The value of the triple integral is 7/180.
To evaluate the triple integral, we first need to set up the limits of integration. Since the solid tetrahedron T is defined by the four vertices (0, 0, 0), (1, 0, 0), (0, 1, 0), and (0, 0, 1), we can use these points to set up the limits of integration as follows:
For z, we integrate from the bottom of the solid (z = 0) to the top (z = 1 - x - y).
For y, we integrate from the left side of the solid (y = 0) to the right (y = 1 - x).
For x, we integrate from the back of the solid (x = 0) to the front (x = 1).
Therefore, the triple integral can be written as:
∫∫∫ t 7x^2 dv = ∫∫∫t 7x^2 dV
= ∫[0,1] ∫[0,1-x] ∫[0,1-x-y] 7x^2 dz dy dx
∫[0,1] ∫[0,1-x] ∫[0,1-x-y] 7x^2 dz dy dx
= ∫[0,1] ∫[0,1-x] 7x^2 (1 - x - y) dy dx
= ∫[0,1] [7x^2 (1 - x) (1/2 - x/3)] dx
= 7/180
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Question 6 of 10
Ashlee is purchasing a $125,000 home and her bank is offering her a 30-year
mortgage at a 4.75% interest rate. In order to lower her monthly payment,
Ashlee will make a 20% down payment and is considering a purchase of 2
points. How much lower will her monthly payment be if she purchases the
points?
A. $16.69
B. $15.98
C. $12.09
D. $14.96
SUBMIT
Answer:
D
Step-by-step explanation:
First, let's calculate the initial monthly payment without purchasing any points.
The amount of the mortgage after the 20% down payment is:
$125,000 x 0.8 = $100,000
To calculate the monthly payment, we can use the formula:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]
Where:
M = Monthly payment
P = Principal (loan amount)
i = Interest rate (per month) = 4.75% / 12 = 0.0039583
n = Number of payments = 30 years x 12 months per year = 360
So, plugging in the values:
M = $100,000 [ 0.0039583(1 + 0.0039583)^360 ] / [ (1 + 0.0039583)^360 – 1]
M = $522.12 (rounded to the nearest cent)
Now, let's calculate the new monthly payment if Ashlee purchases 2 points. Each point costs 1% of the loan amount, so for a $100,000 loan, each point is $1,000.
By purchasing 2 points, Ashlee would pay an additional $2,000 upfront (2 x $1,000). This will lower the interest rate on the loan by 0.5%, from 4.75% to 4.25%.
Using the same formula as before, but with the new interest rate of 4.25% / 12 = 0.0035417, we get:
M = $100,000 [ 0.0035417(1 + 0.0035417)^360 ] / [ (1 + 0.0035417)^360 – 1]
M = $505.16 (rounded to the nearest cent)
The difference in monthly payments is:
$522.12 - $505.16 = $16.96
Rounding to the nearest cent, the answer is option D, $14.96.
Divide 18a6b2 by 9a3b.
2a9b3
2a2b2
2a3b2
2a3b
Answer: Choice D) [tex]2a^3b[/tex]
Work Shown:
[tex]\frac{18a^6b^2}{9a^3b}=\frac{18a^6b^2}{9a^3b}\\\\\frac{18a^6b^2}{9a^3b}=\frac{18}{9}*\frac{a^6}{a^3}*\frac{b^2}{b}\\\\\frac{18a^6b^2}{9a^3b}=2a^{6-3}b^{2-1}\\\\\frac{18a^6b^2}{9a^3b}=2a^3b\\\\[/tex]
The formula used on the 3rd line was (a^b)/(a^c) = a^(b-c). We subtract the exponents when dividing exponential expressions with the same base.
Question
Jaq rode their bike for 3 1/3
hours at 15 miles per hour. How far did they ride?
✪
Answer:
Step-by-step explanation:
We can use the formula distance = rate x time to solve the problem.
The rate is 15 miles per hour and the time is 3 1/3 hours.
To work with the time, we need to convert it to an improper fraction:
3 1/3 = (3 x 3 + 1)/3 = 10/3
Now we can plug in the values:
distance = 15 x 10/3
distance = 50 miles (rounded to the nearest mile)
Therefore, Jaq rode 50 miles.
Determine the interval(s) over which the graph of f left parenthesis x right parenthesis equals short dash x to the power of 6 minus 6 x to the power of 5 plus 12 x minus 2 is concave up or concave down.
