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2 years ago

How do you find the length of arc and area of sector

1 answer:

6 0

To do this I must first determine what fraction of the circle is represented by the central angle 30°. Since there are 360° in a full circle, I can find the fraction of a circle by simplifying . The sector represents of the circle. To find the arc length, I now need to find the circumference of the entire circle.

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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

Which expression is equivalent to (X^1/4 y^16)^1/2?

lawyer [7]

Answer:

$x^{\frac{1}{8} } y^{8}$

Step-by-step explanation:

Given :

$(x^\frac{1}{4} y^{16} )^{1/2}$

Now,

$(x^\frac{1}{4} y^{16} )^{1/2}\\x^{\frac{1}{8} } y^{8}$

Therefore, expression is equivalent to $x^{\frac{1}{8} } y^{8}$

3 0

2 years ago

Please help ....this is due tomorrow

marshall27 [118]

A) 0.15 times $2,570 = $412.50

B) $122.85 times 2( 12 ) = $2,948.40

C) $2,570

D) All together it's $2,948.40 + $2,570 = $5,518.40

For D I didn't add the down payment because it's not an additional charge.

I only did the first one because I don't know if you want me to finish the rest.

Hope I helped :)

5 0

3 years ago

Neil and Zack are working on a project that requires both research and presentation. Neil is better at research, so he gives the

djverab [1.8K]

The question provides us with the following scenario: "Neil and Zack are working on a project that requires both research and presentation. Neil is better at research, so he gives the presentation to Zack. " A comparative advantage is when an agent is better at something or can produce something at a lower cost. Here, Neil can do research better, so the answer is: A.) Neil doing the research

6 0

3 years ago

Read 2 more answers

Write an expression for the operation described below. the product of 2 and c

PtichkaEL [24]

Answer:

2c or 2 x c

Step-by-step explanation:

Product means multiplication, they put 2 first then c last.

Hope this helps

~R3V0

3 0

2 years ago