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guajiro [1.7K]
3 years ago
9

A set of 10 coins may contain any combination of pennies, nickels, dimes, quarters, or half-dollars. In how many different ways

can the set of 10 coins have a total value of 59 cents?
Mathematics
1 answer:
Iteru [2.4K]3 years ago
4 0

that is a very complicated question with alot of variable to figure out

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A piece of wire 11 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral tria
forsale [732]

Answer:

11 meters

Step-by-step explanation:

First, we can say that the square has a side length of x. The perimeter of the square is 4x, and that is how much wire goes into the square. To maximize the area, we should use all the wire possible, so the remaining wire goes into the triangle, or (11-4x).

The area of the square is x², and the area of an equilateral triangle with side length a is (√3/4)a². Next, 11-4x is equal to the perimeter of the triangle, and since it is equilateral, each side has (11-4x)/3 length. Plugging that in for a, we get the area of the equilateral triangle is

(√3/4)((11-4x)/3)²

= (√3/4)(11/3 - 4x/3)²

= (√3/4)(121/9  - 88x/9 + 16x²/9)

= (16√3/36)x² - (88√3/36)x + (121√3/36)

The total area is then

(16√3/36)x² - (88√3/36)x + (121√3/36) + x²

= (16√3/36 + 1)x² -  (88√3/36)x + (121√3/36)

Because the coefficient for x² is positive, the parabola would open up and the derivative of the parabola would be the local minimum. Therefore, to find the maximum area, we need to go to the absolute minimum/maximum points of x (x=0 or x=2.75)

When x=0, each side of the triangle is 11/3 meters long and its area is

(√3/4)a² ≈ 5.82

When x=2.75, each side of the square is 2.75 meters long and its area is

2.75² = 7.5625

Therefore, a maximum is reached when x=2.75, or the wire used for the square is 2.75 * 4 = 11 meters

3 0
3 years ago
I) 43x + 31y = 98<br> 31x + 43y = 50
Neko [114]

There are no solutions to the given system of equations.

Hope this helps.

4 0
3 years ago
Hypothesis Test by Hand
inna [77]

Answer:

ummm i think it is b  or c no its b becuse nah i not gone tell u

Step-by-step explanation:

6 0
3 years ago
PLEASE ANSWER QUICKLY
Travka [436]

Answer:

63 :)

Step-by-step explanation:

3 0
3 years ago
What does x equal in 5x+y=-24
qaws [65]

Answer

24/5

Step-by-step explanation:

5 0
3 years ago
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