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The width, length, and height of a rectangular prism are each increased by 10% . What is the percent increase in the volume of the prism? Express your answer to the nearest whole number.

waffles  Nov 10, 2017

Best Answer 

 #3
avatar+1375 
+1

1. Find the Slope

 

Finding the slope is relatively simple once you remember the formula. For me, I could not memorize any formulas unless I put them in words. I remember this formula as the ratio of the difference in y-values to x-values, if that helps. Anyway, here is the formula.

 

\(m=\frac{y_2-y_1}{x_2-x_1}\)

 

\(m=\frac{y_2-y_1}{x_2-x_1}\) Now, plug in the coordinates into their respective positions in the formula. 
\(m=\frac{5+16}{4+3}\) Simplify the value of the slope completely.
\(m=\frac{21}{7}=3\)  
   

 

Now that the slope has been determined, one can move on to the next step.

 

2. Plug in a Coordinate for X and Y to Solve for B.

 

We now know the slope, so the equation of the line is now \(y=3x+b\). Based on the given info, we know that both Cartesian coordinates, (-3,-16) and (4,5) lie on this line. Substitute one point in its place for x and for y to findt he answer.

 

\(y=3x+b\) I will substitute the second point, \((\textcolor{red}{4},\textcolor{blue}{5})\) in the equation. It does not matter which point one chooses to substitute in.
\(\textcolor{blue}{5}=3*\textcolor{red}{4}+b\) Notice how the substitution replaces the coordinate. Now, solve for b.
\(5=12+b\) Subtract 12 from both sides to isolate b.
\(b=-7\)  
   

 

3. Write the Final Equation

 

Now that the only two necessary items, m and b, have been solved for, write the equation in y=mx+b format. 

 

m=3

b=-7

 

\(y=3x-7\)

 

You are done now!

TheXSquaredFactor  Nov 11, 2017
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3+0 Answers

 #1
avatar
+2

V =W x H x L

V =1.1 x 1.1 x 1.1

V =1.331 - 1 x 100 =33.1%=~33%. No matter what dimensions you choose for W, H, L, if you increase them ALL by 10%, the increase in volume will always be 33.1%.

Guest Nov 10, 2017
 #2
avatar+378 
0

Find the equation of the line passing through the points (-3, -16) and (4,5). Enter your answer in "y=mx+b" form.

waffles  Nov 10, 2017
 #3
avatar+1375 
+1
Best Answer

1. Find the Slope

 

Finding the slope is relatively simple once you remember the formula. For me, I could not memorize any formulas unless I put them in words. I remember this formula as the ratio of the difference in y-values to x-values, if that helps. Anyway, here is the formula.

 

\(m=\frac{y_2-y_1}{x_2-x_1}\)

 

\(m=\frac{y_2-y_1}{x_2-x_1}\) Now, plug in the coordinates into their respective positions in the formula. 
\(m=\frac{5+16}{4+3}\) Simplify the value of the slope completely.
\(m=\frac{21}{7}=3\)  
   

 

Now that the slope has been determined, one can move on to the next step.

 

2. Plug in a Coordinate for X and Y to Solve for B.

 

We now know the slope, so the equation of the line is now \(y=3x+b\). Based on the given info, we know that both Cartesian coordinates, (-3,-16) and (4,5) lie on this line. Substitute one point in its place for x and for y to findt he answer.

 

\(y=3x+b\) I will substitute the second point, \((\textcolor{red}{4},\textcolor{blue}{5})\) in the equation. It does not matter which point one chooses to substitute in.
\(\textcolor{blue}{5}=3*\textcolor{red}{4}+b\) Notice how the substitution replaces the coordinate. Now, solve for b.
\(5=12+b\) Subtract 12 from both sides to isolate b.
\(b=-7\)  
   

 

3. Write the Final Equation

 

Now that the only two necessary items, m and b, have been solved for, write the equation in y=mx+b format. 

 

m=3

b=-7

 

\(y=3x-7\)

 

You are done now!

TheXSquaredFactor  Nov 11, 2017

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