Answer:
gdiduusuehfuehvv
Step-by-step explanation:
bbzbhshxhdhhd are the best and my mom I WINNNNNN you want it to be over with you guys to come in and your mom are doing ghhdhhsuwuwhsh and your family are doing well and your family are doing well and your family are doing well and your family are doing well and your family and my wife was the best and I WINNNNNN and my mom are doing ghhdhhsuwuwhsh and what is the only ones I WINNNNNN with the kids I WINNNNNN and I will be over and I can do i and eat early for you and Darshanie and I WINNNNNN and my friend and your mom and my mom ever had a great day I love ever and your mom are the kids I will get you a great mom and I will send you a link and I WINNNNNN with the only ones I WINNNNNN with you don't need me I can get it and I will be over and your mom and your mom I will send it out tomorrow night I will send it out tomorrow night with you guys and I can send the best ones that have to do i I will send you and Darshanie and your mom I will send it and your family and I WINNNNNN and my friend are doing errands to run out to do i you guys and I WINNNNNN you want me I will send you and Darshanie is done now we have a great day for a great mom I will be over there and I WINNNNNN you and everyone and my friend and my friend and what time do the kids have a whole new world we live together I will be home tomorrow night with the only one that has to wait until the way home tomorrow morning to run out of wo you guys to run out with the best ones that w with the kids I will get you guys want me when we good day for you it
PLS HELP ME with all 4 questions!!
By answering the presented question, we may conclude that so by SAS congruency property we have said that all these triangles are similar.
What precisely is a triangle?A triangle is a closed, a double geometric shape made up of three line segments known as sides that connect at three parameters known as vertices.
Triangles are differentiated by their angles and their sides. Triangles can be collinear (all sides equal), angles, or scalene dependent on their sides.
Triangles are classed as acute (all angles just under 90 degrees), right (one angle of approximately to 90 degrees), or ambiguous (all angles greater than 90 degrees).
The area of a triangle may be determined with the formula A = (1/2)bh, where A is the surface, b is really the right triangle base, and h is the triangle's height
here, from the figure, we have
Two sides of the triangle are equal.
And also all angles are also same.
Therefore, so by SAS congruency property we have say that all these triangles are similar.
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Last weekend, Mrs. Nelson earned $132 selling rings. She earned $6 for each ring she sold.
How many rings did she sell?
Hi!
Let's think about this really quick.
Each ring is $6. She made $132.
In order to find the solution, we need to divide the total from the original price of the ring, making the equation: 132÷6.
132÷6= 22.
So, she sold 22 rings. To verify that answer, we'll multiply 6 to 22.
6x22=132.
22 Is your answer.
Hope this helps!
Appreciated if you mark brainliest <3
~~~PicklePoppers~~~
Answer:
22 rings :)
Step-by-step explanation:
By diving 132 by 6 we can determine the number of rings she sold.
After dividing, we get 22 rings!
May I please have a brainliest? I put a lot of thought and effort into my answers, so I would really appreciate it!
26. Paul, Raul, and Saul had a competition to see who could pick the greatest amount of strawberries
in three minutes. Paul picked 1 pounds of strawberries, Raul 1 pounds, and Saul 1 pounds.
Who came in second? Show your work.
There is no second place winner. all three competitors picked the same amount of strawberries, so there is a tie for first place.
What is probability?Probability is a branch of mathematics that deals with the study of randomness and uncertainty in events. It is the measure of the likelihood or chance that an event will occur. Probability is expressed as a number between 0 and 1, where 0 indicates that the event will not occur and 1 indicates that the event will occur with certainty.
According to the given information:The problem states that each of the three competitors picked 1 pound of strawberries. Since all of them picked the same amount, there is no way to determine who came in second. All three competitors can be considered tied for first place. If the problem had given different weights of strawberries picked by each competitor, then we could have compared the weights and determined who picked the second greatest amount of strawberries. But since all three competitors picked the same amount, there is no way to determine a second place winner.
Therefore, there is no second place winner. all three competitors picked the same amount of strawberries, so there is a tie for first place.
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g suppoe x follows a distribution with pdf given by...show that the moment generating function of x is mx(t)
The distribution of Z=X+Y is gamma(1,10), which has a probability density function f(z) = 10 × e^(-10z), 0 ≤ z.
