Find a set of parametric equations of the line with the given characteristics. (Enter your answers as a comma-separated list.)
The line passes through the point (-9, 3, 6) and is perpendicular to the plane given by -x+9y+z=3
Answers
P = (-9 + t, 3 - (1/9)t, 6 - t)
How to find the parametric equations of the line?A line perpendicular to the plane -x + 9y + z = 3 can be described by a vector that is orthogonal to the normal vector of the plane. The normal vector of the plane is < -1, 9, 1 >, so a direction vector for the line is < 1, -1/9, -1 >.
To find the parametric equations of the line, we need a point on the line. We're given that the line passes through (-9, 3, 6), so that can be our starting point.
Let's call it P.
We can write the parametric equations of the line as:
x = -9 + t
y = 3 - (1/9)t
z = 6 - t
where t is a parameter.
These equations describe a line that passes through the point (-9, 3, 6) and is perpendicular to the plane -x + 9y + z = 3.
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Related Questions
Please help!!!!!!!!!
Answers
Answer:
f(-4) = 19
Step-by-step explanation:
Since -4 < 1, we need to use the bottom part of the function:
\(f( - 4) = {( - 4)}^{2} + 3 = 16 + 3 = 19\)
DETAILS WANEFM7 5.2.004. MY NOTES ASK YOUR TEACHER Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. (Enter EMPTY if the region is empty. Enter UNBOUNDED if the function is unbounded.) Minimize c = x + 2y subject to x + 3y 223 8x + y 2 23 x3 0, y 20. (x, y) =
Answers
The feasible region is not empty and the objective function is bounded because it achieves its minimum value at the corner point (0, 0). Hence, the solution to the given LP problem is (x, y) = (0, 0).
Given an LP problem Minimize \(c = x + 2y\) subject to the constraints \(x + 3y ≤ 223 8x + y ≤ 23 x ≥ 0, y ≥ 0\)
Now we can start solving this LP problem by drawing the graph for the given constraints :
Plotting the constraints on a graph.
We can see that the feasible region is the shaded region bounded by the lines x = \(0, y = 0, 8x + y = 23, and x + 3y = 223\)
Now we can check the corner points of this region for finding the optimal solution of the given problem.
Corner points of the feasible region are:
(0, 0), (0, 7.67), (2.88, 71.07), (23, 66.33), and (27.33, 65).
Now we can substitute these values of x and y into the objective function \(c = x + 2y\) and see which corner point gives us the minimum value of c.
The table below summarizes this calculation.
Corner point
\((x, y)c = x + 2y\) (0,0)0(0,7.67)15.34(2.88,71.07)145.03(23,66.33)112.67(27.33, 65)157.67.
Thus, we can see that the minimum value of the objective function \(c = x + 2y\) is achieved at (0, 0),
which is one of the corner points of the feasible region.
Therefore, the optimal solution of the given LP problem is \(x = 0\) and \(y = 0\)
Also, we can see that the feasible region is not empty and the objective function is bounded because it achieves its minimum value at the corner point (0, 0).
Hence, the solution to the given LP problem is \((x, y) = (0, 0)\)
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Encierra todo los números que sean mayores a 18,031 2
Answers
no se me alludas a saber cual es
PLEASEEE HELP I BEGGG
Answers
Answer:
B and then A
Step-by-step explanation:
volume is × so the . means times
so it's the only option
and then the second area is
6×3×4= 72cm³
A freight forwarder has a weekly consolidated service Mumbai - Marsellle, with direct costs as follows: Ocean freight: US \( \$ 1,250.00 / 40-\mathrm{ft} \) standard container. Container loading in Mu
Answers
The correct answers are: 1. Total revenue for this consolidation: $750,000.00. 2. Total costs for this consolidation: $201,162.22. 3. Profit/loss on this consolidation: $548,837.78.
To calculate the total revenue, costs, and profit/loss for the consolidation, we need to break down the given information and perform the necessary calculations. Let's go step by step:
1. Calculate the total revenue:
The cargo is charged based on revenue tons, so we need to convert the volume of cargo loaded (30 m³) and the weight (20,000 kg) into revenue tons.
