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azamat
3 years ago
8

Use spherical coordinates. let h be a solid hemisphere of radius 1 whose density at any point is proportional to its distance fr

om the center of the base. (let k be the constant of proportionality.) (a) find the mass of h.

Mathematics
1 answer:
MA_775_DIABLO [31]3 years ago
7 0
Whereas the density of the hemisphere at any point is proportional to it's density, then 

 The full answer in attachment, we use the partial integral using the <span>spherical coordinates, 

and we find that </span>the mass of h = <span>πK/2</span>

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A line passes through the point (6, -2) and has a slope of 4/3 Write an equation in point-slope form for this line.​
kumpel [21]

Answer:

y = 4/3x - 10

Step-by-step explanation:

Slope: 4/3

y-intercept: -2 - (4/3)(6) = -2 - 8 = -10

5 0
2 years ago
Ice Cream Scoops - In shops with lots of ice-cream flavors there are many different flavor combinations, even with only a 2-scoo
blondinia [14]

Answer:

The general formula that can be used to find the required combinations for n flavor ice-cream.

N_n = \frac{n(n+1)}{2}

For 10 ice-cream flavors

N_{10} = \frac{10(10+1)}{2}

N_{10} = 55

Step-by-step explanation:

Let V = Vanila, C = Chocolate, S = Strawberry, P = Pineapple, B = Berry

2 ice-cream flavor:

V, C

{V/V, V/C, C/C}

3 possible combinations

3 ice-cream flavor:

V, C, S

{V/V, V/C, V/S, C/S, C/C, S/S}

6 possible combinations

4 ice-cream flavor:

V, C, S, P

{V/V, V/C, V/S, V/P, C/S, C/P, S/P, C/C, S/S, P/P}

10 possible combinations

5 ice-cream flavor:

V, C, S, P, B

{V/V, V/C, V/S, V/P, V/B, C/S, C/P, C/B, S/P, S/B, P/B, C/C, S/S, P/P, B/B }

15 possible combinations

So we have a series of

3, 6, 10, 15...

This series is known as Triangular number series

1 + 2 = 3

1 + 2 + 3 = 6

1 + 2 + 3 + 4 = 10

1 + 2 + 3 + 4 + 5 = 15

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N_n = \frac{n(n+1)}{2}

Using the above formula we can predict the number of 2-scoop combinations with 10 flavors.

N_{10} = \frac{10(10+1)}{2}

N_{10} = 55

Therefore, there are 55 different combinations of 2-scoop  with 10 flavors.

5 0
3 years ago
What is the simplified form of the expression of the square root of 121/81
larisa [96]
Decimal form : 2.61728395
Mixed Number: 2  50/81
3 0
3 years ago
Write the line in slope-intercept form, that is (a) parallel and (B) perpendicular to the line 4x + 2y = 6 that passes through t
zaharov [31]
The answer to the question

8 0
3 years ago
What is the value of y?
Anastaziya [24]
Y=8 I hope I helped. also I attached a map of a 30,60,90 Triangle

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3 years ago
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