The question is Fiona's swimming pool is a right rectangular prism. It holds 137 1/2 cubic feet of water. The length of the pool is 6 1/4 feet. The width of the pool is 5 1/2 feet. What is the height of the pool? I searched it up but it gave me different questions that have the name Fiona. I was wondering if you were able to answer it.

The width is 4 feet

Step-by-step explanation:

Yes, I might be able to answer it! Hello there!

In this question, we are asked to calculate the height of a pool which has a shape of right rectangular prism.

The key to solving this problem is simply by knowing the formula for the volume of a right rectangular prism.

Mathematically the volume V is w * h * l where w , h and l are the width, height and length respectively.

Now let’s input these values and get what the height of the pool is.

It would be easier if you had the measurements are in decimals;

137 1/2 becomes 137.5

6 1/4 becomes 6.25

5 1/2 becomes 5.5

kindly note the fraction 1/2 is 0.5 in decimals while the fraction 1/4 is 0.25 in decimals

So now let’s compute the height;

137.5 = w * 6.25 * 5.5

w = 137.5/(6.25 * 5.5)

w = 137.5/(34.375)

w = 4 feet

part a

answer: a reasonable domain is where n is a real number. so n can be between 0 and 10. both endpoints are included.

work shown:

n is the number of days after the experiment starts. the smallest n can be is n = 0 which means that 0 days have gone by, and we're at the start. to find out how large n should be, then replace f(n) with 16.13 and solve for n. use logarithms to isolate the exponent.

f(n) = 12*(1.03)^n

16.13 = 12*(1.03)^n

16.13/12 = (1.03)^n

1.34416666666667 = (1.03)^n

(1.03)^n = 1.34416666666667

log[ (1.03)^n ] = log[ 1.34416666666667 ]

n*log[ 1.03 ] = log[ 1.34416666666667 ]

n = log[ 1.34416666666667 ]/log[ 1.03 ]

n = 10.0062999823929

this rounds to n = 10 which is fairly close but not 100% perfect. so this is the largest n can be.

note: if you plug n = 10 into f(n), you'll get roughly 16.127 which rounds to 16.13 (this comes up again in part c)

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part b

answer: the y intercept is 12. it represents the starting height of the plant in cm.

work shown:

plug n = 0 into the f(n) function. simplify

f(n) = 12*(1.03)^n

f(0) = 12*(1.03)^0

f(0) = 12*(1)

f(0) = 12

on day n = 0, aka the starting point, the height f(n) is 12 cm

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part c

answer: the average rate of change is approximately 0.43061036458991 (round however you need to). this represents the average growth rate from day n = 3 to day n = 10. so the plant grew roughly 0.43 cm per day during this timespan, assuming you round to 2 decimal places.

work shown:

compute f(3)

f(n) = 12*(1.03)^n

f(3) = 12*(1.03)^3

f(3) = 13.112724 < we'll use this later

compute f(10)

f(n) = 12*(1.03)^n

f(10) = 12*(1.03)^10

f(10) = 16.1269965521294 < we'll use this later

now use the formula below with a = 3 and b = 10

aroc = average rate of change

aroc = [ f(b) - f(a) ]/[ b - a ]

aroc = [ f(10) - f(3) ]/[ 10 - 3 ]

aroc = (16.1269965521294 - 13.112724)/(10 - 3)

aroc = 3.0142725521294/7

aroc = 0.43061036458991

round this however you need to

note: the plant grew approximately 3.01 cm over 7 days, so roughly 0.43 cm per day is the average growth rate (if you were to round to 2 decimal places).

126 maybe. sorry