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Allisa [31]
2 years ago
8

Volume of a cone = r²h,

Mathematics
1 answer:
inessss [21]2 years ago
6 0

Answer:

7.5 m           457.5\pi m^{2}

Step-by-step explanation:

First, visualize the original cone and the smaller cone as overlapping similar triangles. The scale factor of the original cone to the smaller cone is 50:40, so if the smaller cone has a radius of 6 m, then the radius of the original cone would be 7.5 m.

The volume of the frustum is the volume of the original cone minus the volume of the smaller cone. The formula for the volume of a cone is V = \frac{1}{3} \pi r^{2}h.

Original Cone = \frac{1}{3} \pi r^{2}h = \frac{1}{3} \pi *7.5^{2}*50 = 937.5\pi

Smaller Cone = \frac{1}{3} \pi r^{2}h =  \frac{1}{3} \pi *6^{2}*40 = 480\pi

Frustum = 937.5\pi - 480\pi = 457.5\pi

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A shipping service restricts the dimensions of the boxes it will ship for a certain type of service. The restriction states that
Igoryamba

Answer:

w =< 70

(width is less or equal to 70 inches)

Step-by-step explanation:

Let l = length, w = width, h = height

Restrictions given in this question:

'sum of perimeter of the base and the height cannot exceed 130 inches'

perimeter of the base is 2 width and 2 length of the box

perimeter = 2w + 2l

Therefore, inequality involves here is

2w + 2l + h =< 130

(Note that =< here means less or equal)

Then a new condition given with

height, h = 60 in

and length is 2.5 times the width

l = 2.5w

Substitute this new condition into the equation will give us the following:

2w + 2(2.5w) + 60 =< 130

2w + 5w + 60 =< 130

7w + 60 =< 130

7w =< 130-60

7w =< 70

w =< 10

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3 years ago
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Leya [2.2K]

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My brother took this test and said it was 35. Im not sure but try it

Step-by-step explanation:

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3 years ago
Evaluate 6 over 3 plus 7 times 4
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the answer is B. 244

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PLEASE HELP ASAP!!!!
musickatia [10]
Let us model this problem with a polynomial function.

Let x =  day number (1,2,3,4, ...)
Let y = number of creatures colled on day x.

Because we have 5 data points, we shall use a 4th order polynomial of the form
y = a₁x⁴ + a₂x³ + a₃x² + a₄x + a₅

Substitute x=1,2, ..., 5 into y(x) to obtain the matrix equation
|   1     1    1    1    1  |  | a₁ |      | 42 |
| 2⁴  2³  2²  2¹  2⁰  |  | a₂ |      | 26 |
| 3⁴  3³  3²  3¹  3⁰   |  | a₃ |  =  | 61 |
| 4⁴  4³  4²  4¹  4⁰   |  | a₄ |      | 65 |
| 5⁴  5³  5²  5¹  5⁰  |  | a₅ |      | 56 |

When this matrix equation is solved in the calculator, we obtain
a₁ =      4.1667
a₂ =  -55.3333
a₃ =  253.3333
a₄ =  -451.1667
a₅ =   291.0000

Test the solution.
y(1) = 42  
y(2) = 26
y(3) = 61
y(4) = 65
y(5) = 56

The average for 5 days is (42+26+61+65+56)/5 = 50.
If Kathy collected 53 creatures instead of 56 on day 5, the average becomes
(42+26+61+65+53)/5 = 49.4.

Now predict values for days 5,7,8.
y(6) = 152
y(7) = 571
y(8) = 1631


3 0
3 years ago
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