On a shopping trip, Peter spent 1/3 of his money for a jacket and another $5 for a hat. If peter still had 1/2 of his money left
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Answer:
Step-by-step explanation:
Consider the revenue function given by . We want to find the values of each of the variables such that the gradient( i.e the first partial derivatives of the function) is 0. Then, we have the following (the explicit calculations of both derivatives are omitted).
From the first equation, we get, .If we replace that in the second equation, we get
From where we get that . If we replace that in the first equation, we get
So, the critical point is . We must check that it is a maximum. To do so, we will use the Hessian criteria. To do so, we must calculate the second derivatives and the crossed derivatives and check if the criteria is fulfilled in order for it to be a maximum. We get that
We have the following matrix,
.
Recall that the Hessian criteria says that, for the point to be a maximum, the determinant of the whole matrix should be positive and the element of the matrix that is in the upper left corner should be negative. Note that the determinant of the matrix is and that -10<0. Hence, the criteria is fulfilled and the critical point is a maximum
Answer:
Step-by-step explanation:
<u>Surface Area</u>
The surface area of a cylinder of height h and radius r is given by:
It only covers the lateral side of the cylinder. If both the top and the bottom sides are to be included, then:
The label will cover only the lateral side of the soup can that has a height of h=8.5 cm and a diameter of 6.5 cm. We need to calculate the radius which is half of the diameter r=6.5 cm / 2 = 3.25 cm.
Now we calculate the side area of the can:
We need to add the 0.8 cm overlap to the total area already calculated. This overlap has 0.8 cm of width and 8.5 cm of height, so this overlap area is:
The total area of the label is:
The area of the label is