- Volume: 30 m³
To determine the revenue tons, we'll assume the cargo is loaded to its maximum capacity of 40 m³ in a 40-ft standard container. We can calculate the revenue tons using the formula: Revenue Tons = (Volume Loaded / Maximum Volume) * Weight
Revenue Tons = (30 m³ / 40 m³) * 20,000 kg
Revenue Tons = 0.75 * 20,000 kg = 15,000 kg
- Weight: 20,000 kg
Since the weight is already in kilograms, we can directly use this value.
Now, we can calculate the total revenue:
Total Revenue = Revenue Tons * Selling Rate per Revenue Ton
Total Revenue = 15,000 kg * $50.00/kg (assuming the selling rate is $50.00 per revenue ton)
Total Revenue = $750,000.00
Therefore, the total revenue for this consolidation is $750,000.00.
2. Calculate the total costs:
We need to consider the costs of ocean freight, container loading in Mumbai, and Marseille unloading.
- Ocean Freight:
The cost of ocean freight per 40-ft standard container is given as $1,250.00.
Since the cargo loaded is less than the maximum capacity, we'll consider only a fraction of the cost based on the loaded volume:
Ocean Freight Cost = (Volume Loaded / Maximum Volume) * Ocean Freight Cost per Container
Ocean Freight Cost = (30 m³ / 40 m³) * $1,250.00
Ocean Freight Cost = 0.75 * $1,250.00 = $937.50
- Container Loading in Mumbai:
The cost of container loading in Mumbai is given as $10.00 per revenue ton.
Container Loading Cost = Weight * Cost per Revenue Ton
Container Loading Cost = 20,000 kg * $10.00/kg = $200,000.00
- Marseille Unloading:
The cost of Marseille unloading is €10.00 per revenue ton, but we need to convert it to USD using the given exchange rate.
Exchange Rate = €1.00 = $1.06
Marseille Unloading Cost = (Weight / 1,000) * Cost per Revenue Ton * Exchange Rate
Marseille Unloading Cost = (20,000 kg / 1,000) * €10.00/kg * $1.06/€
Marseille Unloading Cost = 20 * €10.00 * $1.06 = €212.00
Converting to USD: €212.00 * $1.06 = $224.72
Now, we can calculate the total costs:
Total Costs = Ocean Freight Cost + Container Loading Cost + Marseille Unloading Cost
Total Costs = $937.50 + $200,000.00 + $224.72
Total Costs = $201,162.22
Therefore, the total costs for this consolidation amount to $201,162.22.
3. Calculate the profit/loss:
Profit/Loss = Total Revenue - Total Costs
Profit/Loss = $750,000.00 - $201,162.22
Profit/Loss = $548,837.78
Therefore, the profit/loss on this consolidation is $548,837.78.
Note: The complete question is:
A freight forwarder has a weekly consolidated service Mumbai - Marseille, with direct costs as follows:
Ocean freight: US $1,250.00/40-ft standard container.
Container loading in Mumbai: US $10.00 per revenue ton.
Marseille unloading: €10.00 per revenue ton.
Exchange rate is = €1.00 US $1.06.
From past experience, the marketing department has determined that they need to load 40 m³ of cargo in a 40-ft standard container to break even and be able to sell to their customers an all-inclusive rate of US $50.00 per revenue ton.
Based on the above shipment details, answer the following scenario: Last week they loaded 30 m³, 20000 kg in their consolidation.
1: What was their total revenue for this consolidation? Select one answer.
2: what were their total costs for this consolidation?
3: what was the profit /loss on this consolidation?
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a
Play 3)
What is the mean of the data set?
8, 16, 9, 11
Answers
Answer:
Well, you would need to divide 44 by the numbers you have so 44/4=11
Calculate the slope given points (1,2) and (3, 4).
And reduce or simplify your answer if possible. Please watch your signs.
Answers
Answer:
slope: 1
Step-by-step explanation:
(1, 2) and (3, 4)
To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)
Plug in these values:
(4 - 2) / (3 - 1)
Simplify the parentheses.
= (2) / (2)
Simplify the fraction.
2/2
= 1
This is your slope.
Hope this helps!
Find end and mid point
Answers
Answer:
You already post your answer!
Step-by-step explanation:
Maybe you should get two points in order to find midpoint and endpoint!
or you should give other information!
Direct materials $ 5.50 direct labor $ 3.00 variable manufacturing overhead $ 1.50 fixed manufacturing overhead $ 4.00 fixed selling expense $ 2.50 fixed administrative expense $ 2.00 sales commissions $ 1.00 variable administrative expense $ 0.50 13. if the selling price is $21.50 per unit, what is the contribution margin per unit? (do not round intermediate calculations. round your answer to 2 decimal places.)
