Given a dilation where k=2, would the image be an enlargement or a reduction?

1 answer:

6 0

The image would be an enlargement since K>1, and any K values greater than one is essentially enlarging the graph by that factor

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a large water tank measures 6 feet across and 4 feet high. it is being filled with water at a rate of 10 gallons per minute. abo

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Both circle Q and circle R have a central angle measuring 140°. The area of circle Q's sector is 25π m2, and the area of circle

taurus [48]

Solution:

we are given that

Both circle Q and circle R have a central angle measuring 140°. The area of circle Q's sector is 25π m^2, and the area of circle R's sector is 49π m^2.

we have been asked to find the ratio of the radius of circle Q to the radius of circle R?

As we know that

Area of the sector is directly proportional to square of radius. So we can write

$Area \ \ \alpha \ \ r^2\\ \\ \Rightarrow A=kr^2\\ \\ \text{where k is some proportionality constant }\\ \\ \Rightarrow \frac{A_1}{A_2}=\frac{r_1^2}{r_2^2}\\ \\ \Rightarrow \frac{r_1^2}{r_2^2}=\frac{A_1}{A_2}\\ \\ \Rightarrow \frac{r_1^2}{r_2^2}=\frac{25 \pi}{49 \pi}\\ \\ \Rightarrow \frac{r_1}{r_2}=\sqrt{\frac{25 \pi}{49 \pi}} \\ \\ \Rightarrow \frac{r_1}{r_2}=\frac{5}{7} \\$