Two cylindrical swimming pools are being filled simultaneously at the same rate. The smaller pool has a radius of 5 m, and the water level rises at a rate of 0.5m/min. The larger pool has a radius of 8 m. How fast is the water level rising in the larger pool?

0.195m/min

Step-by-step explanation:

The radii of the smaller pool =5m

The radii of the larger pool = 8m

DEFINITION:

Given two similar shapes, and the ratio of lengths in the two similar shapes, the ratio of the areas is a square of the ratio of the lengths.

The radii of the pools have a ratio of 5:8

Therefore, the ratio of surface areas will be  

Since the pools are being filled at the same rate  

Let the Volume of the Smaller Pool, and the height of the water be

Let the Volume of the Larger Pool, and the height of the water be

Volume of a cylinder = Base surface area X Height

The water level is rising in the larger pool at a rate of 0.195m/min

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.