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4 years ago

6

Suppose a square has side length equal to 16 inches. a circle with radius equal to 8 inches is inscribed inside the square. what

is the total area of

1 answer:

astraxan [27]4 years ago

8 0

Well the area of the square is is 54.94^2 but the area of the circle is <span>201.06^2. I hope this helped ^^</span>

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Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by

a_sh-v [17]

Answer:

Dimension of the box is $16.1\times 7.1\times 2.45$

The volume of the box is 280.05 in³.

Step-by-step explanation:

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

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

Solution :

Let h be the height of the box which is the side length of a corner square.

According to question,

A sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

The length of the box is $L=21-2h$

The width of the box is $W=12-2h$

The volume of the box is $V=L\times W\times H$

$V=(21-2h)\times (12-2h)\times h$

$V=(21-2h)\times (12h-2h^2)$

$V=252h-42h^2-24h^2+4h^3$

$V=4h^3-66h^2+252h$

To maximize the volume we find derivative of volume and put it to zero.

$V'=12h^2-132h+252$

$0=12h^2-132h+252$

Solving by quadratic formula,

$h=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$h=\frac{-(-132)\pm\sqrt{132^2-4(12)(252)}}{2(12)}$

$h=\frac{132\pm72.99}{24}$

$h=2.45,8.54$

Now, substitute the value of h in the volume,

$V=4h^3-66h^2+252h$

When, h=2.45

$V=4(2.45)^3-66(2.45)^2+252(2.45)$

$V\approx 280.05$

When, h=8.54

$V=4(8.54)^3-66(8.54)^2+252(8.54)$

$V\approx -170.06$

Rejecting the negative volume as it is not possible.

Therefore, The volume of the box is 280.05 in³.

The dimension of the box is

The height of the box is h=2.45

The length of the box is $L=21-2(2.45)=16.1$

The width of the box is $W=12-2(2.45)=7.1$

So, Dimension of the box is $16.1\times 7.1\times 2.45$

6 0

4 years ago

Represente em uma reta numérica os conjuntos indicados abaixo (cada conjunto deve ser representado em uma reta numérica diferent

zmey [24]

La respuesta es C(-2,3) n(3,6)

3 0

3 years ago

Which is a y-intercept of the graphed function?<br><br> (–9, 0)<br> (–3, 0)<br> (0, –9)<br> (0, –3)

Nana76 [90]

Answer:

C is the answer

Step-by-step explanation:

The Y intercept of the graphed function would be,

(0,-9) because the graph (which is a function) intercepts on (0,-9) therefore the function's y-intercept is,

b= -9

8 0

3 years ago

Read 2 more answers

PLEASE HELP I AM STUCK ON THIS

Fofino [41]

Answer:

Step-by-step explanation:

This is a right triangle problem. The reference angle is x, the side opposite the reference angle is 32, and the hypotenuse is 58. The trig ratio that relates the side opposite a reference angle to the hypotenuse is the sin. Filling in accordingly:

$sin(x)=\frac{32}{58}$

Because you are looking for a missing angle, you will use your 2nd button and then the sin button to see on your display:

$sin^{-1}($

Within the parenthesis enter the 32/58 and you'll get your angle measure. Make sure your calculator is in degree mode, not radian mode!!!

4 0

4 years ago

Use the model to solve for x. A) x = 1 B) x = 3 C) x = 5 D) x =

Novay_Z [31]

Answer:

<h3> D){?} x = 7</h3>

Step-by-step explanation:

x + 3•(+1) = 2•x + 4•(-1)

x + 3 = 2x - 4

-3 -3

x = 2x - 7

-2x -2x

- x = -7

÷(-1) ÷(-1)

x = 7

7 0

3 years ago