answer:
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Explanation:
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2 years ago