The moment generating function (mgf) of Z=X+Y can be found by taking the product of the mgfs of X and Y
Mz(t) = Mx(t) × My(t) = (e^(-4+4t))×(e^(-6+6t)) = e^(-10+10t)
We recognize that Mz(t) is the mgf of the gamma distribution with shape parameter k=1 and rate parameter λ=10. Therefore, Z=X+Y follows a gamma distribution with shape parameter k=1 and rate parameter λ=10.
In summary, the distribution of Z is gamma(1,10), which has a probability density function f(z) = λ^k × z^(k-1) × e^(-λz) / Γ(k) where k=1 and λ=10. Therefore, the probability density function of Z is f(z) = 10 × e^(-10z), 0 ≤ z.
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I have solved the question in general, as the given question is incomplete.
The complete question is:
What is the distribution of Z and the value of the parameter?
Please help !!!! Given m∥n, find the value of x.
(3x+5) (x-25) = 180 degrees
Answer:
Step-by-step explanation:
[tex](3x+5)+(x-25)=180 \text{ \ (angles on a straight line are supplementary)}[/tex]
[tex]4x-20=180[/tex]
[tex]4x=200[/tex] (+20 both sides)
[tex]x=50[/tex] (÷4 both sides)
Tell me which brand or which size is a better buy.
Answer:
The answer is brand B
Step-by-step explanation:
You divide $14.88 by 24 which equals 68 cents per item.
Then brand B is 60 cents per item which is the better buy!
Use the Law of Cosines to solve the problem. You must solve for BC first. Solve this order
A ship travels due west for 94 miles. It then travels in a northwest direction for 119 miles and ends up 173 miles from its original position. To the nearest tenth of a degree, how many degrees north of west (x) did it turn when it changed direction? Show you Work.
answer: 175
Step-by-step explanation:
Answer:
71.9 degrees
Step-by-step explanation:
The find the value of x on the given diagram, we must first find the included angle between the two line segments labelled 94 mi and 119 mi in the triangle. To do this, we can use the Law of Cosines.
[tex]\boxed{\begin{minipage}{6 cm}\underline{Law of Cosines} \\\\$c^2=a^2+b^2-2ab \cos C$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}[/tex]
The values to substitute into the formula are:
a = 119b = 94c = 173Solving for the angle C:
[tex]\begin{aligned}173^2&=119^2+94^2-2(119)(94)\cos C\\\\29929&=14161+8836-22372\cos C\\\\29929&=22997-22372\cos C\\\\6932&=-22372\cos C\\\\-\dfrac{6932}{22372}&=\cos C\\\\C&=\cos^{-1}\left(-\dfrac{6932}{22372}\right)\\\\C&=108.0502874...^{\circ}\end{aligned}[/tex]
As angles on a straight line sum to 180°, the value of x can be calculated by subtracting the found value of C from 180°:
[tex]x=180^{\circ}-108.0502874...^{\circ}[/tex]
[tex]x=71.9497125...^{\circ}[/tex]
[tex]x=71.9^{\circ}\; \sf (nearest\;tenth)[/tex]
Therefore, the ship turned 71.9 degrees north of west when it changed direction.
when a certain number is doubled and then decreased by 9, the result is not more than 19. Find the range of values of the number
Answer:
The number must be at most 10.
If the number is doubled and then decreased by 9, the result is 2x - 9.
2x - 9 ≤ 19
2x ≤ 28
x ≤ 14
Therefore, the range of values of the number is 0 to 10.
one ticket is drawn at random from each of the two boxes below: 1 2 6 1 4 5 8 find the chance that the both numbers are even numbers.
The chance that both numbers drawn are even numbers is 8/21.
The probability refers to the measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain.
There are 4 even numbers and 3 odd numbers in the first box, and 2 even numbers and 1 odd number in the second box.
The probability of drawing an even number from the first box is 4/7, and the probability of drawing an even number from the second box is 2/3.
By the multiplication rule of probability, the probability of drawing an even number from both boxes is
(4/7) × (2/3) = 8/21
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At age 39, you start saving for retirement. If your investment plan pays an APR of 4% and you want to have $0.8 million when you retire in 26 years, how much should you deposit monthly?
Answer:
Step-by-step explanation:
Calculate the bearing of G from H.
The bearing of G from H at the given point location is determined as 155⁰.
What is bearing?
