The amount of money divided by the amount of hours will give you how much money she makes per hour.
451.78/14=32.27.
She earned $32.27 per hour.
Answer:
first one
2m=1 == 2+m-1+m
Step-by-step explanation:
Answer:
The edge length will be equal to 4 inches.
Step-by-step explanation:
The volume of a cube = s * s * s (in which s represent side of the cube)
V = s * s * s
V = s³
64 = s³
64 = 4³
So edge length of the cube will be 4 inches.
Answer:
89.1° or -1.4°
Step-by-step explanation:
1. Location:
You are on the Mont-Saint-Jean escarpment, near the Belgian town of Waterloo.
The French troops are about 50 m below you and 1.2 km distant.
2. Finding the firing angle
Data:
R = 1200 m
u = 600 m/s
h = -50 m (the height of the target)
a = 9.8 m/s²
We have two conditions.
Horizontal distance
(1) 1200 = 600t cosθ
Vertical distance
(2) -50 = 600t sinθ - 4.9t²
Divide each side of (1) by 600cosθ.
![(3) \, t =\dfrac{2}{\cos \theta}](https://tex.z-dn.net/?f=%283%29%20%5C%2C%20t%20%3D%5Cdfrac%7B2%7D%7B%5Ccos%20%5Ctheta%7D)
Substitute (3) into (2)
![-50 = 600t \sin \theta - 4.9t^{2} = 600 \left( \dfrac{2}{\cos \theta} \right ) \sin \theta - 4.9 \left( \dfrac{2}{\cos \theta} \right )^{2}\\\\(4) \, -50 = 1200 \tan \theta - \dfrac{19.6}{\cos^{2} \theta}](https://tex.z-dn.net/?f=-50%20%3D%20600t%20%5Csin%20%5Ctheta%20-%204.9t%5E%7B2%7D%20%3D%20%20600%20%5Cleft%28%20%5Cdfrac%7B2%7D%7B%5Ccos%20%5Ctheta%7D%20%5Cright%20%29%20%5Csin%20%5Ctheta%20-%204.9%20%5Cleft%28%20%5Cdfrac%7B2%7D%7B%5Ccos%20%5Ctheta%7D%20%5Cright%20%29%5E%7B2%7D%5C%5C%5C%5C%284%29%20%5C%2C%20-50%20%3D%201200%20%5Ctan%20%5Ctheta%20-%20%5Cdfrac%7B19.6%7D%7B%5Ccos%5E%7B2%7D%20%5Ctheta%7D)
Recall that
(5) sec²θ = 1/cos²θ = tan²θ + 1
Substitute (5) into (4)
![-50 = 1200 \tan \theta - 19.6 \left(\tan^{2} \theta}+ 1\right )](https://tex.z-dn.net/?f=-50%20%3D%201200%20%5Ctan%20%5Ctheta%20-%2019.6%20%5Cleft%28%5Ctan%5E%7B2%7D%20%5Ctheta%7D%2B%201%5Cright%20%29)
Set up a quadratic equation
![\begin{array}{rcl}-50 & = & 1200 \tan \theta - 19.6\tan^{2} \theta -19.6 \\0 & = & 1200 \tan \theta - 19.6\tan^{2} \theta + 30.4\\0 & =&19.6\tan^{2} \theta - 1200 \tan \theta - 30.4\\0 & =&\tan^{2} \theta - 61.224 \tan \theta - 1.551\\\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcl%7D-50%20%26%20%3D%20%26%201200%20%5Ctan%20%5Ctheta%20-%2019.6%5Ctan%5E%7B2%7D%20%5Ctheta%20-19.6%20%5C%5C0%20%26%20%3D%20%26%201200%20%5Ctan%20%5Ctheta%20-%2019.6%5Ctan%5E%7B2%7D%20%5Ctheta%20%2B%2030.4%5C%5C0%20%26%20%3D%2619.6%5Ctan%5E%7B2%7D%20%5Ctheta%20-%201200%20%5Ctan%20%5Ctheta%20-%2030.4%5C%5C0%20%26%20%3D%26%5Ctan%5E%7B2%7D%20%5Ctheta%20-%2061.224%20%5Ctan%20%5Ctheta%20-%201.551%5C%5C%5Cend%7Barray%7D)
Solve for θ
Use the quadratic formula.
tanθ = 61.249 or -0.025
θ = arctan(61.249) = 89.1° or
θ = arctan(-0.025) = -1.4°