Answer:
![27 {m}^{6} {n}^{12}](https://tex.z-dn.net/?f=27%20%7Bm%7D%5E%7B6%7D%20%20%7Bn%7D%5E%7B12%7D%20)
Step-by-step explanation:
3 is the power of whole expression.
so,
that can be expressed as
![= {3}^{3} { ({m}^{2} })^{3} { ({n}^{4}) }^{3} \\ = 27 {m}^{6} {n}^{12}](https://tex.z-dn.net/?f=%20%20%3D%20%7B3%7D%5E%7B3%7D%20%20%7B%20%28%7Bm%7D%5E%7B2%7D%20%7D%29%5E%7B3%7D%20%20%7B%20%28%7Bn%7D%5E%7B4%7D%29%20%7D%5E%7B3%7D%20%20%5C%5C%20%20%3D%2027%20%7Bm%7D%5E%7B6%7D%20%20%7Bn%7D%5E%7B12%7D%20)
Answer:
The equation of the graph after translating one unit to the left is;
![y = \left | \dfrac{x}{2} - \dfrac{3}{2} \right |+3](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cleft%20%7C%20%5Cdfrac%7Bx%7D%7B2%7D%20-%20%5Cdfrac%7B3%7D%7B2%7D%20%20%5Cright%20%7C%2B3)
Step-by-step explanation:
The given equation is ![y = \left | \dfrac{1}{2}\cdot x - 2 \right |+3](https://tex.z-dn.net/?f=y%20%3D%20%5Cleft%20%7C%20%5Cdfrac%7B1%7D%7B2%7D%5Ccdot%20x%20-%202%20%5Cright%20%7C%2B3)
We note that minimum value of y = 3, where 1/2·x - 2 = 0 and x = 4
Therefore, in moving one unit to the left, we have at the y-intercept where slope of the graph has become inverted (reflection of the real graph) we add one to the x value as follows;
![y = \left | \dfrac{1}{2}\cdot (x+1) - 2 \right |+3 = \left | \dfrac{x}{2} + \dfrac{1}{2} - 2 \right |+3 = \left | \dfrac{x}{2} - \dfrac{3}{2} \right |+3](https://tex.z-dn.net/?f=y%20%3D%20%5Cleft%20%7C%20%5Cdfrac%7B1%7D%7B2%7D%5Ccdot%20%28x%2B1%29%20-%202%20%5Cright%20%7C%2B3%20%3D%20%20%5Cleft%20%7C%20%5Cdfrac%7Bx%7D%7B2%7D%20%2B%20%5Cdfrac%7B1%7D%7B2%7D%20%20-%202%20%5Cright%20%7C%2B3%20%3D%20%20%5Cleft%20%7C%20%5Cdfrac%7Bx%7D%7B2%7D%20-%20%5Cdfrac%7B3%7D%7B2%7D%20%20%5Cright%20%7C%2B3)
The equation of the graph becomes;
.
Answer:
0.44 seconds
Step-by-step explanation:
<u>Time period is the time duration for completing one oscillation:</u>
<u>Answer is</u> 0.44 seconds
The first step in 'working' the equation is <u>knowing</u> the equation,
and writing it down. You're not even there yet.
I think this picture is saying that all the sides of the little squares are
all congruent ... all the same length ... and the distance from 'C' to 'D' is
two of them.
Also, the length of one of them is x²-x+8 , and the length of another one
is x²+2x-7. . . . the ones that are marked in yellow.
Well, what now ? Do you think it might help if you knew the size of 'x' ?
Is there a way to find it ?
Remember . . . all the sides of all the little squares are marked congruent.
So both yellow pieces are the same length !
<u>x² - x + 8 = x² + 2x - 7</u>
<em>THAT</em>'s the equation you have to 'work'. Now you're off and running !
Subtract x² from each side: -x + 8 = 2x - 7
Add 'x' to each side: 8 = 3x - 7
Add 7 to each side: 15 = 3x
Divide each side by 3 : <em>5 = x </em>.
There you are. Now you know what 'x' is. So you can find
the length of either yellow piece, and the length of 'CD' is
just two of those.
I'm sure you can handle it from here.
Answer:
360
Step-by-step explanation: