Find the parametric equation of the line passing through points (−9,5,−9)-9,5,-9 and (−9,−10,−6)-9,-10,-6.
Write your answer in the form 〈x,y,z〉x,y,z and use tt for the parameter.
Answers
The parametric equation of the line is:
〈x(t), y(t), z(t)〉 = 〈-9, 5 - 15t, -9 + 3t〉
for 0 ≤ t ≤ 1
How to find the parametric equation of the line?We want to find the parametric equation for the line passing through points (−9,5,−9) and (−9,−10,−6).
Where we want the answer in vector form 〈x,y,z〉, and use t for the parameter.
Let's denote the points as P₁ and P₂:
P₁ = (-9, 5, -9)
P₂ = (-9, -10, -6)
The direction vector of the line can be obtained by subtracting the coordinates of P₁ from P₂:
Direction vector = P₂ - P₁ = (-9, -10, -6) - (-9, 5, -9)
= (-9 + 9, -10 - 5, -6 + 9)
= (0, -15, 3)
Now, we can write the parametric equation of the line in vector form as:
R(t) = P₁ + t * Direction vector
Substituting the values of P1 and the direction vector, we have:
R(t) = (-9, 5, -9) + t * (0, -15, 3)
Expanding the equation component-wise, we get:
x(t) = -9 + 0 * t = -9
y(t) = 5 - 15 * t
z(t) = -9 + 3 * t
Therefore, the parametric equation of the line passing through the points (-9, 5, -9) and (-9, -10, -6) is:
〈x(t), y(t), z(t)〉 = 〈-9, 5 - 15t, -9 + 3t〉
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Related Questions
Make a conjecture. let points a and b stay in the same position. what would happen to the angle formed if the vertex of angle aob was moved from the center to point c, which lies on the circle? the measure of angle acb is the measure of angle aob.
Answers
It is conjectured that the angle measure would remain the same if the vertex of angle AOB is moved from O to a point C on the circle.
The Centre of the circle is the location of a point whose separation from a fixed point is constant (h, k). The equation of the circle is given by (x - h)² + (y - k)² = r², where r is the circle's radius and h, k is the coordinate of the circle's Centre on the coordinate plane.
Based on the given information, it appears that the points A, O, and B form an angle AOB with vertex O at the center of a circle. When the vertex of angle AOB is moved from O to point C on the circle, the angle formed would be angle ACB, which is the same measure as angle AOB.
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Answer:
Less than on Edge 2023
Step-by-step explanation:
Which of the following is most likely the next step in the series?
Look at the photo
Answers
11. Arianna wants to paint her bedroom. The room is 21 feet by 14 feet by 6 feet high. How many cans of paint will she need if each gallon covers 120 square feet.
Answers
Answer:
Step-by-step explanation:
Which is the graph of the solution set of −2x + 5y > 15?
Answers
Answer:
given below
Step-by-step explanation:
−2x + 5y > 15
5y > 15 + 2x
if x is 0 then y is 3 and its greater than so increasing
therefore answer is graph A
Answer:
graph a
Step-by-step explanation:
hes right
Work out 4/5 X 1 2/9
Give your answer as a fraction its simplest form.
Answers
Answer:
\(\huge\boxed{\frac{44}{45}}\)
Step-by-step explanation:
To solve this problem first change the mixed number into an improper fraction.
1 2/9 --> 1 = 9/9 --> 9/9 + 2/9 = 11/9
Then, simply multiply the numerator and denominator of each fraction.
4 * 11 = 44
——————
5 * 9 = 45
44/45
Hope it helps :) and let me know if you want me to elaborate.
Please draw this: points a(2,3) and b(2,-3), c and d are collinear, but a,b,c,d, and f are not.
Answers
Here is a diagram of the points described:
(2,3) (2, -3)
| |
| |
c----------d
Based on the given points, let's consider the following:
Point A: A (2, 3)
Point B: B (2, -3)
Points A and B have the same x-coordinate, indicating that they lie on a vertical line. The y-coordinate of A is greater than the y-coordinate of B, suggesting that A is located above B on the y-axis.
Now, you mentioned that points C and D are collinear. Collinear points lie on the same line. Assuming that points C and D lie on the same vertical line as A and B, but at different positions.
