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bearhunter [10]
3 years ago
12

A mini-cone has a diameter of 3 inches and holds 10 in3 of ice cream. A mega-cone holds 49.13 in3 of ice cream. If the cones hav

e the same height, what is the diameter of the mega-cone?
A. 6.65 in.
B. 4.27 in.
C. 3.32 in.
D. 2.55 in.
Mathematics
1 answer:
marissa [1.9K]3 years ago
3 0
The answer would be D
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Find the surface area of the part of the circular paraboloid z=x^2+y^2 that lies inside the cylinder X^2+y^2=1
hichkok12 [17]

Answer:

\mathbf{\dfrac{\pi}{6}[5 \sqrt{5}-1]}

Step-by-step explanation:

Given that:

The surface area (S.A) z = x^2 +y^2

Hence the S.A is of form z = f(x,y)

Then the S.A can be represented with the equation

A(S) = \iint _D \sqrt{1+ (\dfrac{\partial z}{\partial x})^2+ (\dfrac{\partial z}{\partial y})^2} \ dA

where :

D = cylinder x^2 +y^2 =1

In polar co-ordinates:

D = {(r, θ): 0≤ r ≤ 1, 0 ≤ θ ≤ 2π)

Similarly, \dfrac{\partial z}{\partial x} = 2x and \dfrac{\partial z}{\partial y} = 2y

Therefore;

S.A = \iint_D \sqrt{1+4x^2+4y^2} \ dA

= \iint_D \sqrt{1+4(x^2+y^2)} \ dA

= \int^{2 \pi}_{0} \int^{1}_{0}  \sqrt{1+4r^2} \ r \ dr \d \theta

= [\theta]^{2 \pi}_{0} \dfrac{1}{8}\times \dfrac{2}{3}\begin {bmatrix} (1+4r^2)^{\dfrac{3}{2}}\end {bmatrix}^1_0

= 2 \pi \times \dfrac{1}{12}[5^{\dfrac{3}{2}} - 1]

\mathbf{=\dfrac{\pi}{6}[5 \sqrt{5}-1]}

6 0
3 years ago
The total cost C for p pounds of plutonium if each pound costs $3.32
fgiga [73]
Each pound cost $3.32

p pounds would cost = p*3.32 = 3.32p

Total cost C =  $3.32p

I hope this explains it.
3 0
3 years ago
Please find the value of X for number 4 5 and 6 thank you :)
antiseptic1488 [7]

Answer:

4. x = 6

5. x = 31

6. x = 34

Step-by-step explanation:

4. vertical angles

- 36/6 = 6

5. supplementary angles

180 - 56 = 124

124/4 = 31

6. complementary angle

90 - 22 = 68

68/2 = 34

6 0
2 years ago
Read 2 more answers
A square has a side length 9 cm. What is its area? A square has an area of 9 cm2. What is its side length?
Kay [80]

Answer:

Area = 81; Side Length = 3

Step-by-step explanation:

The area of a square is the side lenght squared, and 9² is 81.

The side lengh can be found by taking the square root of the area. √9 = 3

5 0
2 years ago
Please help me 30 points please help me
Romashka [77]

Answer:

y = + 1x - 4y

Step-by-step explanation:

This could be the wrong way of writing it but thats the pattern ❤

4 0
2 years ago
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