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Irina-Kira [14]
3 years ago
11

Find the ratio in which the line joining the points (2, 4, 16) and (3, 5, -4) is divided by the plane 2x – 3y+ z+ 6 = 0. Also fi

nd the co-ordinates of the point of division
Mathematics
1 answer:
Nastasia [14]3 years ago
5 0

Answer:

Step-by-step explanation:

let the plane intersects the join of points in the ratio k:1

let (x,y,z) be the point of intersection.

x=\frac{3k+2}{k+1} \\y=\frac{5k+4}{k+1} \\z=\frac{-4k+16}{k+1} \\\because ~(x,y,z)~lies~on~the~plane.\\2(\frac{3k+2}{k+1} )-3(\frac{5k+4}{k+1} )+\frac{-4k+16}{k+1} +6=0\\multiply~by~k+1\\2(3k+2)-3(5k+4)+(-4k+16)+6(k+1)=0\\6k+4-15k-12-4k+16+6k+6=0\\-7k+14=0\\k=2\\x=\frac{3*2+2}{2+1} =\frac{8}{3} \\y=\frac{5*2+4}{2+1}=  \frac{14}{3} \\z=\frac{-4*2+16}{2+1} =\frac{8}{3}

point of intersection is (8/3,14/3,8/3)

and ratio of division is 2:1

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Step-by-step explanation:

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3 years ago
PLEASE HELP WITH MATH CONSTRUCTED RESPONSE!!
strojnjashka [21]

Answer:

  1. y = 0.937976x +12.765
  2. $12,765
  3. $31,524
  4. the cost increase each year

Step-by-step explanation:

1. For this sort of question a graphing calculator or spreadsheet are suitable tools. The attached shows the linear regression line to have the equation ...

... y = 0.937976x + 12.765

where x is years since 2000, and y is average tuition cost in thousands.

2. The y-intercept is the year-2000 tuition: $12,765.

3. Evaluating the formula for x=20 gives y ≈ 31.524, so the year-2020 tuition is expected to be $31,524.

4. The slope is the rate of change of tuition with respect to number of years. It is the average increase per year (in thousands). It amounts to about $938 per year.

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5 0
3 years ago
What is the perimeter of the triangle?<br>​
Naya [18.7K]

Answer:

30 units

Step-by-step explanation:

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Please mark as brainliest :)

7 0
3 years ago
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One fifth of a number plus three times the number is equal to twice the number plus 42. What is the number
borishaifa [10]

Equation to find number's value: \frac{1}{5}n + 3n = 2n + 42

Number's value: n = 35


Explanation:

Let n be the unknown number for this problem.

One fifth of a number is the same as \frac{1}{5}n.

Three times the number is the same as 3n.

Twice the number plus 42 is the same as 2n + 42.

So, using the information we've gathered so far, we can create the equation that will provide us with n's value.

Equation: \frac{1}{5}n + 3n = 2n + 42

We can use this equation to find n's value.

You can subtract 2n from both sides to get the equation \frac{1}{5}n + n = 42, which is the same thing as the equation we were using.

Now add n and \frac{1}{5}n together to get 1\frac{1}{5}n.

After you do this, your equation should look like 1\frac{1}{5}n=42.

Now divide both sides by 1\frac{1}{5} to get n's value.

n = 35

7 0
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