Th Write an explicit formula for ans then term of the sequence 40,50,60, ....
1 answer:
<h3>Answer: 
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n starts at 1, and n is a positive whole number (1,2,3,...)
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Explanation:
The sequence is arithmetic with first term 40 and common difference 10. Meaning we add 10 to each term to get the next one.
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a1 = 40 = first term
d = 10 = common difference
is the general nth term of this arithmetic sequence
Plug in n = 1 and you should get
Plug in n = 2 and you should get
and so on
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The initial length of the pine tree=5 feet.
Groth rate of pine tree =3 feet/year.
The initial length of the pine tree =10 feet.
Groth rate of the maple tree =2 feet/year.
After x years, the height of the pine tree= 5+3x feet and
after x years, the height of the maple tree= 10+2x feet.
The inequality for which, after x year, the pine tree is taller than the maple tree is
.
The inequality for which, the pine tree is at least as tall as the maple tree is .
.
Again, after 3x years, the height of the pine tree= 5+3(3x)=5+9x feet and
after 2x years, the height of the maple tree= 10+2(2x)=10+4x feet.
The inequality for which, after 3x years, the pine tree is taller than the maple tree was after 2x years is
The inequality for which, the pine tree is at least as tall as the maple tree is .
Q(p) = k/p^3 . . . . . . . . we want to find k
q(10) = k/10^3 = 64
k = 64,000
Revenue = q(p)*p = 64000/p^2
Cost = 150 +2q = 150 +2*64000/p^3
Profit = Revenue -Cost = 64000/p^2(1 -2/p) -150
Differentiating to find the maximum profit, we have
.. dProfit/dp = -2(64000/p^3) +6(64000/p^4) = 0
.. -1 +3/p = 0
.. p = 3
A price of $3 per unit will yield a maximum profit.
q(10) = k/10^3 = 64
k = 64,000
Revenue = q(p)*p = 64000/p^2
Cost = 150 +2q = 150 +2*64000/p^3
Profit = Revenue -Cost = 64000/p^2(1 -2/p) -150
Differentiating to find the maximum profit, we have
.. dProfit/dp = -2(64000/p^3) +6(64000/p^4) = 0
.. -1 +3/p = 0
.. p = 3
A price of $3 per unit will yield a maximum profit.