The points A (2,3) and B (2, -3) are collinear, but the points A, B, C, D, and F are not. This is because the points A and B have the same x-coordinate, so they lie on the same vertical line. The points C and D also have the same x-coordinate, so they lie on the same vertical line. However, the point F does not have the same x-coordinate as any of the other points, so it does not lie on the same vertical line as any of them.
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in the context of rm and range safety mitigation of risk is the ability
Answers
In the context of Range Safety and Risk Mitigation, the ability to detect, assess, and respond to potential hazards is essential.
Range safety and risk mitigation involve identifying and minimizing potential hazards associated with range operations, such as the launch or test of rockets, missiles, or unmanned aerial vehicles. To ensure safety, it is critical to have the ability to detect and assess potential hazards, such as debris, vehicle or equipment malfunctions, and human error. Once hazards have been identified and assessed, the next step is to develop and implement appropriate safety measures to mitigate the risk associated with those hazards. These measures may include the use of safety protocols, engineering controls, or administrative procedures to ensure that all personnel and equipment are protected. In summary, the ability to detect, assess, and respond to potential hazards is critical for effective range safety and risk mitigation. By implementing appropriate safety measures and protocols, the risks associated with range operations can be minimized, ensuring the safety of personnel and equipment.
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The triangles are similar.
What is the value of x?
Answers
Answer:
x = 16
Step-by-step explanation:
We can use ratios to solve
12 x
--------- = ----------
3 4
Using cross products
12*4 = 3x
Divide each side by 3
48/3 = 3x/3
16 =x
Pls help I don’t have much time.
Answers
Answer:
Dude dont spend 100 points! This place is scamming people
Step-by-step explanation:
find the sum and product of the zeros 2 X square + X - 5 = 0
Answers
Answer:
x=2
Step-by-step explanation:
2x+x- 5 =0
Parallel to the graph of y = 7x - 6 with y-intercept (0,3)
Answers
Answer:
The graph of the lines is given in the picture below:
What is the slope of this line?
Answers
Answer:
3/4
Step-by-step explanation:
Gradient=6/8=3/4
Answer: 3/4
Solve for y in the two equations below using substitution.
3x - 9y = 9
-2x - 2y = 8
Answers
Answer:
C
Step-by-step explanation:
3x - 9y = 9 → (1)
- 2x +2y = 8 ( subtract 2y from both sides )
- 2x = - 2y + 8 ( divide through by - 2 )
x = y - 4
substitute x = y - 4 into (1)
3(y - 4) - 9y = 9
3y - 12 - 9y = 9
- 6y - 12 = 9 ( add 12 to both sides )
- 6y = 21 ( divide both sides by - 6 )
y = \(\frac{21}{-6}\) = - \(\frac{7}{2}\)
a triangle has sides with lengths of 6 kilometers, 7 kilometers, and 10 kilometers. is it a right triangle?
Answers
Answer:
Step-by-step explanation:
no because 6 , 7 and 10 doesn't add up to 180 so it is not
A triangle has sides with lengths of 6 kilometers, 7 kilometers, and 10 kilometers is not a right triangle.
To determine if a triangle is a right triangle, you can use the Pythagorean Theorem. The Pythagorean Theorem states that "In a right-angled triangle, the sum of the square of the two shorter sides is equal to the square of the longest side." It can be written as:
a² + b² = c², where 'a' and 'b' are the lengths of the two legs of a right triangle, and 'c' is the length of the hypotenuse.
In this triangle, the two shorter sides have lengths of 6 kilometers and 7 kilometers and the longest side is 10 kilometers.
The square of 6 kilometers is 36 kilometers and the square of 7 kilometers is 49 kilometers.
The sum of 36 kilometers and 49 kilometers is 85 kilometers.
The longest side of the triangle has a length of 10 kilometers, and the square of 10 kilometers is 100 kilometers.
Since 85 kilometers is not equal to 100 kilometers, this triangle is not a right triangle.
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Here is an equation that is true for all values of x: 5(x + 2) = 5x + 10. Jenny
saw this equation and says she can tell 20(x + 2) + 31 = 4(5x + 10) + 31 is
also true for any value of x. How can she tell? Explain your reasoning.
