Answer:
The answers are given in the photo
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Answer:
Step-by-step explanation:
For this case we assume that the total perimeter is 18 ft, we have a wall and the two sides perpendicular to the wall measure x units each one so then the side above measure P-2x= 18-2x.
And we are interested about the maximum area.
For this case since we have a recatangular area we know that the area is given by:
Where L is the length and W the width, if we replace from the values on the figure we got:
And as we can see we have a quadratic function for the area, in order to maximize this function we can use derivates.
If we find the first derivate respect to x we got:
We set this equal to 0 in order to find the critical points and for this case we got:
And if we solve for x we got:
We can calculate the second derivate for A(x) and we got:
And since the second derivate is negative then the value for x would represent a maximum.
Then since we have the value for x we can solve for the other side like this:
And then since we have the two values we can find the maximum area like this:
Answer:
Shopper spend $3 on Apples, $4 on Grapes and $3.5 on Oranges
Step-by-step explanation:
Cost of one pound of Apple = $2x
Cost of one pound of Grapes = $(6x-5)
Cost of one pound of Oranges = $(x+2)
A shopper purchases one pound each of apples, grapes, and oranges and spends $10.50.
It can be written as:
We need to find how much the shopper spend on each fruit.
First we need to find value of x by solving equation
Solving:
The value of x is: x=1.5
Now finding cost of one pound each fruit by putting x=1.5
Cost of one pound of Apple = $2x = 2(1.5) = $3
Cost of one pound of Grapes = $(6x-5) = (6(1.5)-5)= $4
Cost of one pound of Oranges = $(x+2)=(1.5+2)=$3.5
So,
Cost of one pound of Apple = $3
Cost of one pound of Grapes = $4
Cost of one pound of Oranges = $3.5
So, shopper spend $3 on apples, $4 on Grapes and $3.5 on Oranges