Micah deposited $4000 between two savings account. One account earns 4%

If there are 7.48 gallons in a cubic foot, and the volume of the tower is around 36000in cubed. Residents of the apartment building are using the water from the tower at an average rate of 56 gallons per minute, determine how long it will take to drain the entire tower.

Solution:

Volume = 36000in³

Conversion of in³ to ft³

1 inch = 0.0833 feet

12 inch = 1 ft

1 ft³ = 1ft × 1ft × 1ft

= 12 in x 12 in x 12 in = 1728 in³

36000in³ × [(1ft³)/(1728 in³) = (36000/1728)ft³

= 20.833ft³

Volume = 20.833ft³

There are 7.48 gallons in a cubic foot

In 20.833ft³ = 20.833ft³× (7.48 gallons/1ft³)

= 20.833× 7.48gallons

Volume = 155.83 gallons

The rate of usage = 56 gallons per minute

The rate of usage for 155.83 gallons = 155.83 gallons × (1min/56gallons)

= (155.83/56)minute

= 2.8minutes

Time it will take to drain the entire tower = 2.8minutes

5 0

3 years ago

Graph the following three equations on your own device and answer the questions below.

Alina [70]

Due to length restrictions, we kindly invite to read the explanation of this question for further details on functions.

<h3>What are the characteristics of each of the three functions?</h3>

a) In this part we must evaluate each of the three functions at the given value of x:

Case 1

f(10) = 5 · 10 + 7

f(10) = 57

Case 2

f(10) = 10² + 6

f(10) = 106

Case 3

f(10) = 2¹⁰ + 3

f(10) = 1027

b) In this part we must evaluate each of the three functions at the given value of x:

Case 1

f(100) = 5 · 100 + 7

f(100) = 507

Case 2

f(100) = 100² + 6

f(100) = 10006

Case 3

f(100) = 2¹⁰⁰ + 3

f(100) = 1.267 × 10³⁰ + 3

c) In this part we must evaluate each of the three functions at the given value of x:

Case 1

f(1000) = 5 · 1000 + 7

f(1000) = 5007

Case 2

f(1000) = 1000² + 6

f(1000) = 1000006

Case 3

f(1000) = 2¹⁰⁰⁰ + 3

f(1000) = (1.268 × 10³⁰)¹⁰ + 3

f(1000) = 10.744 × 10³⁰⁰ + 3

f(1000) = 1.074 × 10³⁰¹ + 3

e) The third function increases the fastest.

f) In this part we need to compare the third function with respect to the first and second functions:

5 · x + 7 = 2ˣ + 3

2ˣ - 5 · x = 4

The solutions of the equation are x = - 0.675 and x = 4.81. The function will exceed the other first function at x = 4.81.

x² + 6 = 2ˣ + 3

2ˣ - x² = 3

The solution of the equation is x = 4.588. The function will exceed the other second function at x = 4.588.

g) Yes, exponential functions with bases greater than 1 will surpass polynomic function at any point x such that x > 0.

h) The domain represents the set of x-values of a function and the range represents the set of y-values of a function. Then, the domain and range of each function is:

Case 1

Domain - All real numbers.

Range - All real numbers

Case 2

Domain - All real numbers.

Range - [6, +∞)

Case 3

Domain - All real numbers.

Range - (3, +∞)

To learn more on functions: brainly.com/question/12431044

#SPJ1

5 0

1 year ago