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Svetradugi [14.3K]

3 years ago

9

Find an equation of a plane containing the line r=⟨−5,−1,−1⟩+t⟨−6,10,−5⟩r=⟨−5,−1,−1⟩+t⟨−6,10,−5⟩ which is parallel to the plane

5x+4y+2z=−265x+4y+2z=−26

1 answer:

rodikova [14]3 years ago

7 0

Put the coordinates of the point in for x, y, and z and see what the new constant is.

Your plane is
5x +4y +2z = -31

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kipiarov [429]

Answer:

Step-by-step explanation:

For A, 7x=21, it is asking, 7 multiplied by what number is 21? We can try to figure it out. Let's start with 0.

7(0)≠21

Then 1.

7(1)≠21

7(2)≠21

7(3)=21

Therefore, for question a, the answer is 3.

For question b, it's asking 6 minus what is 2.

With this one, we can say it is 4, since 6-4=2.

Now moving on to B.

a) 2x+4=16

We need to isolate x in order to find it's value.

So we can begin with subtracting 4 from both sides, getting us:

2x=12

Then, if we divide both terms by 2, we get x.

x=12/2

x=6.

b)

3 x (z/4)=9

Again, we need to isolate z.

So, we multiply both sides by 4, getting us

3z=36

then we divide by 3

z=36/3

z=12

c) 16-x=2

Here we simply subtract 16 from each side, then flip the signs to get positive x.

So, 16-x=2

-x=-14

x=14

d) 4k=20

This is essentially asking, 4 times what number is 20?

So we can divide both sides by 4 and get

k=20/4

k=5

5 0

3 years ago

For the given polynomials find the sum of the squares of the roots. P(x)=x^3-x^2-18x+k

slega [8]

$\text{Given that,}\\\\P(x) = x^3 -x^2 -18x+k\\\\\text{If the roots are}~ \alpha, ~ \beta,~\text{and}~ \gamma, ~ \text{then},\\\\\alpha +\beta+\gamma= -\dfrac{(-1)}1 = 1\\\\\alpha \beta +\beta \gamma + \gamma \alpha= -\dfrac{18}1 = -18\\ \\\text{Now, sum of the squares of the roots,}\\\\\alpha^2 + \beta^2 + \gamma^2 = ( \alpha + \beta + \gamma)^2 -2(\alpha \beta + \gamma \beta + \gamma \alpha)\\ \\~~~~~~~~~~~~~~~~~~=1^2 - 2(-18)\\\\~~~~~~~~~~~~~~~~~~=1+36\\\\~~~~~~~~~~~~~~~~~~=37$

6 0

2 years ago

A water park charges a rental fee plus $1.50 per hour to rent inflatable rafts. The total cost to rent a raft do 6 hours is $15.

djyliett [7]

Answer:

rental fee = $6

average cost for 6 hours = $2.50/hour.

Step-by-step explanation:

x + 1.50*6 = 15 where x = the initial rental fee

x + 9 = 15

x = $6

The rental fee is $6.

For 6 hours, the cost per hour works out to 15/6 = $2.50

4 0

3 years ago

A company uses the function C(x)=20.50+2000, where C is the cost and x is the number of units it produces, to determine its dail

Kipish [7]

You left it out, but I'm thinking that there must be an 'x' next to the '20.50' in the function. I'm so sure of it that I'll assume it, as I proceed to answer the question:

C(x) = 20.50x + 2,000

Subtract 2,000 from each side: C - 2,000 = 20.50 x

Divide each side by 20.50 : x = (C - 2,000) / 20.50

When C = $625,000 . . .

x = (625,000 - 2,000) / 20.50 = 623,000 / 20.50 = 30,390.2439

<em>30,390 complete units</em> are produced, and there are 5 bucks left over,
to split up among all the loyal employees who worked with such diligence and dedication to make it happen. The company's senior management will graciously add each worker's share to his gross pay before taxes for the second month following the close of the current quarter, with a photocopied note inserted in the pay envelope, expressing management's sincere thanks to everyone, an admonition not to spend it all in one place, and a reminder that no matter how many festivals to their god they need to go out to the desert to celebrate, their tally of bricks for the next quarter shall not be diminished.

6 0

2 years ago

What is 1,936 divided by 546

nalin [4]

Answer:

3.54578755

Step-by-step explanation:

8 0

3 years ago