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3 years ago

What is another name for plane z

Mathematics

2 answers:

jarptica [38.1K]3 years ago

4 0

Plain Z is the plane that is width basicly if looking at a 3d figure.

Crank3 years ago

3 0

If your doing the worksheet I think you are doing then plane z is XTV, XVL, or LTV.

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Find the distance between a point (– 2, 3 – 4) and its image on the plane x+y+z=3 measured parallel to a line

Ber [7]

Answer:

The distance is:

$\displaystyle\frac{3\sqrt{142}}{10}$

Step-by-step explanation:

We re-write the equation of the line in the format:

$\displaystyle\frac{x+2}{3}=\frac{y+\frac{3}{2}}{2}=\frac{z+\frac{4}{3}}{\frac{5}{3}}$

Notice we divided the fraction of y by 2/2, and the fraction of z by 3/3.

In that equation, the director vector of the line is built with the denominators of the equation of the line, thus:

$\displaystyle\vec{v}=\left< 3, 2, \frac{5}{3}\right>$

Then the parametric equations of the line along that vector and passing through the point (-2, 3, -4) are:

$x=-2+3t\\y=3+2t\\\displaystyle z=-4+\frac{5}{3}t$

We plug them into the equation of the plane to get the intersection of that line and the plane, since that intersection is the image on the plane of the point (-2, 3, -4) parallel to the given line:

$\displaystyle x+y+z=3\to -2+3t+3+2t-4+\frac{5}{3}t=3$

Then we solve that equation for t, to get:

$\displaystyle \frac{20}{3}t-3=3\to t=\frac{9}{10}$

Then plugging that value of t into the parametric equations of the line we get the coordinates of the intersection:

$\displaystyle x=-2+3\left(\frac{9}{10}\right)=\frac{7}{10}\\\displaystyle y=3+2\left(\frac{9}{10}\right)=\frac{24}{5} \\\displaystyle z=-4+\frac{5}{3}\left(\frac{9}{10}\right)=-\frac{5}{2}$

Then to find the distance we just use the distance formula:

$\displaystyle d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2}$

So we get:

$\displaystyle d=\sqrt{\left(-2-\frac{7}{10}\right)^2+\left(3-\frac{24}{5}\right)^2+\left(-4 +\frac{5}{2}\right)^2}=\frac{3\sqrt{142}}{10}$

3 0

3 years ago

Which expresions are equivalent to x+2y+x+2? yall please help....

Iteru [2.4K]

Answer:

2x + 2y + 2

Step-by-step explanation:

x+ 2y + x +2 (combine like terms)

x + x + 2y + 2

2x + 2y + 2

8 0

2 years ago

This table represents a quadratic function with a vertex at (1, 0). What is the

inn [45]

Answer:

Step-by-step explanation:

7 0

1 year ago

Tanya's rotation maps point K(24, –15) to K'(–15, –24). Which describes the rotation? 90 degrees clockwise rotation 270 degrees

alexira [117]

Answer:

A. 90 degrees clockwise rotation

Step-by-step explanation:

Of we have a coordinate axis (x,y), if this axis is rotated 90° clock wide, the resulting coordinate of the pre-image will be the coordinate (y -x). Note that the coordinates was swapped and then the new y coordinate negated.

Given the coordinate K(24, -15). If we rotate this clockwisely, first we swap the coordinate axis to have (-15, 24)

Them we will negate the new y coordinate axis to have;

K'(-15, -24)

Therefore the correct answer is 90° clockwise rotation.

7 0

2 years ago

Read 2 more answers

What is 925/1000 in simplest form

mojhsa [17]

37/40 37 divide it by 25 and it comes out 37 and if you divide 25 into 1000 in comes out to be 40

8 0

3 years ago