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3 years ago

A circle with area 36pi has a sector with a central angle of 48°. what is the area of the sector?

Mathematics

1 answer:

Elza [17]3 years ago

4 0

Answer:4.8π

Step-by-step explanation:

Φ=48°

Area of circle=36π

Area of circle=π x r^2

36π=πr^2

Dividing both sides by π we get

r^2=36π/π

r^2=36

Take them square root of both sides

√(r^2)=√(36)

r=6

Area of sector=Φ/360 x π x r x r

Area of sector=48/360 x π x 6 x 6

Area of sector=(48xπx6x6)/360

Area of sector=1728π/360

Area of sector=4.8π

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The safety director of an insurance company took samples at random from his minor accidents file and classified them according t

lina2011 [118]

Answer:

Step-by-step explanation:

A. H0: accident are evenly distributed

H1: accident are not evenly distributed

B. The critical value is chi²(0.01,7) = 18.4753

C. The decision rule would be to reject h0 and accept h1 if the test statistic is higher than the critical value

D. Test statistic = summation (Oi-Ei)²/E

This gives 24.6 from the table.

E. Based on these calculations, test statistic is > than critical value

24.6> 18.4753

F. The inference is that accidents are not evenly distributed at 0.01 level of significance.

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3 years ago

10. George earns $455 per week. He receives a 20% raise. What is George's new weekly salary?

djverab [1.8K]

Answer:

$546

Step-by-step explanation:

455*.20=91

91+455+546

8 0

3 years ago

Read 2 more answers

How can elimination and substitution adapt to solve a system with nonlinear equations

larisa [96]

Because your gonna elminate the loners and soon your going to substitute them for numbers

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3 years ago

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

3 years ago

Could someone help me with this? Please No guessing! Explain how you got the answer! And make sure your answer is correct! :) th

stealth61 [152]

The numbers on the left represent 10 times that number

The numbers on the right are added to the end of the number on the left so

3I1=31 and 4I8=48 and 3I 1 1 2= 31 31 32

4 0

3 years ago