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mr Goodwill [35]
3 years ago
11

A box (with no top) is to be constructed from a piece of cardboard of sides a and b by cutting out squares of length h from the

corners and folding up the sides. find the value of h that maximizes the volume of the box if a = 8 and b = 9.
Mathematics
1 answer:
melisa1 [442]3 years ago
3 0
<span>The volume of the box is h(8-2h)(9-2h). Differentiating this gives dV/dh = 12h^2-68h+72. The derivative is zero when h = (17+sqrt(73))/6 or (17-sqrt(73))/6. The second derivative is positive for the first value, so this gives a minimum volume. The second derivative is negative for the second value, so this gives the maximum volume. So the value of h that maximizes the volume of the box is (17-sqrt(73))/6, which is approximately 1.41.</span>
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Find the minimum product of two numbers whose difference is 17. <br> what are the numbers?
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A number is an arithmetic value that is used to represent a quantity and calculate it. The two numbers will be 17 and 0, so the product of the two is minimal.

<h3>What are Numbers?</h3>

A number is an arithmetic value that is used to represent a quantity and calculate it. Numericals are written symbols that represent numbers, such as "3."

Given the difference between the two numbers is 17. Let the first number be zero, then the second number will be 17. Thus, the product of the two numbers will be 0, which is the minimum.

If the first number is further increased such as 1, then the other number will be 18, and the product of the two will be 18, which is greater than zero.

Hence, the two numbers will be 17 and 0, so the product of the two is minimal.

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1 year ago
The cost of catering a dinner is $11.95 per person plus $25 for delivery and setup. Which statement is true about the graph of t
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If you draw a card with a value of four or less from a standard deck of cards, I will pay you $162. If not, you pay me $45. (Ace
DanielleElmas [232]

Answer: 2.77

The expected value is positive, so you expect to gain on average $2.77 per draw.

================================================

Explanation:

Define two events

W = winning = getting a card 4 or less

L = losing = getting 5 or higher

P(W) = probability of winning

P(W) = 12/52 since there are 12 cards that are four or less out of 52

P(W) = 3/13 for any suit of 13, there are 3 cards that are four or less

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P(L) = 1-3/13

P(L) = 13/13 - 3/13

P(L) = 10/13

V(W) = net value of winning

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V(L) = net value of losing

V(L) = -45

------------------

E(X) = expected value

E(X) = P(W)*V(W) + P(L)*V(L)

E(X) = (3/13)*162 + (10/13)*(-45)

E(X) = 36/13

E(X) = 2.76923076923077

E(X) = 2.77 rounding to two decimal places (to the nearest cent)

This game is in favor to the player since we got a positive expected value. A fair game would occur if the expected value was 0.

4 0
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