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Dovator [93]
3 years ago
10

Find a vector equation and parametric equations for the line. (Use the parameter t.) The line through the point (0, 11, −8) and

parallel to the line x = −1 + 4t, y = 6 − 4t, z = 3 + 6t
Mathematics
1 answer:
NNADVOKAT [17]3 years ago
3 0

Answer:

The vector equation of the line is \overrightarrow {r}=(11j-8k)+t(4i-4j+6k) and parametric equations for the line are x=4t, y=11-4t, z=-8+6t.

Step-by-step explanation:

It is given that the line passes through the point (0,11,-8) and parallel to the line

x=-1+4t

y=6-4t

z=3+6t

The parametric equation are defined as

x=x_1+at,y=y_1+bt,z=z_1+ct

Where, (x₁,y₁,z₁) is point from which line passes through and <a,b,c> is cosine of parallel vector.

From the given parametric equation it is clear that the line passes through the point (-1,6,3) and parallel vector is <4,-4,6>.

The required line is passes through the point (0,11,-8) and parallel vector is <4,-4,6>. So, the parametric equations for the line are

x=4t

y=11-4t

z=-8+6t

Vector equation of a line is

\overrightarrow {r}=\overrightarrow {r_0}+t\overrightarrow {v}

where, \overrightarrow {r_0} is a position vector and \overrightarrow {v} is cosine of parallel vector.

\overrightarrow {r}=(11j-8k)+t(4i-4j+6k)

Therefore the vector equation of the line is \overrightarrow {r}=(11j-8k)+t(4i-4j+6k) and parametric equations for the line are x=4t, y=11-4t, z=-8+6t.

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Which angle is an alternate exterior angle to 28?
MA_775_DIABLO [31]

9514 1404 393

Answer:

  ∠4

Step-by-step explanation:

"Alternate" means the angle is on the other side of the transversal t. "Exterior" means it is on the outside of line e crossing the transversal. The alternate exterior angle to angle 8 is angle 4.

7 0
2 years ago
George and Carmen went on a bicycle trip. they took a bus to their starting point, and then biked the rest. they traveled 325 ki
chubhunter [2.5K]
In the question there are numerous information's of immense importance already given. Let us write them down first
Distance traveled by bike = x km
Distance traveled by bus = y km
Total distance traveled by George and Carmen = 325 km
Then
x + y = 325
Another equation can be determined by
x - y = 75
x = y + 75
Now we will put the value of x in relation to y in the first equation.
x + y =325
y + 75 + y = 325
2y = 325 - 75
2y =250
y = 250/2
  = 125 km
Now putting the value of y in equation given below, we get
x + y = 325
x + 125 = 325
x = 325 - 125
  = 200 km
So the distance they biked is 200 km and the distance they traveled by bus is 125 km.
6 0
3 years ago
Which expression could be substituted for y in the second equation to find the value of x?
EastWind [94]

value of x is x=-\frac{29}{4} and value of y is y=-\frac{9}{2}

Step-by-step explanation:

We need to find Which expression could be substituted for y in the second equation to find the value of x

The given equations are:

2x-y=-10\,\,\,(1)2x - 3y= -1\,\,\,\,(2)

For putting value of y in second equation, we will find from equation 1

From equation 1:

2x-y=-10\\-y=-10-2x\\y=10+2x

Putting value of y i.e y=10+2x in equation (2) to find value of x

2x-3y=-1\\2x-3(10+2x)=-1\\2x-30-6x=-1\\-4x=-1+30\\-4x=29\\x=\frac{29}{-4}\\x=-\frac{29}{4}

So, now finding value of y by putting value of x= -29/4 in eq(1)

2x-y=-10\\2(-\frac{29}{4})-y=-10\\-\frac{29}{2}-y=-10\\-y=-10+\frac{29}{2}\\ -y=\frac{-20+29}{2}\\ -y=\frac{9}{2}\\ y=-\frac{9}{2}

So, value of x is x=-\frac{29}{4} and value of y is y=-\frac{9}{2}

Keywords: System of equations

Learn more about System of equations at:

  • brainly.com/question/6075514
  • brainly.com/question/7490805
  • brainly.com/question/13168205

#learnwithBrainly

6 0
3 years ago
The product of 4 and 1/6 is _
Elis [28]

Answer:

2/3

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
Suppose a plane has 500 seats. From experience, it's known that 10% of people who have bought the ticket do not show up. Now, 55
oksano4ka [1.4K]

Answer:

The probability that there will be enough seats for all people who turn up is 0.78

Step-by-step explanation:

Given:

A = 500

B = 550

Since it is known from experience that 10% of people who bought tickets don't show up, to find the probability that there will be enough seats for those who show up, we have:

Percentage that will turn up = 100℅ - 10℅ = 90℅

Since 90℅ will turn up, that means the number of passengers will be less than 500.

Therefore for P less than or equal to 500, we use:

P ( X <_ 500) =

= [500 + 0.5 - (550 * 0.9)] / sqrt*(550 * 0. 9 * 0.1)

= 0.78

Therefore, the probability that there will be enough seats for all people who turn up is 0.78

7 0
3 years ago
Read 2 more answers
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