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3 years ago

Find the coordinates of the point (x,y,z)(x,y,z) on the plane z=2x+3y+3z=2x+3y+3 which is closest to the origin.

1 answer:

4 0

The vector equation of the line through the origin perpendicular to the plane is
.. (x, y, z) = t(2, 3, -1)
so the point of interest will satisfy
.. 2(2t) +3(3t) -(-t) = -3
.. 14t = -3
.. t = -3/14
and its coordinates are (x, y, z) = (-3/7, -9/14, 3/14)

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So what exactly is a,b,c

Gala2k [10]

If you’re talking about answers a would be the option first b would be 2nd and c would be 3rd

4 0

2 years ago

for each of the number lines, write an absolute value equation in the form |x-c|=d, where c and d are some numbers, to satisfy t

Ganezh [65]

Answer:

The absoulute value is 4 and 6

Step-by-step explanation:

Every Absolute value is a postive number

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2 years ago

A park is rectangular with a length of 12 miles. If the area of the park is 68 square miles, what is its width? Input your answe

Veronika [31]

Answer:

17/3

Step-by-step explanation:

to find out the width, we need to divide the area by the length.

68/12=5.666666667

fraction form: 17/3 (5 2/3)

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1 year ago

The population of Detroit, Michigan, decreased from 1,027,974 in 1990 to 688,701 in 2013 (Source: U.S. Census Bureau). Find the

AleksandrR [38]

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

to get the slope of any straight line, we simply need two points off of it, so let's use the ones provided in that

$\begin{array}{|cc|ll} \cline{1-2} \stackrel{years}{x}&\stackrel{population}{y}\\ \cline{1-2} 1990&1027974\\ 2013&688701\\ \cline{1-2} \end{array}\hspace{5em} (\stackrel{x_1}{1990}~,~\stackrel{y_1}{1027974})\qquad (\stackrel{x_2}{2013}~,~\stackrel{y_2}{688701}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{688701}-\stackrel{y1}{1027974}}}{\underset{run} {\underset{x_2}{2013}-\underset{x_1}{1990}}} \implies \cfrac{-339273}{23}\implies -14751\qquad \stackrel{rate~of}{change}$

let's notice, is negative since the population decreased.

5 0

1 year ago

The point (-5,-4)<br> is rotated 90<br> counterclockwise .

ELEN [110]

(-4,5) is the correct answer because it needs to be (-y,x) meaning the original x value stays the same because we’re going backwards and the y value changes signs

5 0

2 years ago