1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
MAVERICK [17]
3 years ago
5

Find parametric equations for the line through point P(-4,5,2) in the direction of the vector (-6,6,-5)

Mathematics
1 answer:
tigry1 [53]3 years ago
4 0

The vector <em>v</em> (-6, 6, -5) points in the direction of itself, so we start there.

We can capture all points on the line through the origin and the point (-6, 6, -5) by scaling <em>v</em> by an arbitrary real number <em>t</em>.

The line through point <em>P</em> and pointing in the same direction as <em>v</em> is parallel to the other line that passes through the origin. Then the line we want can be obtained by translating the line through the origin by a vector <em>p</em> that points to (-4, 5, 2), so the vector equation for this line is

<em>r </em>(<em>t </em>) = <em>p</em> + <em>t v</em>

<em>r </em>(<em>t </em>) = (-4, 5, 2) + <em>t</em> (-6, 6, -5)

<em>r </em>(<em>t </em>) = (-4 - 6<em>t</em>, 5 + 6<em>t</em>, 2 - 5<em>t</em> )

To get the parametric equations, simply take out the components:

<em>x</em> (<em>t</em> ) = -4 - 6<em>t</em>

<em>y </em>(<em>t</em> ) = 5 + 6<em>t</em>

<em>z</em> (<em>t</em> ) = 2 - 5<em>t</em>

You might be interested in
PLZ HELP ME I REALLY NEED IT
kenny6666 [7]

r = 2 inches

total h of the cylinder = 6+6+6 = 18 inches

SA = 2\pi {r}^{2}  + 2\pi \: rh

= 2\pi \: r(r + h)

= 2 \times 3.14 \times 2(2 + 18)

= 2 \times 3.14 \times 2 \times 20

= 251.2square \: inches

4 0
3 years ago
In a representative sample of 1000 adult Americans, only 400 could name at least one justice who is currently serving on the U.S
lys-0071 [83]

Answer:

1) z = -6.32

2) p-value = 0.001 × 10^(-2)

3) we will reject the null hypothesis and conclude that there is enough evidence to support the claim that fewer than half of adult Americans can name at least one justice currently serving on the Supreme Court

Step-by-step explanation:

We are told that In a representative sample of 1000 adult Americans, only 400 could name at least one justice.

Thus:

Sample proportion; p^ = 400/1000 = 0.4

Sample size: n = 1000

We want to find if there is convincing evidence to support the claim that fewer than half of adult Americans can name at least one justice.

Thus, the hypothesis is defined as;

Null hypothesis:H0: p ≥ 0.5

Alternative hypothesis: Ha < 0.5

Formula for the test statistic is;

z = (p^ - p)/√(p(1 - p)/n)

Plugging in the relevant values;

z = (0.4 - 0.5)/√(0.5(1 - 0.5)/1000)

z = -6.32

From online p-value from z-score calculator attached, using z = -6.32; significance level of 0.01; one tailed hypothesis;

We have:

p-value = 0.00001 = 0.001 × 10^(-2)

The p-value is less than the significance level and so we will reject the null hypothesis and conclude that there is enough evidence to support the claim that fewer than half of adult Americans can name at least one justice currently serving on the Supreme Court

8 0
2 years ago
2. During a 5-day training at your department, the number of visitors tripled each day. If the training started on a Monday with
bixtya [17]
Monday/345
345×3=
Tuesday/1,035
1,035×3=
Wendsday/3,105
3,105×3
Thursday=9,315
6 0
3 years ago
A system for tracking ships indicated that a ship lies on a hyperbolic path described by 5x2 - y2 = 20. the process is repeated
zysi [14]
Answer:
The ship is located at (3,5)

Explanation:
In the first test, the equation of the position was:
5x² - y² = 20 ...........> equation I
In the second test, the equation of the position was:
y² - 2x² = 7 ..............> equation II
This equation can be rewritten as:
y² = 2x² + 7 ............> equation III

Since the ship did not move in the duration between the two tests, therefore, the position of the ship is the same in the two tests which means that:
equation I = equation II

To get the position of the ship, we will simply need to solve equation I and equation II simultaneously and get their solution.

Substitute with equation III in equation I to solve for x as follows:
5x²-y² = 20
5x² - (2x²+7) = 20
5x² - 2y² - 7 = 20
3x² = 27
x² = 9
x = <span>± </span>√9

We are given that the ship lies in the first quadrant. This means that both its x and y coordinates are positive. This means that:
x = √9 = 3

Substitute with x in equation III to get y as follows:
y² = 2x² + 7
y² = 2(3)² + 7
y = 18 + 7
y = 25
y = +√25
y = 5

Based on the above, the position of the ship is (3,5).

Hope this helps :)
8 0
3 years ago
Please explain if you can. And don’t say to Google it.
Marrrta [24]
So the coordinates are written (x,y) so if you have a graph you would oput the first dot at 1 over,2 up as x avis is the horizontal axis and y is vertical, then your next dot would be three over ,10 up and then your last dot would be 5 over and 18 up, your intercept is where your line meets your axis
7 0
3 years ago
Read 2 more answers
Other questions:
  • You borrow $350 from a friend the first week and pay the friend back $25 week thereafter
    7·2 answers
  • Find the volume of the square pyramid shown. Round to the nearest tenth if necessary.
    15·1 answer
  • Someone help me please
    14·2 answers
  • Solve the inequality. 6 &gt;= -3/2d
    5·1 answer
  • Which of the following describes the transformation of g (x) = 3 (2) Superscript negative x Baseline + 2 from the parent functio
    10·2 answers
  • Naoya read a book cover to cover in a single session, at a rate of 55 pages per hour. After 4 hours, he had 350 pages left to re
    11·1 answer
  • What is the formula for Inflation Rate?
    15·1 answer
  • 4000(1+0.03)over 4 it's compound interest ​
    13·1 answer
  • What is the sign of -4 divided by -8
    14·1 answer
  • Simplify the linear expression. −2x+3(−5x+1) Enter your answer in the box.
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!