Answer:
The kinetic energy is 20,000\ J
Step-by-step explanation:
The kinetic energy of a body is defined as:
![k = \frac{1}{2}ms ^ 2](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B1%7D%7B2%7Dms%20%5E%202)
Where <em>m</em> is the mass of the roller coaster car
<em>s</em> is the speed and <em>k</em> is the kinetic energy
We know that ![s = 20\ m/s](https://tex.z-dn.net/?f=s%20%3D%2020%5C%20m%2Fs)
![m = 100\ kg](https://tex.z-dn.net/?f=m%20%3D%20100%5C%20kg)
Then the kinetic energy of the roller coaster car is:
![k = \frac{1}{2}(100)(20) ^ 2\\\\k = 50(20) ^ 2\\\\k = 50 * 400\\\\k = 20,000\ J](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B1%7D%7B2%7D%28100%29%2820%29%20%5E%202%5C%5C%5C%5Ck%20%3D%2050%2820%29%20%5E%202%5C%5C%5C%5Ck%20%3D%2050%20%2A%20400%5C%5C%5C%5Ck%20%3D%2020%2C000%5C%20J)
![\frac{3x}{x-4} - \frac{x+3}{x-4} = \frac{2x+7}{x^2-16}](https://tex.z-dn.net/?f=%5Cfrac%7B3x%7D%7Bx-4%7D%20%20-%20%5Cfrac%7Bx%2B3%7D%7Bx-4%7D%20%3D%20%5Cfrac%7B2x%2B7%7D%7Bx%5E2-16%7D)
We factor the denominators
Factor x^2 - 16
x^2 - 4^2
We use a^2 - b^2 = (a+b)(a-b)
so x^2 - 4^2 = (x+4)(x-4)
Replace it in the given equation
![\frac{3x}{x-4} - \frac{x+3}{x-4} = \frac{2x+7}{(x+4)(x-4)}](https://tex.z-dn.net/?f=%5Cfrac%7B3x%7D%7Bx-4%7D%20%20-%20%5Cfrac%7Bx%2B3%7D%7Bx-4%7D%20%3D%20%5Cfrac%7B2x%2B7%7D%7B%28x%2B4%29%28x-4%29%7D)
Excluded values are the values that makes the denominator 0
we have (x-4) and (x+4) in the denominator
We set the denominator =0 and solve for x
x-4 =0
Add 4 on both sides
x= 4
x+4=0
subtract 4 onboth side
so x= -4
Excluded values are x=-4 and x=4
Answer:
0.20 - $117.76= $16.62
Step-by-step explanation:
if you have a percentage you can always turn it into a decimal just put the number behind the period: 70% = .70, 49% = .49% ....
then you do the rest of the equation and BOOM!
20% - $117.76 = $16.62 = 0.20 - $117.76= $16.62.
So you make common denominators 5/10 + 6/100 so it would be 5x10/10x10 would become 50/100 + 6/100
and would equal 56/100.
Answer: 3/5
Step-by-step explanation:
1. Multiply 30 by 3 (90)
2. 90 becomes the numerator and 150 becomes the denominator
3. Divide the numerator (90) and the denominator (150) by the greatest common factor (30), to simplify the fraction
4. You should come to the answer 3/5
Hope this helps.