Answer:
X= 10, 20, 30, 40, 50, 60
Step-by-step explanation:thats
thats all i know
Answer:
Step-by-step explanation:
eq. of circle is x²+y²+2gx+2fy+c=0
center=(-g,-k)
given eq. is x²+y²+4x-8y+11=0
comparing
2gx=4x
g=2
2fy=-8y
f=-4
center=(-2,4)
Answer:
Step-by-step explanation:
a) period is the length of one cycle ( one full squiggle ) If you are lucky and the graph is on exact numbers.. at a high point and to the next high point.. then just take that horizontal distance, that's one period also if it's not you could find the period, T, by using T = 2pi / k where k is a number that represents how fast , or how many times the wave cycles in one second or some other amount of time.
b) Amplitude is a number that goes right before the sinusoid, which is multiplied by it because, sin , cos, are at max 1 or at min -1
c) vertical shift is what is added , for upwards shift... before or after the sinusoid ie sin , cos, ect ect.
does this help?
Answer:
Step-by-step explanation:
We are given the function:
And we want to determine:
Substitute:
![\displaystyle \begin{aligned}g(x + a) - g(x) &=\left[5(x+a)^2 + 2(x+a)\right] -\left[5x^2+2x\right] \end{aligned}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cbegin%7Baligned%7Dg%28x%20%2B%20a%29%20-%20g%28x%29%20%26%3D%5Cleft%5B5%28x%2Ba%29%5E2%20%2B%202%28x%2Ba%29%5Cright%5D%20-%5Cleft%5B5x%5E2%2B2x%5Cright%5D%20%20%20%20%5Cend%7Baligned%7D)
And simplify:
![\displaystyle \begin{aligned}g(x + a) - g(x) &=\left[5(x+a)^2 + 2(x+a)\right] -\left[5x^2+2x\right] \\ \\ &= \left(5(x^2 + 2ax + a^2) + (2x + 2a) \right) + \left(-5x^2 - 2x\right) \\ \\ &= \left((5x^2 + 10ax + 5a^2) + (2x + 2a)\right) + \left(-5x^2 - 2x\right) \\ \\ &= (5x^2-5x^2) + (10ax + 2x - 2x) + (5a^2+2a) \\ \\ &= 10ax + 5a^2 + 2a \end{aligned}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cbegin%7Baligned%7Dg%28x%20%2B%20a%29%20-%20g%28x%29%20%26%3D%5Cleft%5B5%28x%2Ba%29%5E2%20%2B%202%28x%2Ba%29%5Cright%5D%20-%5Cleft%5B5x%5E2%2B2x%5Cright%5D%20%5C%5C%20%20%5C%5C%20%26%3D%20%5Cleft%285%28x%5E2%20%2B%202ax%20%2B%20a%5E2%29%20%2B%20%282x%20%2B%202a%29%20%5Cright%29%20%2B%20%5Cleft%28-5x%5E2%20-%202x%5Cright%29%20%5C%5C%20%5C%5C%20%26%3D%20%5Cleft%28%285x%5E2%20%2B%2010ax%20%2B%205a%5E2%29%20%2B%20%282x%20%2B%202a%29%5Cright%29%20%2B%20%5Cleft%28-5x%5E2%20-%202x%5Cright%29%20%5C%5C%20%5C%5C%20%26%3D%20%285x%5E2-5x%5E2%29%20%2B%20%2810ax%20%2B%202x%20-%202x%29%20%2B%20%285a%5E2%2B2a%29%20%20%20%20%20%5C%5C%20%5C%5C%20%26%3D%2010ax%20%2B%205a%5E2%20%2B%202a%20%5Cend%7Baligned%7D)
In conclusion:
