Okay, so i’m taking a final on Monday and basically EVERYTHING that’s on our study guide is on the test. Easy right? Not so much… I have issues with a few problems:
Find the Vertex of the parabola 2x = y^2 – 6y
Answer: (-9/2 , 3)
If f(x) = x+4/2 and g(x) = 2x-4, find g(f(x))
Answer: x
Find sum of infinite geometric series 81+54+36+24+…
Answer: 243
I can’t figure them out. If someone can show me how to solve any of the above, much appreciation. Just sitting here until Monday.. Thanks!
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The y coordinate (or whichever variable is squared) of the vertex is found, after getting the x by itself (so divide by 2 here)
by the equation y = -b over 2a. So here that is y = -(-3) over 2•(1/2) = 3/1
So then plug in 3 for y and see what x is
g(f(x)) means do f(x) first then replace the x in g(x) with the whole f(x) so it is
([2x - 4] + 4)/2 = 2x/2 = x
Sum of infinite geometric series has to have |r| < 1, and its formula is
a1 /(1 – r)
Here r = 54÷81 = 2/3 so 1 – r = 1/3 and a1 = 81
so 81 / (1/3) = 81 • 3/1 = 243
Good luck and I hope this makes sense
August 11th, 2010 at 5:36 pm
The y coordinate (or whichever variable is squared) of the vertex is found, after getting the x by itself (so divide by 2 here)
by the equation y = -b over 2a. So here that is y = -(-3) over 2•(1/2) = 3/1
So then plug in 3 for y and see what x is
g(f(x)) means do f(x) first then replace the x in g(x) with the whole f(x) so it is
([2x - 4] + 4)/2 = 2x/2 = x
Sum of infinite geometric series has to have |r| < 1, and its formula is
a1 /(1 – r)
Here r = 54÷81 = 2/3 so 1 – r = 1/3 and a1 = 81
so 81 / (1/3) = 81 • 3/1 = 243
Good luck and I hope this makes sense
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