Answers
Answer:
20(x + 2) = 20x + 40 = 4(5x + 10)
Calculate minimum and maximum frequency for acoustic
and optic mode.
( short question (
Answers
The specific range depends on the material properties and the energy levels involved.
The minimum and maximum frequencies for the acoustic and optic modes depend on the specific system or material under consideration. However, I can provide some general information.
Acoustic Mode:
The acoustic mode refers to the propagation of sound waves or vibrations in a material. In a solid, the acoustic mode can have different types, such as longitudinal and transverse modes.
The minimum frequency for the acoustic mode is typically determined by the size and physical properties of the material. In general, it can be close to zero for macroscopic objects or materials with low elasticity.
The maximum frequency for the acoustic mode depends on factors such as the speed of sound in the material and the characteristic dimensions of the system. It can range from a few kilohertz to several gigahertz.
Optic Mode:
The optic mode is related to the interaction of light with a material. It typically refers to the vibrations of charged particles (such as electrons) in a solid or the oscillations of electric or magnetic fields associated with photons.
The minimum frequency for the optic mode is typically determined by the energy gap between electronic states in the material. For example, in a semiconductor, the minimum frequency is usually in the infrared range.
The maximum frequency for the optic mode is not strictly defined, as it can extend into the terahertz, infrared, visible, ultraviolet, X-ray, and even gamma-ray regions. The specific range depends on the material properties and the energy levels involved.
It's important to note that these frequency ranges are general guidelines and can vary depending on the specific system or material being studied.
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Please help me please
Answers
The probability of a penny falling out is 0.3 or 30%.
What is probability?The study of probability is a branch of mathematics that focuses on calculating the possibility or chance that an event will occur. It is expressed as a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty, and numbers in between denoting likelihood.
The number of favourable outcomes for an event A divided by the total number of possible outcomes is the definition of P(A), which stands for probability. The classical definition of probability is this.
From the given table we see that, the total coins in the cup are:
3+5+2+1=11.
Now, for the number of penny are: 3
Thus,
P(penny falls out) = 3/10 = 0.3
Hence, the probability of a penny falling out is 0.3 or 30%.
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Find the point-slope equation for the line that passes through the points (-6, 24) and (5, -31). Use the first point in your equation. y - [?] = [ ](x-[ ])
Answers
I end up getting -31 - 24/5 + 6 or -31 -24/5 - (-6)
Action potentials play a key role in the contraction of cardiac muscle cells. Two different muscle cell types can be found in the heart: cells initiate and conduct action potentials to cells, which, subsequently, do the mechanical pumping of the heart. The following graphs depict the action potentials found in the two different cardiac muscle cells. Use the dropdown menus to match the type of action potential found in each type of cell.
Answers
The first graph depicts the action potential found in cells that initiate and conduct impulses, also known as pacemaker cells.
These cells have an unstable resting membrane potential that gradually depolarizes until it reaches the threshold for firing an action potential. This results in a gradual increase in voltage known as the pacemaker potential or prepotential.
Once the threshold is reached, the cell fires an action potential characterized by a rapid depolarization phase, followed by a brief repolarization and a slow depolarization phase before returning to its resting state.
This pattern of depolarization and repolarization allows pacemaker cells to generate and conduct electrical impulses throughout the heart, initiating and coordinating the contraction of cardiac muscle cells.
The second graph depicts the action potential found in cardiac muscle cells responsible for mechanical pumping, also known as contractile cells. These cells have a stable resting membrane potential that remains constant until depolarized by an action potential from a pacemaker cell.
Once depolarized, contractile cells rapidly depolarize and reach a peak voltage, followed by a prolonged plateau phase that maintains the cell in a depolarized state, allowing for sustained contraction of the cell.
Finally, the cell undergoes a repolarization phase, returning to its resting membrane potential and allowing for relaxation. This pattern of depolarization, plateau, and repolarization allows contractile cells to contract and relax in a coordinated manner, effectively pumping blood through the heart.
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PLSSS HELP IF YOU TURLY KNOW THISS
Answers
Answer:
A or 2
Step-by-step explanation:
Reason:
The 5's cancel out leaving the 2 behind as the final answer.