Answers
The contribution margin per unit is $ 1.50
The contribution margin is the percentage of a product's sales revenue that isn't consumed by variable costs and goes toward paying the firm's fixed expenses.
One of the main components of break-even analysis is the idea of contribution margin.
Labor-intensive businesses with few fixed expenses tend to have low contribution margins, whereas capital-intensive, industrial businesses have more fixed costs and, thus, higher contribution margins.
According to the question,
Total expenses per unit = $(5.50+3.00+1.50+4.00+2.50+2.00+1.00+0.50)
= $ 20
Selling Price per unit = $ 21.50
Thus, contribution margin per unit = $ (21.50 - 20)
= $ 1.50
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If the area of a rectangle is 260, and the length is 16 feet longer than the width, what are the dimensions of the rectangle?
Answers
Answer:
w = 10
l = 26
Step-by-step explanation:
A = l x w
260 = w x (w + 16)
w^2 + 16w = 260
w^2 + 16 w - 260 = 0
w^2 - 10w + 26w - 260 = 0
w (w-10) + 26 (w - 10)
w = -26 or +10
width can not be negative so w = 10
l = w +16
l = 10+16
l = 26
Write an equivalent equation to AB = AC using A^-1 such that, when it is simplified, the resulting equation will simplify to B = C. What property should be used to continue simplifying the above equation? A. (AB)^-1 = B^-1A^-1 B. (A^-1)^T = (A^T)^-1 C. A-^1A = 1 D. (A^-1)^-1 = A
Answers
The property that should be used to continue simplifying the above equation is A-^1A = 1. So, correct option is C.
We can start with the equation AB = AC and multiply both sides by A^-1 on the left:
A^-1(AB) = A^-1(AC)
Using the associative property of matrix multiplication, we can simplify the left-hand side:
(A^-1A)B = (A^-1A)C
Using the fact that A^-1A = I (the identity matrix), we get:
IB = IC
Simplifying further using the fact that I times any matrix is that matrix itself, we obtain:
B = C
Therefore, the equivalent equation to AB = AC using A^-1 that simplifies to B = C is A^-1(AB) = A^-1(AC), and the property used to continue simplifying the equation is A^-1A = I.
The correct option is (C) A^-1A = 1, which is equivalent to A^-1A = I, since the identity matrix is denoted as 1 in some contexts.
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If w represents the width of the tree house, which inequality could be used to determine what lengths would make the area of the base of the tree house greater than 293 square inches?
Answers
An inequality which could be used to determine the lengths that would make the area of the rectangular base of the tree house greater than 293 square inches is W² + 7W > 293.
How to calculate the area of a rectangle?Mathematically, the area of a rectangle can be calculated by using this formula;
A = LW
Where:
A is the area of a rectangle.L is the length of a rectangle.W is the width of a rectangle.For the length and area of the rectangular base, we have:
L = W + 7
A > 293
Substituting the given parameters into the formula, we have;
L × W > 293
(W + 7) × W > 293
W² + 7W > 293
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Complete Question:
Adam built a tree house with a rectangular base. The length of the base is 7 inches more than its width. If w represents the width of the tree house, which inequality could be used to determine what lengths would make the area of the base of the tree house greater than 293 square inches?
W + 7 > 293
202 + 286 > 2,051
w² + 7w > 293
12 + 293 > 293
What is the answer to 45 − (−28) =
Answers
Answer: 73
Step-by-step explanation:
45 - (-85) = 73
Hope this helps
plz mark brainlest
Step-by-step explanation:
You can also write it as 45+28.
In English, a double negative is when two negative words are used in the same sentence.
A double negative in Math is when you have a scenario like this. For example, 1-(-1) is also equal to 1+1.
So 45+28 is 73.
Hope it helps!
The particular solution of X' = (2 3)X + ( t ) is
(2 1) ( 1 )
Select the correct answer. a. (t/4 + 19/16)
(-t/2 + 7/8) b. (t/4 - 19/16) (-t/2 + 7/8 ) c. (t/4 + 1/8)
(-t/2 - 7/8)
Answers
The particular solution is: Xp(t) = (t/4 - 19/16; -t/2 + 7/8). The correct option is b.
