4. Think about it, it would mean that 4 is the result of 0.4 (40%) multiplied by a number. Therefore, you would divide 4 by 0.4. The answer would be 10.
5. To do this, multiply 0.2 by 700. This gives you 140.
6. Think about it, what percent of 25 is 12. Divide 12 by 25, then multiply by 100 and add a percent sign after it. 12/25 is 0.48. Multiply that by 100 to get 48%.
Answer:
The easiest way to solve this system would be to use substitution since x is already isolated in the first equation. Whenever one equation is already solved for a variable, substitution will be the quickest and easiest method
Answer:
Step-by-step explanation:
1-true
2-false
3-true
4-false
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°
Answer:
The equations for the growth of two type of species are
H(m) = 12 + 2m
H(m) = 10 + 3m
Step-by-step explanation:
As given
The growth rate of two species of plants.
Species A is 12 cm tall and grows 2 cm per month.
The height of each species is represented by H(m) as a function of months m.
Than the equation becomes
H(m) = 12 + 2m
As given
Species B is 10 cm tall and grows 3 cm per month.
Than the equation becomes
H(m) = 10 + 3m
Than the equations for the growth of two type of species are
H(m) = 12 + 2m
H(m) = 10 + 3m