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Find parametric equations for the line. (Enter your answers as a comma-separated list of equations. Let x, y, and z be functions of t.) The line in the direction of the vector 5 i + 5 j − 6k and through the point (−4, 4, −2).

Answers

Answer 1

Answer:

The parametric equations are:

x = -4 + 5t

y = 4 + 5t

z = -2 - 6t

The given direction vector is:

$\bar{V} = 5i + 5j - 6k$

The direction vector can also be written as:

$\bar{V} = <a, b, c> = <5, 5, -6>$

The point X₀ = (x₀, y₀, z₀) = (-4, 4, -2)

The parametric equation is of the form:

$X = X_(0) + \bar{V}t$

This is:

$\left[\begin{array}{ccc}x\ny\nz\end{array}\right] = \left[\begin{array}{ccc}x_0\ny_0\nz_0\end{array}\right] + \left[\begin{array}{ccc}a\nb\nc\end{array}\right]t$

$\left[\begin{array}{ccc}x\ny\nz\end{array}\right] = \left[\begin{array}{ccc}-4\n4\n-2\end{array}\right] + \left[\begin{array}{ccc}5\n5\n-6\end{array}\right]t$

The parametric equations are therefore:

x = -4 + 5t

y = 4 + 5t

z = -2 - 6t

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Answer 2

Answer:

Answer:

x=5t-4 , y=5t+4 , z=-6t-2

Step-by-step explanation:

So we are going to use (-4,4,-2) as an initial point, p.

The direction vector is v=5i+5j-6k or <5,5,-6>.

The vector equation is r=vt+p.

That means we have r=<5,5,-6>t + <-4,4,-2>.

So the parametric equations are

x=5t-4

y=5t+4

z=-6t-2

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You are going to play mini golf. A ball machine that contains 23 green golf balls, 24 red golf balls, 18 blue golf balls, and 24 yellow golf balls, randomly gives you your ball. What is the probability that you end up with a red golf ball?

Answers

Answer:

$(24)/(89)$ chance or ≈27% chance or 0.27

Step-by-step explanation:

P of getting a red golf ball: $(24)/(23+24+18+24) =(24)/(89)$

Turner took a total of 8 quizzes over the course of 4 weeks. How many weeks of school will Turner have to attend this quarter before he will have taken a total of 16 quizzes? Assume the relationship is directly proportional. plz just put the answer

Answers

Answer:

8 wks

Step-by-step explanation:

It's 8 weeks

It's literally 8 weeks

Add (do not round): 10.6 + 6 + 2.09 =

Help please

Answers

The sum of 10.6, 6, and 2.09 is 18.69. The question asks to add the following numbers: 10.6, 6, and 2.09. Adding them together, you simply line up the decimal points and add each column from right to left.

Step 1: Add the numbers in the hundredths place: there are no hundredths in 10.6 or in 6, and there are 9 hundredths in 2.09. So, we simply write down .09.

Step 2: Add the numbers in the tenths place: there are 6 tenths in 10.6, no tenths in 6, and no tenths in 2.09. Combined, we have .60.

Step 3: Add the numbers in the ones place: there are 0 ones in 10.6, 6 ones in 6, and 2 ones in 2.09. Combined, we have 8.0.

Step 4: Add the tens place: there is 1 ten in 10.6, no tens in 6, and no tens in 2.09. We write down 10.

Finally, adding these components together (0.09+,60+8.0+10) we get the total of 18.69.

Learn more about Addition here:

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Answer:

18.69

Step-by-step explanation:

Hey can you please help me posted picture of question

Answers

Horizontal translations
Suppose that h> 0
To graph y = f (x + h), move the graph of h units to the left.
We have then:
G (x) = f (x + h)
G (x) = (x + 5) ^ 2
Answer:
The graph of G (x) is given by:
G (x) = (x + 5) ^ 2
option D

From the graphs we can observe that G(x) is 5 units to the left of F(x).

This means a horizontal translation of 5 units to the left of F(x) will result in G(x). Such a translation can be obtained from adding 5 to each x in the equation.

So,

G(x) = F(x+5)

F(x) = (x+5)²

So the correct answer is option D

HELP QUICK!!!L 18 16 12 10 4 32 34 36 38 40 14 46 54 50 08 The graph shows that as Fincreases, C o decreases increases is constant increases then decreases