DI/dx=-850x+45500
d2l/d2x=-850 so when dl/dx=0 it is an absolute maximum for l(x)...
dl/dx=0 only when:
850x=45500
x=53.53
x=54 years of age (rounded)
We know that a1 = -1, and an = 2 * an-1.
We already know that the first time, a1, is -1. We're given the formula to find the next terms in the sequence.
For a given term in this sequence, it will be 2 times the last item in the sequence.
an = 2 * an-1
a2 = 2 * a2-1 = 2 * a1 = 2 * -1 = -2
a3 = 2 * a3-1 = 2 * a2 = 2 * -2 = -4
a4 = 2 * a4-1 = 2 * a3 = 2 * -4 = -8
a5 = 2 * a5-1 = 2 * a4 = 2 * -8 = -16
a6 = 2 * a6-1 = 2 * a5 = 2 * -16 = -32
Answer: D) 10
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Explanation:
I'm assuming points M and N are midpoints of segments FD and FE respectively. If that's the case, then segment DE is twice as long compared to segment MN. We consider MN to be a midsegment.
So,
DE = 2*(MN)
3x-2 = 2*(x+4)
3x-2 = 2x+8
3x-2x = 8+2
x = 10
Either one of those angles can be 90 degrees if ABC is a right triangle.
Thank you ! You have done all the heavy lifting for us,
and given us the expression in factored form.
The factors are (y - 2) and (x + 3) .