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3 years ago

Match the integrals with the type of coordinates which make them the easiest to do.

Mathematics

1 answer:

WARRIOR [948]3 years ago

6 0

Answer:

1. C. cylindrical coordinates

2 A. spherical coordinates

3. A. spherical coordinates

4. D. Cartesian coordinates

5 B. polar coordinates

Step-by-step explanation:

USE THE BOUNDARY INTERVALS TO IDENTIFY

1. ∭E dV where E is:

x^2 + y^2 + z^2<= 4, x>= 0, y>= 0, z>= 0 -- This is A CYLINDRICAL COORDINATES SINCE x>= 0, y>= 0, z>= 0

2. ∭E z^2 dV where E is:

-2 <= z <= 2,1 <= x^ 2 + y^2 <= 2 This is A SPHERICAL COORDINATES

3. ∭E z dV where E is:

1 <= x <= 2, 3<= y <= 4,5 <= z <= 6 -- This is A SPHERICAL COORDINATES

4. ∫10∫y^20 1/x dx ---- This is A CARTESIAN COORDINATES

5. ∬D 1/x^2 + y^2 dA where D is: x^2 + y^2 <=4 This is A POLAR COORDINATES

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Miranda has a bag of marbles with 5 blue marbles, 1 white marbles, and 1 red marbles. Find the following probabilities of Mirand

kvasek [131]

Answer:

(a) $\frac{5}{7},\frac{1}{6}$ (b) $\frac{1}{7},\frac{1}{6}$ (c) $\frac{5}{7},\frac{2}{3},\frac{3}{5}$

Step-by-step explanation:

GIVEN: Miranda has a bag of marbles with $5$ blue marbles, $1$ white marbles, and

TO FIND: a) A Blue, then a red Preview

,b)A red, then a white Preview

,c) A Blue, then a Blue, then a Blue.

SOLUTION:

Total marbles in bag $=7$

(a)

Probability of drawing blue marble $=\frac{\text{total blue marble}}{\text{total marbles}}$

$=\frac{5}{7}$

As marble is not returned to bag,

Probability of drawing red marble $=\frac{\text{total red marble}}{\text{total marbles}}$

$=\frac{1}{6}$

(b)

Probability of drawing red marble $=\frac{\text{total red marble}}{\text{total marbles}}$

$=\frac{1}{7}$

As marble is not returned to bag,

Probability of drawing white marble $=\frac{\text{total white marble}}{\text{total marbles}}$

$=\frac{1}{6}$

(c)

Probability of drawing blue marble $=\frac{\text{total blue marble}}{\text{total marbles}}$

$=\frac{5}{7}$

As marble is not returned to bag,

Probability of drawing second blue marble $=\frac{\text{total blue marble}}{\text{total marbles}}$

$=\frac{4}{6}=\frac{2}{3}$

As marble is not returned to the bag

Probability of drawing third blue marble $=\frac{\text{total blue marble}}{\text{total marbles}}$

$=\frac{3}{5}$

8 0

3 years ago

What is the quotient of 4 divided by 9/10

kozerog [31]

The answer is 49/9 because you can first convert the fraction into a decimal and devide 4 and 0.9 and you will get 5.4 repeating and which is 49/9

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3 years ago

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The ratio of 48 patients 6 nurse

DanielleElmas [232]

Answer:

8:1

Step-by-step explanation:

Do 48/6 to find the ratio

4 0

3 years ago

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a piece of land 120 ft by 240 ft contains a circular garden. surrounding the garden, there is a circular fence that is 20 ft in

damaskus [11]

the area of the piece of land that is not part of the garden is $28,486ft^2$ .

<u>Step-by-step explanation:</u>

Here we have , a piece of land 120 ft by 240 ft contains a circular garden. surrounding the garden, there is a circular fence that is 20 ft in diameter. We need to find what is the area of the piece of land that is not part of the garden . Let's find out:

Let's calculate area of land and circular garden , and in order to find the area of the piece of land that is not part of the garden we will subtract area of circular garden from land !

Area of Land:

Area of land is given by

⇒ $length(width)$

⇒ $120(240)$

⇒ $28,880ft^2$

Area of Garden:

Area of circular garden given by

⇒ $\pi r^2$

⇒ $\pi (\frac{D}{2})^2$

⇒ $\pi (\frac{20}{2})^2$

⇒ $\pi (10)^2$

⇒ $100\pi$

⇒ $100(3.14)$

⇒ $314ft^2$

Hence , the area of the piece of land that is not part of the garden is 28,880-314 = 28,486 . Therefore , the area of the piece of land that is not part of the garden is $28,486ft^2$ .

8 0

3 years ago

You want to divide a square piece of paper into two equivalent triangle if the square measures 20m in each side what will the th

Zolol [24]

20 √2

It would be a 45 45 90 triangle. So both sides are X (20) and the missing side is X √2 (20 √2).

3 0

3 years ago