Another way to look at it is that the 5*2 up top multiplies to 10, then we divide that by the 5 in the denominator to end up with 10/5 = 2
If you are a visual learner, then draw a circle and divide it into 5 equal slices. Do this a total of five times. Each pizza having 2 slices, and 5 pizzas total, gives 2*5 = 10 slices overall. These ten slices can be rearranged into making 2 full pizzas.
See below.
blake collects coins. he collected a total of 150 coins. if 84% of the coins he collected were foreign,
how many other coins did he collect?
blake collected coins that were not foreign.
Answers
Answer:
Step-by-step explanation:
84% of 150=126 (foreign coins)
150-126=24 (non foreign coins)
Wiseman Video plans to make four annual deposits of $2,000 each to a special building fund. The fund’s assets will be invested in mortgage instruments expected to pay interest at 12% on the fund’s balance. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.)
Using the appropriate annuity table, determine how much will be accumulated in the fund on December 31, 2019, under each of the following situations.
1. The first deposit is made on December 31, 2016, and interest is compounded annually.
Table or calculator function: FVA of $1
Payment: $2,000
n = 4
i = 12%
Fund balance 12/31/2019: $9,559
2. The first deposit is made on December 31, 2015, and interest is compounded annually.
Table or calculator function: FVAD of $1
Payment: $2,000
n = 4
i = 12%
Fund balance 12/31/2019: $10,706
3. The first deposit is made on December 31, 2015, and interest is compounded quarterly.
Using the FV of $1 chart, calculate the fund balance:
Deposit Date i = n = Deposit Fund Balance 12/31/2019
12/31/2015 3% 16 $2,000 $3,209
12/31/2016 3% 12 2,000 2,852
12/31/2017 3% 8 2,000 2,534
12/31/2018 3% 4 2,000 2,251
$10,846
4. The first deposit is made on December 31, 2015, interest is compounded annually, and interest earned is withdrawn at the end of each year.
Deposit Amount No. of Payments Interest left in Fund Fund Balance 12/31/2019
$2,000 $8,000
Answers
The fund balance at the end of 2019 will be $8,000.
The given problem has four different parts, where we are supposed to calculate the accumulation of funds at the end of 2019 in different scenarios.
Scenario 1In the first scenario, the first deposit is made on December 31, 2016, and interest is compounded annually.
Using the FVA of $1 table; Payment: $2,000n = 4i = 12%
Fund balance 12/31/2019: $9,559
Hence, the fund balance at the end of 2019 will be $9,559.Scenario 2In the second scenario, the first deposit is made on December 31, 2015, and interest is compounded annually.
Using the FVAD of $1 table;Payment: $2,000n = 4i = 12%
Fund balance 12/31/2019: $10,706 Therefore, the fund balance at the end of 2019 will be $10,706.Scenario 3In the third scenario, the first deposit is made on December 31, 2015, and interest is compounded quarterly. Using the FV of the $1 chart, we get the following calculation:
Deposit Date i = n = Deposit Fund Balance 12/31/2015 3% 16 $2,000 $3,20912/31/2016 3% 12 $2,000 $2,85212/31/2017 3% 8 $2,000 $2,53412/31/2018 3% 4 $2,000 $2,251
The interest rate is 3%, and the payment is $2,000. Hence, the fund balance at the end of 2019 will be $10,846.Scenario 4In the fourth scenario, the first deposit is made on December 31, 2015, interest is compounded annually, and interest earned is withdrawn at the end of each year.
Deposit Amount No. of Payments Interest left in Fund Fund Balance 12/31/2019$2,000 $8,000 Hence, the fund balance at the end of 2019 will be $8,000.
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Find the measure of each angle of an isosceles right-angled triangle
Answers
Answer:180
Step-by-step explanation: i am in collge
simplify 8/9 over 20. 8/9/20
Answers
2 over 45
Step-by-step explanation:
i divide 8over9 by 20
Rewrite as a simplified fraction.
2.31= ?
But the.01 is repeating
Answers
Answer:
104/45
Step-by-step explanation:
(2.31 x 10) - 2.3/9 =
20.8/9
Which is
208/90
Simplified:
104/45
Hope this helps!
The length of a rectangle is 4 inches more than twice its width. If the
perimeter of the rectangle is 86 inches, find its dimensions. Write answer
as L=#, W=#*
Answers
Answer:
length= 30 inch and width = 13 inch......
Geometry help needed!
