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lakkis [162]
3 years ago
11

A sector with a radius of 15 cm has a central angle measure of 8pie/5

Mathematics
1 answer:
Citrus2011 [14]3 years ago
3 0

Answer:

The area of the sector is 180\pi \ cm^2.

Step-by-step explanation:

We have,

Radius of circle is 15 cm

Central angle is \dfrac{8\pi}{5}\ \text{radian}

It is required to find the area of the sector. The formula used to find the area of sector is given by :

A=\dfrac{1}{2}r^2\theta

Plugging all the values in above formula as :

A=\dfrac{1}{2}\times 15^2\times \dfrac{8\pi}{5}\\A=180\pi \ cm^2

So, the area of the sector is 180\pi \ cm^2.

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A rectangular tank that is 2048 ft cubed with a square base and open top is to be constructed of sheet steel of a given thicknes
ira [324]

Answer:

The box should have base 16ft by 16ft and height 8ft Therefore,dimensions are 16 ft by 16 ft by 8 ft

Step-by-step explanation:

We were given the volume of the tank as, 2048 cubic feet.

Form minimum weight, the surface area must be minimum.

Let the height be h and the lengths be x

the volume will be: V=x²h then substitute the value of volume, we have

2048=hx²

hence

h=2048/x²

Since the amount of material used is directly proportional to the surface area, then the material needs to be minimized by minimizing the surface area.

The surface area of the box described is

A=x²+4xh

Then substitute h into the Area equation we have

A= x² + 4x(2048/x²)

A= x² + 8192/x

We want to minimize

A

dA/dx = -8192/x² + 2 x= 0 for max or min

when dA/dx=0

dA/dx= 2x-8192/x²=0

2x=8192/x²

Hence

2x³=8192

x³=4096

x=₃√(4096)

X=16ft

Then h=2048/x²

h=2048/16²

h=8ft

The box should have base 16ft by 16ft and height 8ft

Hence the dimensions are 16 ft by 16 ft by 8 ft

8 0
3 years ago
How much money must be deposited now in an
Liono4ka [1.6K]

Answer:

\$487.48

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

A=P(1+\frac{r}{n})^{nt}  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

t=10\ years\\ A=\$1,000\\ r=7.25\%=7.25/100=0.0725\\n=4  

substitute in the formula above

1,000=P(1+\frac{0.0725}{4})^{4*10}  

1,000=P(\frac{4.0725}{4})^{40}

P=1,000/(\frac{4.0725}{4})^{40}

P=\$487.48

5 0
3 years ago
Find the scale factor of 1 inch = 9 feet
tino4ka555 [31]

Answer:

9 ft = 9 × 12 = 108 in

ratio is 1:108

Step-by-step explanation:

7 0
3 years ago
What is the y-intercept of this equation?<br> y= 2/9x +13
Ksju [112]

Answer:

13

Step-by-step explanation:

y=mx+b

b= y-intercept

5 0
3 years ago
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The money is a lot so it would be c
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3 years ago
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