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Marina86 [1]
2 years ago
7

Find a vector equation and parametric equations for the line through the point (1,0,6) and perpendicular to the plane x+3y+z=5.

Mathematics
1 answer:
tester [92]2 years ago
5 0

The normal vector to the plane <em>x</em> + 3<em>y</em> + <em>z</em> = 5 is <em>n</em> = (1, 3, 1). The line we want is parallel to this normal vector.

Scale this normal vector by any real number <em>t</em> to get the equation of the line through the point (1, 3, 1) and the origin, then translate it by the vector (1, 0, 6) to get the equation of the line we want:

(1, 0, 6) + (1, 3, 1)<em>t</em> = (1 + <em>t</em>, 3<em>t</em>, 6 + <em>t</em>)

This is the vector equation; getting the parametric form is just a matter of delineating

<em>x</em>(<em>t</em>) = 1 + <em>t</em>

<em>y</em>(<em>t</em>) = 3<em>t</em>

<em>z</em>(<em>t</em>) = 6 + <em>t</em>

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3 0
3 years ago
Two grapefruits and three oranges cost $1.95. Three grapefruits and two oranges cost $2.05.
geniusboy [140]

Answer:

  • one orange costs $0.35  and  one grapefruit costs $0.45

Step-by-step explanation:

<em>let grapefruits be g , let oranges be o</em>

so first equation:

→2g + 3o  = $1.95

→g = ($1.95 - 3o)/2

so second equation:

→ 3g + 2o = $2.05

→ g = ($2.05 - 2o)/3

Solving simultaneously:

→ ($2.05 - 2o)/3 = ($1.95 - 3o)/2

→ 2($2.05 - 2o) = 3($1.95 - 3o)

→ 4.1 - 4o = 5.85 - 9o

→ - 4o + 9o = 5.85 - 4.1

→ 5o = 1.75

→ o = $0.35

Therefore one orange costs $0.35

Then one grapefruit costs g → ($1.95 - 3o)/2

                                               → g = ($1.95 - 3(0.35))/2

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Therefore one grapefruit costs $0.45

4 0
2 years ago
X + 4 is prime x2 – 9 can be factored using the formula.
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We are given two binomials: x+4 , x^2-9.

x+4 can't be factored. Therefore,  it is a prime.

Let us work on x^2-9.

9 could be written as 3^2.

Therefore, x^2-9 = x^2 - 3^2.

Now, we can apply difference of the squares formula to factor it.

We know a^2 -b^2 = (a-b) (a+b).

Therefore,  x^2 - 3^2 can be factored as (x-3) (x+3).

So, x^2-9 is not a prime binomial because it can be factored as (x-3) (x+3).

3 0
3 years ago
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grandymaker [24]

Answer:

50 degrees and 40 degrees

Step-by-step explanation:

50 degrees and 40 degrees

complimentary = add up to 90 degrees

5:4:9

50:40:90

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