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3 years ago

Determine the lateral area of a pipe that is 12 ft long and 25 ft in diameter.

Mathematics

1 answer:

Zina [86]3 years ago

8 0

Answer:

The lateral area of the pipe is 942 sq ft.

Step-by-step explanation:

A pipe can be modeled as a cylinder prism.

The lateral area of a cylinder prism can be expressed as the product of the length by the perimeter of the section.

We start by calculating this perimeter.

As the diameter is 25 ft, the perimeter of the section can be expressed as:

$P=\pi D=3.14\cdot 25=78.5$

Then, to know the lateral surface we multiply this perimeter by the length of the pipe (12 ft):

$A=P\cdot l=78.5\,ft\cdot 12\,ft=942\,ft^2$

The lateral area of the pipe is 942 sq ft.

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HELPPPP 100 points if you help!!!!

nignag [31]

Answer:

Part A)

Chorus:

$c(t)=15(1.12)^t$

Band:

$b(t)=2t+30$

Part B)

After 9 years:

The chorus will have about 41 people.

And the band will have 48 people.

Part C)

About approximately 11 years.

Step-by-step explanation:

We are given that there are 15 people in the chorus. Each year, number of people in the chorus increases by 12%. So, the chorus increases exponentially.

There are 30 people in the band. Each year, 2 new people join the band. So, the band increases linearly.

Part A)

Since after each year, the number of people in the chorus increases by 12%, the new population will be 112% or 1.12 of the previous population.

So, using the standard form for exponential growth:

$c(t)=a(r)^t$

Where a is the initial population and r is the rate of change.

We will substitute 15 for a and 1.12 for r. Hence:

$c(t)=15(1.12)^t$

This represents the number of people in the chorus after t years.

We are given that 2 new people join the band each year. So, it increases linearly.

Since there are already 30 people in the band, our initial point or y-intercept is 30.

And since 2 new people join every year, our slope is 2. Then by the slope-intercept form:

$b(t)=mt+b$

And by substitution:

$b(t)=2t+30$

This represents the number of people in the band after t years.

Part B)

We want to find the number of people in the chorus and the band after 9 years.

Using the chorus function, we see that:

$c(9)=15(1.12)^9\approx41.59\approx41$

There will be approximately 41 people in the chorus after 9 years.

And using the band function, we see that:

$b(9)=2(9)+30=48$

There will be 48 people in the band after 9 years.

Part C)

We want to determine after approximately how many years will the number of people in the chorus and band be equivalent. Hence, we will set the two functions equal to each other and solve for t. So:

$15(1.12)^t=2t+30$

Unfortunately, it is impossible to solve for t using normal analytic methods. Hence, we can graph them. Recall that graphically, our equation is the same as saying at what point will our two functions intersect.

Referring to the graph below, we can see that the point of intersection is at approximately (10.95, 51.91).

Hence, after approximately 11 years, both the chorus and the band will have approximately 52 people.

5 0

3 years ago

Write each equation in slope-intercept form. underline the slope and circle the y-intercept in each equation 5x+3y=30

faust18 [17]

Answer:

The slope is

The y-intercept is

−

Explanation:

−

is the standard form for a linear equation. The slope-intercept form is

, where

is the slope, and

is the y-intercept. To convert from standard form to slope-intercept form, solve the standard form for

−

Subtract

from both sides of the equation.

−

Divide both sides by

−

Rearrange the right hand side.

−

graph{y=5/3x-10 [-10, 10, -5, 5]}

4 0

3 years ago

Read 2 more answers

In the regular pentagon below, if AP = 4 m and BC = 10 m, find it's area.

12345 [234]

First symmetrically cut the pentagon to get 5 pieces. (So that you will get the idea that this polygon is divided into 5 triangles)

Then find the area of one of the triangles:

Area of Triangle = $\frac{1}{2} bh$

A = $\frac{1}{2}$ × 4 × 10

A = 20 m²

To find the area of the whole pentagon shape:

A = 20 × 5 = 100 m²

Hope it helps!

4 0

2 years ago

What equation could be used to determine 23% of 122?

ArbitrLikvidat [17]

First, convert 23% into a fraction.

23% =

$23 \div 100 = \frac{23}{100}$

Now the expression to determine 23% of 122 is

$\frac{23}{100} \times 122 \\ = ( \frac{23}{100} )(122)$

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3 years ago

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Awesome Car company sold 20 cars this week.their goal is to sell at least 25% more next week. Write an inequality that represent

Serga [27]

Twenty-five percent (25%) of 20 is equal to 5. Therefore, the company is planning or targeting to sell at least 25 cars next week. We let the number of cars be x. The inequality that best represent the scenario above is,
x ≥ 25

6 0

3 years ago

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