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Tatiana [17]
3 years ago
12

Please someone help me answer this!!

Mathematics
1 answer:
jekas [21]3 years ago
3 0

Answer:

a^10

Step-by-step explanation:

5*2=10

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A bucket is 20cm in diameter at the open end, 12cm in diameter at the bottom, and 16cm deep. To what depth would the bucket full
Alexus [3.1K]

The bucket has a base diameter of  12  and top opening diameter of  20 . This makes the base radius  6  and top radius  10 .

 

The bucket as shown has the bottom base of radius:

B C = 6

and the top opening of radius:

D E = 10

The depth is:

D B = 16

If we extend the lateral surface of the bucket down it will generate a cone that contains the bucket in it.

To calculate the volume of the bucket, we need to calculate the volume of the large cone with the depth of  D A , then calculate the volume of the small cone with the depth of  B A , and subtract the volume of the small cone from the volume of the large cone.

Let's let  B A = x .The two triangles  Δ A B C  and  Δ A D E are similar due to the Angle Angle theorem because they both share angle  ∠ A D E = 90 ∘  and angle  ∠ D A E .

Therefore, the ratio of their corresponding sides are equal.

B A /D A = B C /D E

x /16 + x = 6 /10

x /16 + x = 3/5

48 + 3 x = 5 x

2 x = 48

x = 24  cm

The volume of a cone is: V = 1 /3 h π r 2

The height  ( h ) , which we are calling the depth, of the small cone is  x = 24 c m  and the depth of the large cone is  x + 16 = 24 + 16 = 40 c m

V Large Cone = 1/ 3 ( 40 ) ( π ) ( 10 ) 2 = 4000 π/3 c m 3  

V Small Cone = 1 /3 ( 24 ) ( π ) ( 6 ) 2 = 288 π c m 3

V Bucket = 4000 π /3 − 288 π = 3136 π /3 c m 3

Volume of a cylinder is:

V Cylinder = π r 2 h  where  h  is the height(depth) and  r  is the radius of the base of the cylinder.

If the base of the cylinder has a diameter of  28 c m  then the radius of the base is  14 c m

( π ) ( 14 ) 2 ( h ) = 3136 π /3

196 π h = 3136 π/ 3

196 h= 3136 /3

h = 3136 /3 /196 = 3136 /588 = 5.33 c m

Let's look at the figure below:

8 0
3 years ago
A square has side lengths that measure 8 inches. A rectangle has a length of ten inches and a width of 5 inches. How many more s
Marysya12 [62]
The answer is seven square inches

6 0
3 years ago
What is the equation of the line in slope-intercept form?
USPshnik [31]

Answer:

y=mx + b (slope intercept form) m= slope, b =y-intercept

slope=rise/ run

Step-by-step explanation:

The slope intercept form is a line (straight line)

y = 3x - 7  slope 3 (rise=3, run = 1), y-intercept = -7

y = - 1 3 x + 7 slope -13 , y-intercept = 7

y=-3x - 7 slope -3, y-intercept = -7

4 0
2 years ago
Y = f(x) = -1^x<br> find f(x) when x=3
Anna [14]
Hello : 
<span>f(x) = (-1)^x
if x=3
f(3) = (-1)^3 = -1</span>
4 0
3 years ago
Read 2 more answers
Building a is 160160 feet shorter than building
Serjik [45]
I assume the heights are 160 ft and 1480 ft.

The two heights are unknown, so we will use variable h to help solve the problem.
The shorter building, building A, has height h.
Since building A is shorter by 160 ft, then building B is taller by 160 ft, so the height of building B is h + 160.

Now we add our two heights to find the total height.

h + h + 160 is the total height.
We can write it as 2h + 160

We are told the total height is 1480 ft, so we let 2h + 160 equal 1480, and we have an equation.

2h + 160 = 1480

Subtract 160 from both sides

2h = 1320

Divide both sides by 2

h = 660

h + 160 = 820

Building A measures 660 ft.
building B measures 820 ft.
7 0
2 years ago
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