Bearing as a direction refers to the direction or angle of an object or location relative to a reference point, usually measured in degrees. For example, a compass can be used to determine the bearing of a landmark or to navigate in a particular direction.
The bearing of G from H is calculated by applying the following principle;
Let the bearing of G from H = θ
θ = 360 - 205 ( sum of angles in a circle )
θ = 155⁰
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I really need help and there also is a part c and d
Part A: The probability of rolling a 5 is 1/6 or approximately 0.167. Part B: the probability of rolling an even number is 3/6 or 1/2 or 0.5.
Describe probability ?Probability is a branch of mathematics concerned with measuring the likelihood or chance of an event occurring. It is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes. Probability is expressed as a number between 0 and 1, where 0 means that the event will not occur and 1 means that the event will definitely occur. For example, if the probability of an event is 0.5, it means that the event has an equal chance of occurring or not occurring. Probability is used in various fields, such as science, engineering, finance, and statistics, to make predictions and make decisions based on uncertain events.
Part A:
The number cube has six faces, and each face has an equal chance of landing face-up. Therefore, the probability of rolling a 5 is 1/6 or approximately 0.167.
Part B:
The even numbers on a number cube are 2, 4, and 6. There are three even numbers out of a total of six possible outcomes. Therefore, the probability of rolling an even number is 3/6 or 1/2 or 0.5.
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Jason invested $5,500 in an account paying an interest rate of 1 7/8 % compounded quarterly. Kayden invested $5,500 in an account paying an interest rate of 1 3/8 % compounded annually. After 8 years, how much more money would Jason have in his account than Kayden, to the nearest dollar?
Using compounding we know that the additional amount Jason has more than Kayden is $249.48.
What is compounding?Calculating interest on the principal borrowed as well as any prior interest.
In order to compute compound interest, multiply the principle of the original loan by the annual interest rate multiplied by the number of compound periods minus one.
So, the amount of Jason after 8 years:
Amount: $5500
Interest: 1.875%
Compounded: Quarterly
Using a compounding calculator:
Amount after 8 years: $6,387.85
The amount of Kayden:
Amount: $5500
Interest: 1.375%
Compounded: Quarterly
Using a compounding calculator:
Amount after 8 years: $6,138.37
The additional amount Jason got: 6,387.85 - 6,138.37 = $249.48
Therefore, using compounding we know that the additional amount Jason has more than Kayden is $249.48.
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Answer:253
Step-by-step explanation:
PLEASEE help!!!! Urgent!!!!!
Answer:
Step-by-step explanation:
Solve for x
(x-14)+(2x+8)= 180
3x-14+8=180
3x-6=180
3x=186
x=62degrees
Solve for y
(7y-15)+62=180
7y+47=180
7y=180-47
7y=133
y=19degrees
how many inches are in 1 1/2 yards
Answer:54 inches
Step-by-step explanation:
HELP MEHHHH! I WILL MARK YOU BRAINLIEST! I NEED AN EXPLANATION
This illustrates the rule of large numbers, according to which the sample mean approaches the population mean as the sample size rises.
what is probability ?The likelihood or chance of an occurrence occurring is measured by probability. It is expressed as a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty of the occurrence. Additionally, probabilities can be stated as percentages, with 0% denoting an improbable event and 100% denoting a specific event. By dividing the number of favourable outcomes by the total number of potential outcomes, the probability of an occurrence is determined.
given
Since there are six potential outcomes and only one of them is a 5, the theoretical probability of rolling a 5 on a fair die is 1/6.
Mya's experimental chance of rolling a 5 after 100 trials is 25/100, which can be expressed as 1/4. Her experimental probability after 200 attempts is 30/200, which can be expressed as 3/20.
This implies that the experimental probability moves closer to the theoretical probability as the number of trials rises.
In other words, Mya's experimental findings get closer to the anticipated theoretical probability the more times she rolls the die.
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The complete question is :- Communicate and Justify Mya rolls a fair die and counts the number of times she rolls a 5. She rolls a 5 on 25 of the first 100 trials. She rolls a 5 on 30 of the first 200 trials. Compare the experimental probability to the theoretical probability after 100 trials and 200 trials. What do you notice? Explain.
Graph to solve the system: y=-3/2 and y=(1/2) × -1 At what x-values are the equations equal?
the x-value that makes the two equations equal is x = -1. and x=0.
equation defineAn equation consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), connected by an equals sign (=). The LHS and RHS may contain one or more variables, which are values that can change or vary.
