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4 years ago

The Truit family rented the cabin shown in the shape in a triangular prism. The cabin is 30 feet deep. What is its volume?

Mathematics

1 answer:

aleksley [76]4 years ago

6 0

Answer:

Volume = 5625ft³

Step-by-step explanation:

Volume of a triangular prism = 1/2bhl

1/2 x base x height x length

Therefore we have in this case

Base = 15ft

Height = 30ft

Length = 25ft

Volume = 1/2 x 30 x 25 x 15

Volume = 5625ft³

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Step-by-step explanation:

We have been given a table, which represents the projected value of two different houses for three years.

Part A:

$\text{Increase in value of house 1 after one year}=294,580-286,000$

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$\text{Increase in value of house 2 after one year}=295,000-286,000$

$\text{Increase in value of house 2 after one year}=9,000$

$\text{Increase in value of house 2 after two years}=304,000-295,000$

$\text{Increase in value of house 2 after two years}=9,000$

We can see from our given table that the value of house 2 is increasing at a constant rat that is $9,000 per year. Since a linear function has a constant rate of change, therefore, a linear function can be used to describe the value of the house 2 after a fixed number of years.

Part B:

Let x be the number of years after Dominique bought the house 1.

Since value of house 1 is increasing exponentially, so let us find increase percent of value of house 1.

$\text{Increase }\%=\frac{\text{Final value-Initial value}}{\text{Initial value}}\times 100$

$\text{Increase }\%=\frac{294,580-286,000}{286,000}\times 100$

$\text{Increase }\%=\frac{8580}{286,000}\times 100$

$\text{Increase }\%=0.03\times 100$

$\text{Increase }\%=3$

$\text{Increase }\%=\frac{303,417.40-294,580}{294,580}\times 100$

$\text{Increase }\%=\frac{8837.4}{294,580}\times 100$

$\text{Increase }\%=0.03\times 100$

$\text{Increase }\%=3$

Therefore, the growth rate of house 1's value is 3%.

Since we know that an exponential function is in form: $y=a*b^x$ , where,

a = Initial value,

b = For growth b is in form (1+r), where, r is rate in decimal form.

$3\%=\frac{3}{100}=0.03$

Upon substituting our values in exponential function form we will get,

$f(x)=286,000(1+0.03)^x$ , where, f(x) represents the value of the house 1, in dollars, after x years.

Therefore, the function $f(x)=286,000(1.03)^x$ represents the value of house 1 after x years.

Let x be the number of years after Dominique bought the house 2.

We can see that when Dominique bought house 2 it has a value of $286,000. This means that at x equals 0 value of house will be $286,000 and it will be our y-intercept.

Since value of house 2 is increasing 9000 per year, therefore, slope of our line be 9000.

Upon substituting these values in slope-intercept form of equation $(y=mx+b)$ we will get,

$f(x)=9000x+286,000$ , where, f(x) represents the value of the house 2, in dollars, after x years.

Therefore, the function $f(x)=9000x+286,000$ represents the value of house 2 after x years.

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Since values in exponential function increases faster than linear function, so the value of house 1 will be greater than value of house 2.

Let us find the value of house 1 and house 2 by substituting x=25 in our both functions.

$f(25)=286,000(1.03)^{25}$

$f(25)=286,000*2.0937779296542148$

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We can see that value of house 1 after 25 years will be approx $598,820.48.

$f(25)=9000*25+286,000$

$f(25)=225,000+286,000$

$f(25)=511,000$

We can see that value of house 2 after 25 years will be approx $511,000.

Since $511,000 is less than $598820.48, therefore, value of house 1 is greater than value of house 2.

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