A ball is thrown directly downward from a cliff 384 feet high with an initial velocity of 48 feet per second. In about how many
seconds will it strike the ground? Recall that the acceleration due to gravity is 32 feet per second squared.
2 answers:
Answer:
about 3.623 seconds
Step-by-step explanation:
The equation for the height can be written as ...
h(t) = -1/2gt^2 -48t +384 . . . . . where g=32
h(t) = -16t^2 -48t +384 = -16(t^2 +3t -24)
We want to find t such that h(t) = 0, so ...
0 = -16(t^2 +3t -24)
0 = t^2 +3t -24 . . . . . . divide by -16
0 = t^2 +3t +2.25 -24 -2.25 . . . . . add/subtract a constant to complete the square
0 = (t +1.5)^2 -26.25 . . . . . rewrite in vertex form
26.25 = (t +1.5)^2 . . . . . . . add 26.25; next, square root, subtract 1.5
t = √26.25 -1.5 ≈ 3.623 . . . . seconds
The ball will strike the ground in about 3.623 seconds.
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Answer:
5 trees should be planted to maximize the yield per acre,
The maximum yield would be 1250
Step-by-step explanation:
Given,
The original number of trees per acre = 20,
Average pounds of nuts by a tree = 60,
Let x be the times of increment in number of trees,
So, the new number of trees planted per acre = 20 + x
∵ for each additional tree planted per acre, the average yield per tree drops 2 pounds,
So, the new number of pounds of nut = (60 - 2x)
Thus, the total yield per acre,
Differentiating with respect to t ( time ),
Again differentiating with respect to t,
For maxima or minima,
⇒ 20 - 4x = 0
⇒ 20 = 4x
⇒ x = 5,
For x = 5, Y''(x) = negative,
Hence, Y(x) is maximum for x = 5,
And, maximum value of Y(x) = (20+5)(60 - 10) = 25(50) = 1250,
i.e. 5 trees should be planted to maximize the yield per acre,
and the maximum yield would be 1250 pounds
Answer:
Step-by-step explanation:
Given
Required
Determine the value of T
Multiply both sides by 2
Divide through by 6