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3 years ago

Which graph represents r = 2 + 2 cos(θ)?

Mathematics

2 answers:

mixas84 [53]3 years ago

8 0

Answer:

Explanation:

Edg2020

Orlov [11]3 years ago

7 0

Answer:Second Graph

Step-by-step explanation:

Did it on Edge

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Suppose that the length of a side of a cube X is uniformly distributed in the interval 9

Nastasia [14]

Answer:

$f(v) = \left \{ {{\frac{1}{3}v^{-\frac{2}{3}}\ 9^3 \le v \le 10^3} \atop {0, elsewhere}} \right.$

Step-by-step explanation:

Given

$9 < x < 10$ --- interval

Required

The probability density of the volume of the cube

The volume of a cube is:

$v = x^3$

For a uniform distribution, we have:

$x \to U(a,b)$

and

$f(x) = \left \{ {{\frac{1}{b-a}\ a \le x \le b} \atop {0\ elsewhere}} \right.$

$9 < x < 10$ implies that:

$(a,b) = (9,10)$

So, we have:

$f(x) = \left \{ {{\frac{1}{10-9}\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.$

Solve

$f(x) = \left \{ {{\frac{1}{1}\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.$

$f(x) = \left \{ {{1\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.$

Recall that:

$v = x^3$

Make x the subject

$x = v^\frac{1}{3}$

So, the cumulative density is:

$F(x) = P(x < v^\frac{1}{3})$

$f(x) = \left \{ {{1\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.$ becomes

$f(x) = \left \{ {{1\ 9 \le x \le v^\frac{1}{3} - 9} \atop {0\ elsewhere}} \right.$

The CDF is:

$F(x) = \int\limits^{v^\frac{1}{3}}_9 1\ dx$

Integrate

$F(x) = [v]\limits^{v^\frac{1}{3}}_9$

Expand

$F(x) = v^\frac{1}{3} - 9$

The density function of the volume F(v) is:

$F(v) = F'(x)$

Differentiate F(x) to give:

$F(x) = v^\frac{1}{3} - 9$

$F'(x) = \frac{1}{3}v^{\frac{1}{3}-1}$

$F'(x) = \frac{1}{3}v^{-\frac{2}{3}}$

$F(v) = \frac{1}{3}v^{-\frac{2}{3}}$

So:

$f(v) = \left \{ {{\frac{1}{3}v^{-\frac{2}{3}}\ 9^3 \le v \le 10^3} \atop {0, elsewhere}} \right.$

8 0

3 years ago

I need help with this math homework and need how u did it

xxTIMURxx [149]

Multiply 45 degrees and 72 degrees

5 0

2 years ago

One side of triangle is 3 times the shortest side. The third side is 24 feet more than the shortest side. The perimeter is 94 .

Gemiola [76]

Answer: x+3x+X+24=94

5x+24=94

-24. -24

5x=70

X=14

One side is 14 second side 3(14)=42. Third side 14+24= 38

14+42+38=94

Step-by-step explanation:

5 0

3 years ago

Trent wants to buy a ham sandwich the original price is six how much will Trent pay if he buys during the sale

Ipatiy [6.2K]

It depends on what happens to the price of the item during the sale which is not stated in your problem. So if it cost 6 dollars and goes on sale it should be 6 dollars.

6 0

3 years ago

One number is five more than another and their sum is three less than three times the smaller

soldier1979 [14.2K]

X = y + 5
(x + y) = 3y - 3

y + 5 + y = 3y - 3
2y + 5 = 3y - 3
5 + 3 = 3y - 2y
8 = y

x = y + 5
x = 8 + 5
x = 13

ur numbers are : 8 and 13

5 0

3 years ago

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