Answer:
A: 1839 ft
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relationships between sides and angles of a right triangle. Here you have an angle and its opposite side, and you want to find the length of the hypotenuse. The appropriate relation is ...
Sin = Opposite/Hypotenuse
sin(22°) = (689 ft)/(ride length)
Solving for ride length, we get ...
ride length = (689 ft)/sin(22°) ≈ 1839.26 ft
The length of the gondola ride is about 1839 feet.
Answer:
The variation equation is
![f = \frac{k.m_1.m_2}{ {r}^{2} }](https://tex.z-dn.net/?f=%20f%20%3D%20%20%5Cfrac%7Bk.m_1.m_2%7D%7B%20%7Br%7D%5E%7B2%7D%20%7D%20)
step-by-step explanation:
From the question, the two masses are
![m_1 \: and \: m_2](https://tex.z-dn.net/?f=m_1%20%5C%3A%20and%20%5C%3A%20m_2)
This implies that the product of the two masses
![= m_1 \times m_2 = m_1.m_2](https://tex.z-dn.net/?f=%20%3D%20m_1%20%5Ctimes%20m_2%20%3D%20m_1.m_2)
Moreover, the force,f varies directly with the products of the two masses
![\implies \: f\propto m_1.m_2....eqn.1](https://tex.z-dn.net/?f=%20%5Cimplies%20%5C%3A%20f%5Cpropto%20m_1.m_2....eqn.1)
Also, the force varies inversely with the square of the distance,r
![\implies \: f\propto \frac{1}{ {r}^{2} }.......eqn.2](https://tex.z-dn.net/?f=%20%5Cimplies%20%5C%3A%20f%5Cpropto%20%5Cfrac%7B1%7D%7B%20%7Br%7D%5E%7B2%7D%20%7D.......eqn.2)
Joining equation 1 and 2, we got
![\implies \: f\propto \frac{1}{ {r}^{2}} \times m_1.m_2](https://tex.z-dn.net/?f=%20%5Cimplies%20%5C%3A%20f%5Cpropto%20%5Cfrac%7B1%7D%7B%20%7Br%7D%5E%7B2%7D%7D%20%5Ctimes%20m_1.m_2)
![\implies \: f \propto\frac{m_1.m_2}{ {r}^{2}}](https://tex.z-dn.net/?f=%20%5Cimplies%20%5C%3A%20f%20%5Cpropto%5Cfrac%7Bm_1.m_2%7D%7B%20%7Br%7D%5E%7B2%7D%7D)
But the constant of variation is k
Multiplying the right hand side of the equation by k, we got
![\implies \:f=\frac{k.m_1.m_2}{ {r}^{2}}](https://tex.z-dn.net/?f=%20%5Cimplies%20%5C%3Af%3D%5Cfrac%7Bk.m_1.m_2%7D%7B%20%7Br%7D%5E%7B2%7D%7D)
Step-by-step explanation:
if we simply add 1 to numerator and denominator (top and bottom of the fraction), we get a fraction that is bigger than the original fraction and smaller than the fraction that added 2 to numerator and denominator.
so, my choice would be
4/5
5/6
6/7
7/8
8/9
9/10
10/11
From all the information given, you're going to have to create two equations and solve accordingly.
If x=cost for one day at hotel; and y=cost for one day at amusement park then,
eq1 : 450=3x+2y ; eq2: 700=5x+3y
The total cost of the trip will be number of days spent at each location multiplied by the cost.
If you multiply equation 1 by 3 and equation 2 by 2 and subtract equation 2 from 1, than you will be able to isolate x.
1400=10x+6y
1350=9x+6y
x=$50; then plug back into any equation to find y.
450=3*50 + 2y
y=$150