Consider the following short explanation.
Answer: a1=15; d= -8.
well then, the volume of the nose cone will just be the sum of the volume of the cylinder below and the cone above.
since the diameter for both is 8, then their radius is half that, or 4.
![\bf \stackrel{\textit{volume of a cone}}{V=\cfrac{\pi r^2 h}{3}}~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=4\\ h=6 \end{cases}\implies V=\cfrac{\pi (4)^2(6)}{3}\implies V=32\pi \\\\\\ \stackrel{\textit{volume of a cylinder}}{V=\pi r^2 h}~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=4\\ h=6 \end{cases}\implies V=\pi (4)^2(6)\implies V=96\pi \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{volume of the nose cone}}{32\pi +96\pi \implies 128\pi }\qquad \approx \qquad 402.12](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7Bvolume%20of%20a%20cone%7D%7D%7BV%3D%5Ccfrac%7B%5Cpi%20r%5E2%20h%7D%7B3%7D%7D~~%20%5Cbegin%7Bcases%7D%20r%3Dradius%5C%5C%20h%3Dheight%5C%5C%20%5Ccline%7B1-1%7D%20r%3D4%5C%5C%20h%3D6%20%5Cend%7Bcases%7D%5Cimplies%20V%3D%5Ccfrac%7B%5Cpi%20%284%29%5E2%286%29%7D%7B3%7D%5Cimplies%20V%3D32%5Cpi%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bvolume%20of%20a%20cylinder%7D%7D%7BV%3D%5Cpi%20r%5E2%20h%7D~~%20%5Cbegin%7Bcases%7D%20r%3Dradius%5C%5C%20h%3Dheight%5C%5C%20%5Ccline%7B1-1%7D%20r%3D4%5C%5C%20h%3D6%20%5Cend%7Bcases%7D%5Cimplies%20V%3D%5Cpi%20%284%29%5E2%286%29%5Cimplies%20V%3D96%5Cpi%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bvolume%20of%20the%20nose%20cone%7D%7D%7B32%5Cpi%20%2B96%5Cpi%20%5Cimplies%20128%5Cpi%20%7D%5Cqquad%20%5Capprox%20%5Cqquad%20402.12)
Answer:
x = 7.5y
Step-by-step explanation:
Simplifying
4.2(2x + -0.5y) + -2(4.1x + -0.3y) = 0
(2x * 4.2 + -0.5y * 4.2) + -2(4.1x + -0.3y) = 0
(8.4x + -2.1y) + -2(4.1x + -0.3y) = 0
8.4x + -2.1y + (4.1x * -2 + -0.3y * -2) = 0
8.4x + -2.1y + (-8.2x + 0.6y) = 0
Reorder the terms:
8.4x + -8.2x + -2.1y + 0.6y = 0
Combine like terms: 8.4x + -8.2x = 0.2x
0.2x + -2.1y + 0.6y = 0
Combine like terms: -2.1y + 0.6y = -1.5y
0.2x + -1.5y = 0
Solving
0.2x + -1.5y = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '1.5y' to each side of the equation.
0.2x + -1.5y + 1.5y = 0 + 1.5y
Combine like terms: -1.5y + 1.5y = 0.0
0.2x + 0.0 = 0 + 1.5y
0.2x = 0 + 1.5y
Remove the zero:
0.2x = 1.5y
Divide each side by '0.2'.
x = 7.5y
Simplifying
x = 7.5y