The first equation, y = -3/2, is a horizontal line with a y-intercept of -3/2. This means that no matter what x-value we plug in, the corresponding y-value will always be -3/2.
The second equation, y = (1/2) x - 1, is the equation of a line with slope 1/2 and y-intercept -1. To find the x-value(s) where this equation equals -3/2, we can set the two equations equal to each other:
-3/2 = (1/2) x - 1
Adding 1 to both sides, we get:
-1/2 = (1/2) x
Multiplying both sides by 2, we get:
-1 = x
At x=0, two equation satisfy the condition.
Therefore, the x-value that makes the two equations equal is x = -1 and 0.
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What is the probability that a 43% free-throw shooter will miss her next free throw?
Answer:
57%
Step-by-step explanation:
Answer:
.57 or 57%
Step-by-step explanation:
If a basketball player has a free-throw shooting percentage of 43%, it means that she makes 43% of her free throws on average. Therefore, the probability that she will miss her next free throw is equal to the complement of her shooting percentage, which is 1 minus 0.43. This simplifies to 0.57 or 57%. So, the probability that she will miss her next free throw is 57%.
Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading between 0°C and 1.08°C. Round your answer to 4 decimal places
Answer: We are given that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C.
To find the probability of obtaining a reading between 0°C and 1.08°C, we need to calculate the z-scores for these values using the formula:
z = (x - mu) / sigma
where x is the value we are interested in, mu is the mean, and sigma is the standard deviation.
For x = 0°C, we have:
z1 = (0 - 0) / 1.00 = 0
For x = 1.08°C, we have:
z2 = (1.08 - 0) / 1.00 = 1.08
Using a standard normal table or a calculator, we can find the probability of obtaining a z-score between 0 and 1.08.
Using a standard normal table or a calculator, we find that the probability of obtaining a z-score between 0 and 1.08 is 0.3583.
Therefore, the probability of obtaining a reading between 0°C and 1.08°C is 0.3583, rounded to 4 decimal places.
Step-by-step explanation:
Determine the equation of the ellipse with foci (15,-2) and (3,-2), and co-vertices (9,6) and (9,-10).
Answer: We know that the center of the ellipse is the midpoint of the line segment joining the foci. So, the center is ((15+3)/2, (-2-2)/2) = (9, -2).
The distance between the foci is 2c, where c is the distance between the center and each focus. So, 2c = 15 - 3 = 12, which means c = 6.
The distance between the center and each co-vertex is b. So, b = 10 - (-2) = 12.
The semi-major axis is a, which is the distance from the center to a vertex. Since we have the co-vertices, we can use the Pythagorean theorem to find a:
a^2 = b^2 - c^2
a^2 = 12^2 - 6^2
a^2 = 108
a = sqrt(108) = 6*sqrt(3)
Therefore, the equation of the ellipse is:
(x - 9)^2 / (6*sqrt(3))^2 + (y + 2)^2 / 12^2 = 1
Simplifying, we get:
(x - 9)^2 / 72 + (y + 2)^2 / 144 = 1
So, the equation of the ellipse is (x - 9)^2 / 72 + (y + 2)^2 / 144 = 1.
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20/8as a mixed number in its simplest form
Answer:
2 1/2
Step-by-step explanation:
20/8=2r4
2r4= 2 4/8
2 4/8 = 2 1/2
Answer:
2 1/2
Step-by-step explanation:
Step 1:
We first want to find the whole number, and to do this we divide the numerator by the denominator. Since we are only interested in whole numbers, we ignore any numbers to the right of the decimal point.
20/8= 2.5 = 2
Now that we have our whole number for the mixed fraction, we need to find our new numerator for the fraction part of the mixed number.
Step 2: Get the new numerator
To work this out we'll use the whole number we calculated in step one (2) and multiply it by the original denominator (8). The result of that multiplication is then subtracted from the original numerator:
20 - (8 x 2) = 4
Step 3: Our mixed fraction
We've now simplified 20/8 to a mixed number. To see it, we just need to put the whole number together with our new numerator and original denominator:
2 4/8
Step four: Convert it by simplifying
2 4/8 = 2 1/2
When a stone is dropped from the top of a tower, the distances metres it falls in t seconds is given by s = 10?. Find how far it falls in 3 seconds?
