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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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In a class of 7, there are 3 students who have done their homework.
max2010maxim [7]

Answer:

4/35

Step-by-step explanation:

Probability of 1 student having no hw is 4/7, then 3/6, then 2/5

4/7 x 3/6 x 2/5 reduces to 4/35

5 0
3 years ago
There are 22 events at an indoor track and field meet. The ratio of track events to field events is 8:3. How many of the events
MA_775_DIABLO [31]
First, let's look at the ratio.
You also know that for every 8 indoor events, there is 3 field events.
Therefore, the amount of indoor events is 8 on 11 events total, as 8 + 3 = 11
 

Then, let's look at the actual number of events. If there is 22 events total, you need to solve this proportion :

\frac{8}{11} =  \frac{?}{22}
4 0
3 years ago
How many meters are in 3.7 km?
Mashcka [7]

Answer:

3700 m.

Step-by-step explanation:

3.7km= 3.7* 1000

3.7 km = 3700 m

3 0
3 years ago
Consider the equation below. f(x) = 2x3 + 3x2 − 336x (a) Find the interval on which f is increasing. (Enter your answer in inter
Olegator [25]

Answer:

The function f(x) = 2x³ + 3x² - 336x

is

Increasing on: (-∞, -8) U (7, ∞)

and

Decreasing on: (-8, 7)

Step-by-step explanation:

Given the function

f(x) = 2x³ + 3x² - 336x

We need to find the interval on which f is increasing, and the interval on which it is decreasing.

First, we take the derivative of f with respect to x to obtain

f'(x) = 6x² + 6x - 336

Next, set f'(x) = 0 and solve for x.

f'(x) = 6x² + 6x - 336 = 0

Dividing by 6, we have

x² + x - 56 = 0

(x - 7)(x + 8) = 0

x = 7 or x = -8

Now we have the interval

(-∞, -8) ∪ (-8, 7) ∪ (7, ∞)

Let us substitute a value from the interval (-∞, -8) into the derivative to determine if the function is increasing or decreasing.

Let us choose x = -9, then

f'(-9) = 6(-9)² + 6(-9) - 336

= 96 > 0

Since 96 is positive, the function is increasing on (-∞, -8).

Again, substitute a value from the interval (-8, 7) into the derivative to determine if the function is increasing or decreasing.

Choose -2

f'(-2) = 6(-2)² + 6(-2) - 336

= -324 < 0

Since -324 is negative, then the function is decreasing on (-8, 7)

Lastly, substitute a value from the interval (7, ∞) into the derivative

Choose x = 9

6(9)² + 6(9) - 336

= 204

The function is increasing on (8, ∞)

f'(x) > 0

Collating these, we have the function to be

Increasing on:

(-∞, -8) U (7, ∞)

Decreasing on:

(-8, 7)

7 0
4 years ago
Read 2 more answers
Can someone tell me step by step how to solve this
Igoryamba

Answer:

Step-by-step explanation:

14b = -56

Divide both sides by 14

\frac{14b}{14}=\frac{-56}{14}

b = -4

3 0
3 years ago
Read 2 more answers
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