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labwork [276]
3 years ago
6

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

ngle. (a) How much wire should be used for the square in order to maximize the total area
Mathematics
1 answer:
forsale [732]3 years ago
3 0

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

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Joe’s annual income has been increasing each year by the same dollar amount the first year his income was 19,500. 8 years later
Anna007 [38]

Answer:

The question is either poorly constructed or it is a trick question. We do not know "In what year was his income 30,300" because the years correlating to his income are not disclosed.  Even assuming the question was meant to be posed as "how many years later was his income 30,300" it is still flawed.

Step-by-step explanation:

To arrive at Joe's annual income increase, first subtract 19,500 from 27,900 to get 8400, which is his overall increase over the 8 years. Now divide 8400 by 8. You will get 1050.  Beginning with his income of 27,900, add 1,050 to each successive income amount and you will get the following progression:

27,900, 28,950, 30,000, 31,050, 32,100, 33,150, 34,200, 35,250, 36,300.

Therefore, two years after his income was 27,900 it would be 30,000 and 6 years after that it would be 36,300.  It would  never be 30,300.

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3 years ago
You purchase 4 videos. The original price of each video is x dollars. You decide to purchase the limited edition versions of the
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You purchase 4 videos

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You decide to purchase the limited edition versions of the videos for an additional cost

Your total cost is (4x + 20) dollars

So, total additional cost is $20

since, we are purchasing 4 videos

so, additional cost in each videos is

=\frac{20}{4}

=5

So, limited edition cost additional $5 per videos.........Answer

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3 years ago
Two cats, Fluffy and Fireball, met in the park. Fluffy's tail is 1/3​​, of a meter long. Fireball's tail is 1/4 of a meter long.
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1/3 - 1/4 = 4/12 - 3/12 = 1/12....Fluffy's tail is 1/12 meters longer then Fireball's tail
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3 years ago
Read 2 more answers
You borrow $5,000 from your parents to purchase a used car. The arrangements of the loan are such that you make payments of $250
AfilCa [17]
Part A:
1st month: Interest payable = 1% of $5,000 = $50.00
Amount paid in first month = $250 + $50.00 = $300
Unpaid balance = $5,000 - $250 = $4,750

2nd month: Interest payable = 1% of $4,750 = $47.50
Amount paid in second month = $250 + $47.50 = $297.50
Unpaid balance = $4,750 - $250 = $4,500

3rd month: Interest payable = 1% of $4,500 = $45.00
Amount paid in third month = $250 + $45.00 = $295.00
Unpaid balance = $4,500 - $250 = $4,250

4th month: Interest payable = 1% of $4,250 = $42.50
Amount paid in fouth month = $250 + $42.50 = $292.50
Unpaid balance = $4,250 - $250 = $4,000

5th month: Interest payable = 1% of $4,000 = $40.00
Amount paid in fifth month = $250 + $40.00 = $290.00
Unpaid balance = $4,000 - $250 = $3,750

6th month: Interest payable = 1% of $3,750 = $37.50
Amount paid in sixth month = $250 + $37.50 = $287.50
Unpaid balance = $3,750 - $250 = $3,500

7th month: Interest payable = 1% of $3,500 = $35.00
Amount paid in seventh month = $250 + $35.00 = $285.00
Unpaid balance = $3,500 - $250 = $3,250

8th month: Interest payable = 1% of $3,250 = $32.50
Amount paid in eighth month = $250 + $32.50 = $282.50
Unpaid balance = $3,250 - $250 = $3,000

9th month: Interest payable = 1% of $3,000 = $30.00
Amount paid in ninth month = $250 + $30.00 = $280.00
Unpaid balance = $3,000 - $250 = $2,750

10th month: Interest payable = 1% of $2,750 = $27.50
Amount paid in fouth month = $250 + $27.50 = $277.50
Unpaid balance = $2,750 - $250 = $2,500

11th month: Interest payable = 1% of $2,500 = $25.00
Amount paid in seventh month = $250 + $25.00 = $275.00
Unpaid balance = $2,500 - $250 = $2,250

12th month: Interest payable = 1% of $2,250 = $22.50
Amount paid in eighth month = $250 + $22.50 = $272.50
Unpaid balance = $2,250 - $250 = $2,000



Part B:
Number of payments = 5000 / 250 = 20
Total amount of interest = 50 + 47.5 + 45 + . . . + upto the 20th payment.
This is an arithmetic sequence with the first term as 50, common difference as -2.5 and number of terms = 20.

Sum of the first 20th term of the GP is given by
S_n= \frac{20}{2}[2(50)+(20-1)(-2.5)] \\  \\ =10(100-2.5(19))=10(100-47.5) \\  \\ =10(52.5)=\$525.00

Therefore, the <span>total amount of interest paid over the term of the loan is $525.00</span>
8 0
3 years ago
A teachers desk is 5.5 meters long a students desk is 220 centimeters long what is the difference in the length in centimeters b
Mama L [17]

so if 5.5 is in meter let change it to cm because the question want us to give the answer in cm.

1cm = 0.01meter

to \: turn \: meters \: into \: \\  cm \: we \: have \: to \: multiply \:  by \: 100

now we multiply 5.5 times 100 which is equal to 550.

next we subtract 550 - 220= 330.

finally, the difference between a teacher and student is 330cm .meaning the teacher's desk is 330 cm longer or taller than the student.

7 0
3 years ago
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