Answer: 45 meters
Step-by-step explanation:
The given equation is:
s = (1/2) * g * t^2
Where,
g = acceleration due to gravity = 10 m/s^2 (approximate value)
To find the distance it falls in 3 seconds, we can substitute t = 3 in the above equation:
s = (1/2) * g * t^2
s = (1/2) * 10 * 3^2
s = (1/2) * 10 * 9
s = 45 meters
Therefore, the stone falls 45 meters in 3 seconds.
you are computing a confidence interval for the difference in 2 population proportions. which of the following could be negative? select all.OP1Op 1 - 2Standard errorCritical valueLower bound of the confidence intervalUpper bound of the confidence interval
For the computation of confidence interval for the difference in two population proportions following are negative,
p₁(cap) - p₂(cap)
Lower bound of the confidence interval
Upper bound of the confidence interval
For the computation of confidence interval,
The difference in two population proportions,
p₁ - p₂, can be negative or positive.
This implies,
The sample estimate of the difference in proportions,
p₁(cap) - p₂(cap), can also be negative or positive.
The standard error and critical value are always positive values and cannot be negative.
The lower and upper bounds of the confidence interval can be negative or positive.
Depending on the sample estimate and the margin of error.
So, both the lower and upper bounds can be negative.
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The above question is incomplete, the complete question is:
You are computing a confidence interval for the difference in 2 population proportions. which of the following could be negative?
Select all.
a. p₁
b. p₁(cap) - p₂(cap)
c. Standard error
d. Critical value
e. Lower bound of the confidence interval
f. Upper bound of the confidence interval
A baseball diamond is shaped like a square. The perimeter is 360 feet. What is the length of each side?
Answer: 90 feet
Step-by-step explanation:
Since the baseball diamond is shaped like a square, all sides are equal in length.
Let's denote the length of each side by x.
The perimeter of a square is the sum of the lengths of all four sides, so we can write:
4x = 360
Dividing both sides by 4, we get:
x = 90
Therefore, each side of the baseball diamond is 90 feet long.
please help me with math quiz i’ll give you brainlist
Answer:
Answer: B. Symmetric.
Explanation:
In a symmetric distribution, the data is evenly distributed around the mean or median, creating a mirror image on both sides of the center. In this histogram, the median and mean are very close together at 55 and the bars on both sides of the center are roughly equal in height, indicating a fairly even distribution. Therefore, the histogram is symmetric.
given two nonzero vectors which aren't parallel, there is exactly one plane parallel to both vectors. g
The argument using the components of the non zero vectors which are not parallel are as follow, sa1 + tb1 = c1
sa2 + tb2 = c2
sa3 + tb3 = c3
Geometric argument,
a and b are nonzero vectors that are not parallel.
A plane in three-dimensional space.
Any vector in this plane can be written as a linear combination of a and b.
Let c be any vector in this plane.
Construct a parallelogram with sides a and b, and the diagonal of the parallelogram passing through the point c.
This diagonal is the vector c written as a linear combination of a and b, say c = sa + tb for some scalars s and t.
Diagonal of a parallelogram bisects and is bisected by its opposite sides.
c lies on the line passing through the midpoints of a and b.
c can be expressed as a linear combination of a and b.
Argument using components,
a and b are nonzero vectors that are not parallel, they are linearly independent.
Any vector in the plane determined by a and b can be expressed as a linear combination of a and b.
Let c = (c1, c2, c3) be any vector in this plane.
Now, c as c = sa + tb, where s and t are scalars to be determined.
Writing a and b in terms of their components, we have,
a = (a1, a2, a3) and b = (b1, b2, b3)
Then, we can write c as,
c = (s a1 + t b1, s a2 + t b2, s a3 + t b3)
Values of s and t such that c has the components (c1, c2, c3).
Equating the components of c with those of (c1, c2, c3), to get the system of equations,
sa1 + tb1 = c1
sa2 + tb2 = c2
sa3 + tb3 = c3
Therefore, solution of the argument of non zero vectors solved using standard techniques such as Gaussian elimination or Cramer's rule.
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The above question is incomplete, I answer the question in general according to my knowledge:
Suppose that a and b are nonzero vectors that are not parallel and c is any vector in the plane determined by a and b. Give a geometric argument to show that c can be written as c=sa +tb for suitable scalars s and t. Then give an argument using components.