1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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

You might be interested in
Does each function describe exponential growth or decay?
Aleksandr [31]
<h3>Answer: Only first two are exponential growth function and last three functions are exponential decay functions.</h3>

Step-by-step explanation: We need to describe exponential growth or decay for the given functions.

The standard exponential function equation is

y=a(b)^x.

Where a is the initial value and b is the growth factor.

Note: If value of b > 1, it would be an exponential growth and if b < 1, it would be an exponential decay.

Let us check them one by one.

y=(1.008^{1/12}})^{12t} => y=(1.008^})^{1/12\times{12t} }

=> y= (1.008)^t.

Value of b is 1.008 > 1, therefor it's an exponential growth function.

y=250(1+0.004)^t, also have b>1 therefor it's an exponential growth function.

All other functions has b values less than 1, therefore only first two are exponential growth function and last three functions are exponential decay functions.



5 0
3 years ago
3. (02.02 MC)
LenaWriter [7]

Answer:

O -1+ 3/

Step-by-step explanation:

brainest plz

8 0
2 years ago
If there are 12 boys and 60 girls in a room, fill out all of the possible ratios of boys to girls that could be made.
Oksana_A [137]

Answer:

6:30

1:5

4:20

3:15

2:10

Step-by-step explanation:

im pretty sure these are correct

7 0
3 years ago
There are 2 trucks for every 3 cars in the parking lot. How
daser333 [38]
How many parking spaces are there?????
8 0
2 years ago
What is the least common mulitiple of 6 and 7
Anna35 [415]

Answer:

hi! your answer should be 42.

5 0
3 years ago
Read 2 more answers
Other questions:
  • At a certain college, there are 600 freshman, 400 sophomores, 300 juniors, and 200 seniors. if one student is selected at random
    10·1 answer
  • What is the y intercept of a line that has a slope of -3 and passes through the point (2,7)
    7·1 answer
  • HELP PLEASE I NEED IT ASAP
    14·1 answer
  • (4, -1), (7, 4)<br> find the distance between each pair of points
    11·1 answer
  • Plz help will give brainlyest
    15·2 answers
  • Help!<br> Hint: A nickel is worth $0.05 and a dime is worth $0.10
    12·1 answer
  • 2
    10·1 answer
  • What are the coordinates of the image of vertex G after a reflection across the line y = x?​
    8·1 answer
  • What is the area of the shaded portion of the circle?
    5·1 answer
  • Given: y varies directly as x squared and inversely as z cubed. If y = 12 when x = 4 and z = 2, find x when y = 1.728 and z = 5.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!