What’s the arc length

Find the equation for the plane through the points Upper P 0 (4 comma 5 comma negative 3 )P0(4,5,−3), Upper Q 0 (1 comma 4 comm

alexira [117]

Answer:

4x -4y +z = -7

Step-by-step explanation:

The direction vector will be perpendicular to any/all vectors between the given points. It can be found, for example, using the cross product:

d = (P0Q0) × (P0R0) = (-3, -1, 8) × (-4, -3, 4)

The cross product can be computed by hand or by any of a number of calculators or web tools. Here it will be ...

d = (20, -20, 5)

These can be the coefficients of x, y, and z in the plane equation. However, the equation is better written using coefficients that are mutually prime, so we choose the direction vector to be ...

d = (4, -4, 1)

The constant C in the plane equation

d·(x, y, z) = C

will be the dot product of this direction vector (d) any any of the given points. Using R0, we find the constant to be ...

C = (4, -4, 1)·(0, 2, 1) = 4·0 +(-4)·2 +1·1 = -8+1 = -7

so, the plane equation is ...

4x -4y +z = -7

6 0

3 years ago

Multiply 7/8 and 9/10

Ratling [72]

7 times 8 is 56
9 times 10 is 90

4 0

2 years ago

Read 2 more answers

Use the distributive property to multiply 4(-7x-9y-9)

Illusion [34]

4(-7x - 9y - 9) =
-28x - 36y - 36 <==

4 0

3 years ago

Dora calculated the mean absolute deviation for the data set 35, 16, 23, 42, and 19. Her work is shown below.

Crazy boy [7]

Answer:

The calculation in step 3 is wrong

Step-by-step explanation:

1) The mean of a dataset is given by the sum of the values of the dataset divided by the number of values.

In this problem, the dataset is

35, 16, 23, 42, 19

And the number of data is

N = 5

So the mean is

$\bar x=\frac{35+16+23+42+19}{5}=27$

So, step 1 is correct.

2)

The absolute deviation of a value in the dataset is the absolute value of its difference from the mean value:

$\sigma_i = |x_i-\bar x|$

Since here the mean value is

$\bar x=27$

Then for each of the values in this dataset, we have:

$\sigma_{1}=|35-27|=8\\\sigma_{2}=|16-27|=11\\\sigma_{3}=|23-27|=4\\\sigma_{4}=|42-27|=15\\\sigma_{5}=|19-27|=8$

So calculations in step 2 are also correct.

3)

The mean absolute deviation is given by the sum of the absolute deviations for each data divided by the number of values in the dataset.

Therefore in this problem, it is:

$\bar \sigma = \frac{\sum \sigma_i}{N}=\frac{8+11+4+15+8}{5}=9.2$

While the result reported by Dora is 9.5: therefore, this step is not correct.

5 0

2 years ago

Read 2 more answers

Guido is a citizen and resident of Belgium. He has a full-time job in Belgium and has lived there with his family for the past 1

Korvikt [17]

Answer:

Guido stayed in US in 2018 for 180 days which are greater than 31 days.

Guido Stayed in US in 2018 and in 2017 = (180 + 66) > 183 days.

So, yes Guido does meet US Statutory definition in 2018 and stayed 180 days in 2018.

Step-by-step explanation:

Let's find out how many days in total Guido stayed in US in these 3 years 2017, 2018 and 2019.

Year = 2017

Days = 200

Year = 2018

Days = 180

Year = 2019

Days = 70

Total days stayed = 200 + 180 + 70

Total Days Stayed = 450 days.

In U.S, there are two tests are in place and for non-citizen of U.S and for the resident Alien or non - resident Alien status, one must pass one of these two tests, which are as follows:

1. Green Card Test:

2. Substantial Presence Test:

Here, in this problem, Guido is citizen and resident of Belgium. So, will check his criteria according to the substantial presence test.

So, the question is: how many days Guido was present in the U.S in 2018 under resident alien status.

In 2018, Guido stayed in US for 180 days.

So, according to the Substantial Presence test, one must be physically present in US for more than 31 days to be eligible for resident alien status. In addition, in 2018, his total of physical presence in US in 2018 and one third of physical presence in 2017 must be greater than 183 days.

If we see, both conditions are matched in case of Guido.

Guido stayed in US in 2018 for 180 days which are greater than 31 days.

Guido Stayed in US in 2018 and in 2017 = (180 + 66) > 183 days.

So, yes Guido does meet US Statutory definition in 2018 and stayed 180 days in 2018.

3 0

2 years ago