scott Consider the table below that represents a function Which number(s) below can be placed in the empty cell so that the tabl
1 answer:
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Answer:
a) Y(x) = {900, x≤30; 900-40(x-30), x>30}
b) T(x) = {900x, x≤30; 2100x-40x², x>30}
c) dT/dx = {900, x≤30; 2100-80x, x>30}
Step-by-step explanation:
a) The problem statement gives the function for x ≤ 30, and gives an example of evaluating the function for x = 35. So, replacing 35 in the example with x gives the function definition for x > 30.
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b) The yield per acre is the product of the number of trees and the yield per tree:
T(x) = x·Y(x)
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c) The derivative is ...
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The attached graph shows the yield per acre (purple, overlaid by red for x<30), the total yield (black), and the derivative of the total yield (red). You will note the discontinuity in the derivative at x=30, where adding one more tree per acre suddenly makes the rate of change of yield be negative.
The stake the rope is tied to is the center of the circle. If the goat pulls the rope as far as it can go and walks around like this he makes a circle and he can eat the grass anywhere within this circle.
(a) Since the area of a circle is given by
this is the formula we can use to find the area of the yard where the goat can roam/eat/reach.
(b) Since the rope is 4 feet the radius r = 4 and the area is given by
square feet. That's the exact area. For an approximation you could substitute 3.14 for pi and get 50.24 square feet.
(c)Since the rope is 5 feet the radius r = 4 and the area is given by
square feet. That's the exact area.
For an approximation you could substitute 3.14 for pi and get 78.5
square feet.
(a) Since the area of a circle is given by
(b) Since the rope is 4 feet the radius r = 4 and the area is given by
(c)Since the rope is 5 feet the radius r = 4 and the area is given by