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Dima020 [189]
2 years ago
15

What are the dimensions of the largest rectangular field that can be enclosed with 64m of wire?​

Mathematics
1 answer:
Natalka [10]2 years ago
7 0

Step-by-step explanation:

perimeter = 2*length + 2*width

area = length*width

perimeter = 64

Rectangular means all the corners have to be right angles.

If we say it can be a square, then...

perimeter = 4*side

64 / 4 = side

side = 16 meters

So the dimensions would be 16 m x 16 m

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6th grade math help me, please. :)
postnew [5]

Answer: 120 ice creams total

The answer is option D

4 0
3 years ago
What is the place of the 9 in the number 5,948,003
tino4ka555 [31]
The 9 is in the one hundred thousand's place
4 0
3 years ago
Read 2 more answers
A rectangle box with a square base and no top needs to be made using 300ft^2 of material. Find the dimensions of the box with th
Yuri [45]

The dimensions of the box are 10 ft and 5 ft

The maximum volume is 500 ft³

Step-by-step explanation:

A rectangle box with

  • A square base and no top
  • It needs to be made using 300 ft² of material
  • It has greatest volume

Surface area of a box without top (SA) = perimeter of base × height + area of the base

Volume of a box (V) = base area × height

Assume that the length of the side of the square base is x and the height of the box is y

∵ It needs to be made using 300 ft² of material

∴ The surface area of the box is 300 ft²

∵ Its base is a square of side length x ft

∴ Perimeter of the base = 4 × x = 4 x

∴ Area of the base = x²

∵ The height of the box = y ft

∵ SA = perimeter of base × height + area of the base

∵ SA = (4x)(y) + x²

∴ SA = 4xy + x²

∵ SA of the box = 300 ft²

- Equate the two expressions of SA

∴ 4xy + x² = 300

Now let us find y in terms of x

- Subtract x² from both sides

∴ 4xy = 300 - x²

- Divide each term by 4x to find y

∴ y=\frac{75}{x}-\frac{1}{4}x

∵ V = area of the base × height

∴ V = x² × y = x²y

- Substitute y by the equation of it above

∴ V=x^{2}(\frac{75}{x}-\frac{1}{4}x)

∴ V=75x-\frac{1}{4}x^{3}

∵ The volume of the box is greatest

- That means differentiate V and equate it by 0

∵ \frac{dV}{dx}=75-\frac{3}{4}x^{2}

∵ \frac{dV}{dx}=0 ⇒ greatest volume

∴ 75-\frac{3}{4}x^{2}=0

- Subtract 75 from both sides

∴ -\frac{3}{4}x^{2}=-75

- Divide both sides by -\frac{3}{4}

∴ x² = 100

- Take √ for both sides

∴ x = 10

Substitute the value of x in the equation of y

∵ y=\frac{75}{10}-\frac{1}{4}(10)

∴ y = 5

The dimensions of the box are 10 ft and 5 ft

∵ V=75x-\frac{1}{4}x^{3}

∵ x = 10

∴ V=75(10)-\frac{1}{4}(10)^{3}

∴ V=750-\frac{1}{4}(1000)

∴ V = 750 - 250

∴ V = 500 ft³

The maximum volume is 500 ft³

Learn more:

You can learn more about the volume in brainly.com/question/6443737

#LearnwithBrainly

6 0
3 years ago
Jack is trying to make extra money on his summer vacation from school. He works two different jobs, earning $9 per hour washing
Sveta_85 [38]

Answer:

$57

9w+6d

Step-by-step explanation:

Given that:

Earnings per hour for washing cars = $9

Earnings per hour for walking dogs = $6

Number of hours for which car washing is done = w

Number of hours taken for walking dogs = d

Earnings for w hours for washing cars = Per hour earnings multiplied by number of hours = $9w

Earnings for d hours for walking dogs = Per hour earnings multiplied by number of hours = $6d

Total earnings by both = $(9w+6d)

Now, given that

Number of hours spent washing cars = 5 hours

Number of hours spent walking dogs = 2 hours

Therefore, total earnings by both = 9 \times 5 + 6 \times 2 = <em>$57</em>

5 0
3 years ago
What number must you add to complete the square x^-8x=39
notsponge [240]

Answer:

Given equation: x^2-8x =39

when we complete the square , we take half of the value of 8 , then square it, and added to the left sides, we get;

x^2-8x+4^2 = 39 +4^2

∵8 is the value (\frac{8}{2})^2

Notice that, we add this both sides so that it maintains the equality.

then;

x^2-8x+4^2 = 39 +4^2

(x-4)^2 = 39 + 16   [ (a-b)^2 = a^2-2ab+b^2 ]

Simplify:

(x-4)^2 =55

The number must be added to complete the square is, 4^2 = 16



3 0
3 years ago
Read 2 more answers
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