+647 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.
+2446 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!
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%.
+647 Find the equation of the line passing through the points (-3, -16) and (4,5). Enter your answer in "y=mx+b" form.
+2446 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!
