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3 years ago

7

What are the dimensions of a rectangle with an area of 72 square centimeters and a perimeter of 36 centimeters?

1 answer:

Masja [62]3 years ago

6 0

Answer:

length=12 cm, width=6 cm

Step-by-step explanation:

$lw = 72$

$w = \frac{72}{l}$

$2(l + w) = 36$

$l + w = 18$

$l + \frac{72}{l} = 18$

${l}^{2} + 72 = 18l$

${l}^{2} - 18l + 72 = 0$

$(l - 12)(l - 6) = 0$

$l = 12$

$w = 6$

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Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by

11111nata11111 [884]

Answer:

The dimension of the open rectangular box is $8.216\times 4.216\times 1.392$ .

The volume of the box is 8.217 cubic inches.

Step-by-step explanation:

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by cutting congruent squares from the corners and folding up the sides.

To find : The dimensions and the volume of the open rectangular box ?

Solution :

Let the height be 'x'.

The length of the box is '11-2x'.

The breadth of the box is '7-2x'.

The volume of the box is $V=l\times b\times h$

$V=(11-2x)\times (7-2x)\times x$

$V=4x^3-36x^2+77x$

Derivate w.r.t x,

$V'(x)=4(3x^2)-2(36x)+77$

$V'(x)=12x^2-72x+77$

The critical point when V'(x)=0

$12x^2-72x+77=0$

Solve by quadratic formula,

$x=\frac{18+\sqrt{93}}{6},\frac{18-\sqrt{93}}{6}$

$x=4.607,1.392$

Derivate again w.r.t x,

$V''(x)=24x-72$

Now, $V''(4.607)=24(4.607)-72=38.568>0$ (+ve)

$V''(1.392)=24(1.392)-72=-38.592$ (-ve)

So, there is maximum at x=1.392.

The length of the box is $l=11-2x$

$l=11-2(1.392)=8.216$

The breadth of the box is $b=7-2x$

$b=7-2(1.392)=4.216$

The height of the box is h=1.392.

The dimension of the open rectangular box is $8.216\times 4.216\times 1.392$ .

The volume of the box is $V=l\times b\times h$

$V=8.216\times 4.216\times 1.392$

$V=48.217\ in.^3$

The volume of the box is 8.217 cubic inches.

5 0

3 years ago

Select the statement that best justifies the conclusion based on the given information.

artcher [175]

Hope this helps but I think it is A.)addition property of equality.

6 0

4 years ago

Read 2 more answers

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

yan [13]

Answer:

138.16 in²

Step-by-step explanation:

The surface area SA of the cone is the sum of the base area B and the lateral area LA. The lateral area is half the product of the circumference and the slant height. The radius is half the diameter, so is 4 inches.

SA = B + LA

= πr² + (1/2)(2πrh) . . . . where h is the slant height

= (πr)(r +h)

Filling in the numbers, you have ...

SA = (3.14)(4 in)(4 in + 7 in) = 3.14×(44 in²) = 138.16 in²

7 0

3 years ago

30 tens = ones<br> 30 tens = hundreds

Svetllana [295]

30 tens = 30 x 10 = 300

300 ones = 300 x 1 = 300

300 is your answer

30 tens = 30 x 10 = 300

3 hundreds = 3 x 100 = 300

3 is your answer

<em>~Rise Above the Ordinary</em>

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3 years ago

Callie surveyed 40 students at her school to see how many have dogs and/or cats. She found that 40% of students who have dogs, d

irina [24]

I think you need to show the tablle

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3 years ago