Match each expression in column A with an equivalent expression from column B.
1 answer:
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Answer:
28
Step-by-step explanation:
From the given information:
Let x be the number of trees.
F(x) = (50 +x) (20 - 3x)
F(x) = 1000 - 150x + 20x - 3x²)
F(x) = -3x² - 130x + 1000
Differentiating F(x) with respect to x;
F'(x) = -6x -130
Now; we set F'(x) to be equal to zero to determine the critical value;
-6x - 130 = 0
x = - 130/6
Differentiating F''(x) with respect to x
F''(x) = -6 (<0)
Thus; by the second derivative, the revenue function F(x) is maximum when x = -130/6
Therefore, the number of trees she should plant per acre to maximize her harvest is:
50 + x = 50 - 130/6
= 85/3
28
Therefore, the number of trees per acre to maximize the harvest is 28
Ans(a):
Given that a FedEx freight truck carries three tons of packages 660 miles on 90 gallons of diesel fuel from Miami, FL to Atlanta, GA.
so that means speed of the truck is
speed = distance/time = 660/90 miles per gallon
hence slope of the equation will be
m=660/90 = 66/9= 22/3
There is no information about initial cost or any initial value so that means y-intercept b=0
plug value of m and b into y=mx+b
so we get equation y=22/3x+0
Where x is the number of gallons and y is the number of miles
Now we can easily graph this equation to get the required graph.
when x=0 then y=22/3x=22/3*0=0
so first point is (0,0)
when x=3 then y=22/3x=22/3*3=22
so second point is (3,22)
Now we join them by a line to get the graph
Ans(b):
clearly number of gallons can't be negative. It is also given that truck uses 90 gallons of diesel fuel. so the domain can be any real number from 0 to 90 or we can write domain as [0,90].
Ans(c):
Origin of the graph represents that if there is no gallons of fuel used then there will be no distance traveled.
