The Law of Cosines is useful for this.
d² = e² + f² - 2ef·cos(D)
cos(D) = (e² + f² - d²)/(2ef) = (1.8² + 3.1² - 2²)/(2·1.8·3.1)
D = arccos(8.85/11.16)
D ≈ 37.5°
Answer:
![\mathsf {z = \frac{41}{24}}](https://tex.z-dn.net/?f=%5Cmathsf%20%7Bz%20%3D%20%5Cfrac%7B41%7D%7B24%7D%7D)
Step-by-step explanation:
![\textsf {Given :}](https://tex.z-dn.net/?f=%5Ctextsf%20%7BGiven%20%3A%7D)
![\mathsf {\frac {2x + y - 3z}{y + 3x} = \frac{x}{2y} }](https://tex.z-dn.net/?f=%5Cmathsf%20%7B%5Cfrac%20%7B2x%20%2B%20y%20-%203z%7D%7By%20%2B%203x%7D%20%3D%20%5Cfrac%7Bx%7D%7B2y%7D%20%7D)
![\textsf {Substituting the values given (x = 1, y = 4) :}](https://tex.z-dn.net/?f=%5Ctextsf%20%7BSubstituting%20the%20values%20given%20%28x%20%3D%201%2C%20y%20%3D%204%29%20%3A%7D)
![\mathsf {\frac {2(1) + 4 - 3z}{4 + 3(1)} = \frac{1}{2(4)} }](https://tex.z-dn.net/?f=%5Cmathsf%20%7B%5Cfrac%20%7B2%281%29%20%2B%204%20-%203z%7D%7B4%20%2B%203%281%29%7D%20%3D%20%5Cfrac%7B1%7D%7B2%284%29%7D%20%7D)
![\mathsf {\frac {6 - 3z}{7} = \frac{1}{8} }](https://tex.z-dn.net/?f=%5Cmathsf%20%7B%5Cfrac%20%7B6%20-%203z%7D%7B7%7D%20%3D%20%5Cfrac%7B1%7D%7B8%7D%20%7D)
![\textsf {Cross multiply the values :}](https://tex.z-dn.net/?f=%5Ctextsf%20%7BCross%20multiply%20the%20values%20%3A%7D)
![\mathsf {8(6 - 3z) = 7}](https://tex.z-dn.net/?f=%5Cmathsf%20%7B8%286%20-%203z%29%20%3D%207%7D)
![\mathsf {48 - 24z = 7}](https://tex.z-dn.net/?f=%5Cmathsf%20%7B48%20-%2024z%20%3D%207%7D)
![\mathsf {24z = 41}](https://tex.z-dn.net/?f=%5Cmathsf%20%7B24z%20%3D%2041%7D)
![\mathsf z = {\frac{41}{24}}](https://tex.z-dn.net/?f=%5Cmathsf%20z%20%3D%20%7B%5Cfrac%7B41%7D%7B24%7D%7D)
Y=0.09375 you just divide 3/8 by 1/4 to get the y.
Answer:
The width is 8
Step-by-step explanation:
if the ratio of length to width is 9 to 4. and we know the length is 18, 18 is 2 times as much as 9, so 4*2=8. 9*2=18,4*2=8
1920 fluid ounces
1 gallon = 128 fluid ounces
15 * 128 = 1920 oz