solve p varies directly as the square of s and inversely as r, when s=6,r=3,and p=48 find the value of p when s =10and r=5

see explanation

Step-by-step explanation:

Given that p varies directly as s² and inversely as r then the equation relating them is

p = ← k is the constant of variation

To find k use the condition when s = 6, r = 3 and p = 48, that is

48 = ( multiply both sides by 3 to clear the fraction

144 = 36k ( divide both sides by 36 )

4 = k , thus

p = ← equation of variation

When s = 10 and r = 5 , then

p = = = 80

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.