Answers
The answer is 38 degrees because the angle of HZJ is 38, its a reflection
Answer:
m<FZG= 38
Step-by-step explanation:
<JZG is a straight line equivalent to 180 degrees. Because m<HZJ is 38 degrees, m<HZG is 142 degrees because 180-38=142. Looking now at line HF, equivalent to 180 degrees, we know that m<HZG is 142 degrees. To solve for m<FZG, we use the equation 142+x=180. 180-142=x; x=38. You can also use the vertical angle theorem to solve for m<FZG.
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A dealership tracks the correlation between the age of its used cars and asking price for the car. The regression line is y = 12,338 – 930x, where x is the age of the car, in years.
Which statements are true regarding this model? Check all that apply.
For every one year in age, the price is predicted to increase by $930.
For every one year in age, the price is predicted to decrease by $930.
If the car is new, the car is predicted to cost $12,338.
If the age of the car is 1 year, the price is predicted to be $12,338.
Answers
Answer:
Step-by-step explanation:
The reasonable price of the car after 4 years will be $8618.
What is regression analysis?
Regression analysis is a group of statistical procedures used in statistical modelling to determine the associations between a dependent variable and one or more independent variables.
Given that a dealership tracks the correlation between the age of its used cars and asking price for a car. The regression line is y = 12,338 – 930x, where x is the age of the car, in years.
The price of the car after 4 years will be calculated as follows:-
y = 12338 - 930x
y = 12338 - ( 930 x 4 )
y = 12338 - 3720
y = $8618
Therefore, the reasonable price of the car after 4 years will be $8618.
Answer:
B - For every one year in age, the price is predicted to decrease by $930
C- If the Car is new, the car is predicted to cost $12,338.
Step-by-step explanation:
correct on edge 2022
The data in NutritionStudy include information on nutrition and health habits of a sample of 315 people. One of the variables is VitaminUse, indicating whether a person takes a multivitamin pill regularly or occasionally or not at all. Use technology to test whether the data provide evidence that the proportion taking a vitamin pill regularly is different from 35% given
a) Clearly state the null and alternative hypotheses
b) Calculate the test statistic and p-value.
c)Can we conclude that the proportion taking a vitamin pill regularly is different from 35%?
Answers
The answer to question is given briefly
a) Clearly state the null and alternative hypotheses
In this scenario, we are required to check whether the proportion of people taking a vitamin pill regularly is different from 35%.
The null hypothesis, H0:
The proportion taking a vitamin pill regularly is 35%.
The alternative hypothesis, H1:
The proportion taking a vitamin pill regularly is not equal to 35%.
b) Calculate the test statistic and p-value.
To find the test statistic and p-value, we'll need to perform a hypothesis test. Using the binomial distribution, we can easily determine this.
Binomial probability distribution is used in this scenario to check the data provide evidence that the proportion taking a vitamin pill regularly is different from 35%.
Here, the sample proportion can be calculated as, sample proportion, p = (no. of people taking a vitamin pill regularly) / (total no. of people) = 98/315=0.311
In the binomial distribution, the formula for calculating the test statistic z can be given as,
z = (p - P) / √(P(1 - P)/n)
where p is the sample proportion, P is the hypothesized proportion, and n is the sample size.
Using this formula, we have;
z = (0.311 - 0.35) / √(0.35(1 - 0.35)/315)=-1.89
The calculated test statistic, z = -1.89
Using the z-score table, we can find the p-value. The p-value corresponding to a z-score of -1.89 is 0.0594.
c) Can we conclude that the proportion taking a vitamin pill regularly is different from 35%?
The p-value is greater than the significance level α = 0.05. So, we cannot reject the null hypothesis.
Therefore, we do not have enough evidence to conclude that the proportion taking a vitamin pill regularly is different from 35%.
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School Supplies At the school store, notebooks cost $3.49. How
much will you pay for 4 notebooks?
HURRY!!
Answers
Answer:
3.49x4=$13.96
Step-by-step explanation:
¹3.³49
4
13.96
Answer:
$ 13.56
Step-by-step explanation:
3*4= 12
0.4*4= 1.6
0.09*4=0.36
12+ 1.6+0.36= 13.96
This means you pay $ 13.56 for the notebooks.
Hope that helped.