1. D 12 2/7
2. 22 7/9 which is B hope this helps
V=(4/3)pir^3
r=9
V=(4/3)pi9^3
V=12pi243
V=972pi
aprox pi=3.14
3052.08 mi^3
Answer:
14 miles.
Step-by-step explanation:
Let the distance traveled from home to destination = x miles.
Speed while going to friend's house = 35 miles per hour.
Speed while coming back = 40 miles per hour.
Total Time taken for the journey = 45 minutes = 0.75 hours.
Let the time taken while going to friend's house = y hours.
Therefore, the time taken while going to friend's house = (0.75 - y) hours.
To find x and y, model the speeds of both the journeys.
Speed while going to friend's house = Distance/Time.
35 = x/y.
x = 35y (Equation 1).
Speed while coming back = Distance/Time.
40 = x/(0.75 - y).
x = 40(0.75 - y) (Equation 2).
Since x = x, therefore:
35y = 30 - 40y.
75y = 30.
y = 30/75.
y = 0.4 hours.
Put y = 0.4 hours in Equation 1:
x = 35y.
x = 35(0.4).
x = 14.
Therefore, the distance between my friend's house and my house is 14 miles!!!
Using the Sine rule,
![\begin{gathered} \text{Let A = 14m,} \\ Substituting the variables into the formula,Where the length of the wires are, AP = xm and BP = ym[tex]\begin{gathered} \frac{\sin80^0}{14}=\frac{\sin40^0}{x} \\ \text{Crossmultiply,} \\ x\times\sin 80^0=14\times\sin 40^0 \\ Divide\text{ both sides by }\sin 80^0 \\ x=\frac{14\sin40^0}{\sin80^0} \\ x=9.14m \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctext%7BLet%20A%20%3D%2014m%2C%7D%20%5C%5C%20Substituting%20the%20variables%20into%20the%20formula%2C%3Cp%3EWhere%20the%20length%20of%20the%20wires%20are%2C%20AP%20%3D%20xm%20and%20BP%20%3D%20ym%3C%2Fp%3E%5Btex%5D%5Cbegin%7Bgathered%7D%20%5Cfrac%7B%5Csin80%5E0%7D%7B14%7D%3D%5Cfrac%7B%5Csin40%5E0%7D%7Bx%7D%20%5C%5C%20%5Ctext%7BCrossmultiply%2C%7D%20%5C%5C%20x%5Ctimes%5Csin%2080%5E0%3D14%5Ctimes%5Csin%2040%5E0%20%5C%5C%20Divide%5Ctext%7B%20both%20sides%20by%20%7D%5Csin%2080%5E0%20%5C%5C%20x%3D%5Cfrac%7B14%5Csin40%5E0%7D%7B%5Csin80%5E0%7D%20%5C%5C%20x%3D9.14m%20%5Cend%7Bgathered%7D)
Hence, the length of wire AP (x) is 9.14m.
For wire BP (y)m,
Sum of angles in a triangle is 180 degrees,
Using the side rule to find the length of wire BP,
Hence, the length of wire BP (y) is 12.31m
Therefore, the length of the wires are (9.14m and 12.31m).
