Let x and y be random variables of the continuous type having the joint p.d.f. f(x,y)=8xy

You and your family are planning a vacation of a lifetime around the world that will cost $25,000. You borrowed this amount from

labwork [276]

Answer:

$13,125

Step-by-step explanation:

8 0

2 years ago

This is a 3 part 1 question each part on how to locate the plane and a small explanation report working out the recovery details

sesenic [268]

Third leg.

The crew flies at a speed of 560 mi/h in direction N-20°-E.

The wind has a speed of 35 mi/h and a direction S-10°-E.

We then can draw this as:

We have to add the two vectors to find the actual speed and direction.

We will start by adding the x-coordinate (W-E axis):

$\begin{gathered} x=560\cdot\sin (20\degree)+35\cdot\sin (10\degree) \\ x\approx560\cdot0.342+35\cdot0.174 \\ x\approx191.53+6.08 \\ x\approx197.61 \end{gathered}$

and the y-coordinate (S-N axis) is:

$\begin{gathered} y=560\cdot\cos (20\degree)-35\cdot\cos (10\degree) \\ y\approx560\cdot0.940-35\cdot0.985 \\ y\approx526.23-34.47 \\ y\approx491.76 \end{gathered}$

Then, the actual speed vector is v3=(197.61, 491.76).

The starting location for the third leg is R2=(216.66, 167.67) [taken from the previous answer].

Then, we have to calculate the displacement in 20 minutes using the actual speed vector.

We can calculate the movement in each of the axis. For the x-axis:

$\begin{gathered} R_{3x}=R_{2x}+v_{3x}\cdot t \\ R_{3x}=216.66+197.61\cdot\frac{1}{3} \\ R_{3x}=216.66+65.87 \\ R_{3x}=282.53 \end{gathered}$

NOTE: 20 minutes represents 1/3 of an hour.

We can do the same with the y-coordinate:

$\begin{gathered} R_{3y}=R_{2y}+v_{3y}\cdot t \\ R_{3y}=167.67+491.76\cdot\frac{1}{3} \\ R_{3y}=167.67+163.92 \\ R_{3y}=331.59 \end{gathered}$

The final position is R3 = (282.53, 331.59).

To find the distance from the origin and direction, we transform the cartesian coordinates of R3 into polar coordinates:

The distance can be calculated as if it was a right triangle:

$\begin{gathered} d^2=x^2+y^2_{} \\ d^2=282.53^2+331.59^2 \\ d^2=79823.20+109951.93 \\ d^2=189775.13 \\ d=\sqrt[]{189775.13} \\ d\approx435.63 \end{gathered}$

The angle, from E to N, can be calculated as:

$\begin{gathered} \tan (\alpha)=\frac{y}{x} \\ \tan (\alpha)=\frac{331.59}{282.53} \\ \tan (\alpha)\approx1.1736 \\ \alpha=\arctan (1.1736) \\ \alpha=49.56\degree \end{gathered}$

If we want to express it from N to E, we substract the angle from 90°:

$\beta=90\degree-\alpha=90-49.56=40.44\degree$

Answer: the final location can be represented with the vector (282.53, 331.59).

1) The distance from the origin is 435.63 miles and

2) the direction is N-40°-E.

7 0

11 months ago

How to put y =2x+1 on a table

valentina_108 [34]

Answer:

I put the table below

Step-by-step explanation:

Find x and y values for the equation.

Put these values into a table

If this answer helps, please make me Brainliest!

7 0

3 years ago

Need some help with this soon!

Lena [83]

Answer:

f(x)=|x+6|

Step-by-step explanation:

because it is moving the function without changing the slope

5 0

3 years ago

Two blocks are initially at rest with a compressed spring between them. When the spring is released, the 2m block moves to the l

choli [55]

The statement that best describes the blocks after the spring is released is the total momentum is zero.

<h3 /><h3>Law of conservation of momentum</h3>

From the law of conservation of momentum, the initial momentum of the system, M equals the final momentum of the system M'

M = M'

<h3>Momentum of blocks</h3>

Now, since both blocks are initially at rest, the initial momentum M = 0.

Since the initial momentum equals the final momentum after the blocks are released,

M = M' = 0

So, the total momentum after the blocks are released is zero.

So, the statement that best describes the blocks after the spring is released is the total momentum is zero.

Learn more about total momentum here:

brainly.com/question/25121535

7 0

2 years ago