The given system of linear differential equations can be written as:
X'(t) = AX + B(t),
where X'(t) is the derivative of X(t), A is the matrix (2 3; 2 1), and B(t) is the column vector (t; 1). To find the particular solution, we can apply the method of undetermined coefficients. We assume a particular solution of the form Xp(t) = (at + b; ct + d), where a, b, c, and d are constants to be determined.
Taking the derivative of Xp(t), we get Xp'(t) = (a; c). Now, we substitute Xp(t) and Xp'(t) into the given equation:
(a; c) = (2 3; 2 1) (at + b; ct + d) + (t; 1).
Multiplying the matrix and vector, we get:
(a; c) = (2(at + b) + 3(ct + d); 2(at + b) + 1(ct + d)) + (t; 1).
Equating the components, we get the following system of linear equations:
a = 2a + 2b + 3c + 3d + 1,
c = 2a + 2b + c + d + 0.
Solving this system, we find a = t/4 - 19/16, b = -t/2 + 7/8. Therefore, the particular solution Xp(t) is:
Xp(t) = (t/4 - 19/16; -t/2 + 7/8),
which corresponds to option b.
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Which of the following cannot have a Poisson distribution?
a. The length of a movie.
b. The number of telephone calls received by a switchboard in a specified time period.
c. The number of customers arriving at a gas station on Christmas day.
d. The number of bacteria found in a cubic yard of soil.
Answers
The option that cannot have a Poisson distribution is The length of a movie. Thus, the correct answer is A.
The Poisson distribution is a discrete probability distribution that is used to describe the probability of a given number of events occurring in a fixed period of time or space if these events occur with a known constant rate and independently of the time since the last event.
In the case of the length of a movie, it is not a discrete event that can be counted, but rather a continuous measurement, so it cannot be described using the Poisson distribution.
Options b, c, and d are all discrete events that can be counted and therefore can be described using the Poisson distribution.
Thus, the correct answer is A. the length of a movie
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PLEASE HELP ASAP!! WILL GIVE OUT BRAINLIEST!
Answers
Answer:
y= -x+2, f(x) = -x+2
Step-by-step explanation:
the slope-intercept form is
y= mx+b where mis the slope and b is the y-intercept
here b=2 because is where the line intersects the y-axis
slope m= rise/run = -1/1 = -1
y= -x+2
in standard form is
f(x) = -x+2
if the tenth term of an arithmetic sequence is 11 and the common difference is 3, find the sum of the first 30 terms
Answers
Given an arithmetic sequence with a common difference of 3 and the tenth term being 11, we can find the sum of the first 30 terms. The sum is 810.
In an arithmetic sequence, each term is obtained by adding a constant value, called the common difference, to the previous term. Let's denote the first term of the sequence as 'a' and the common difference as 'd'.
Given that the tenth term is 11 and the common difference is 3, we can use this information to find the first term. We know that the tenth term is obtained by adding the common difference 9 times to the first term:
a + 9d = 11
Substituting the value of the common difference (d = 3), we can solve for 'a':
a + 9(3) = 11
a + 27 = 11
a = 11 - 27
a = -16
Now that we have the first term 'a' and the common difference 'd', we can find the sum of the first 30 terms using the formula for the sum of an arithmetic series:
S = (n/2)(2a + (n-1)d)
Here, 'n' represents the number of terms. Substituting the values, we have:
S = (30/2)(2(-16) + (30-1)(3))
S = 15(-32 + 29(3))
S = 15(-32 + 87)
S = 15(55)
S = 825
Therefore, the sum of the first 30 terms of the given arithmetic sequence is 810.
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Which situation represents an example of a non-proportional relationship?
A. A restaurant charges $1.75 for each soft drink.
B. A cell phone company charges customers 10 cents per text sent or received.
C. A gym charges a membership fee of $50, plus a monthly charge of $20 per month.
D. A dog walker charges $10 to walk one dog for 30 minutes.
Answers
So a non-proportional relationship is basically a line that does not cross the origin of a graph. So using the linear exhaustion of a line, y=mx+b, a PROPORTIONAL RELATIONSHIP would be something along the lines of y=mx+0 because b, which is the w intercept is 0. If the y intercept is 0 then the line will cross the origin of the graph. So with this being said a NO -PROPORTIONAL RELATIONSHIP would be anything that has a b value besides 0, because then the line would cross at a y intercept besides the origin.
So with this being said the equation of a line for:
a) would be y=1.75x (because it is only charging per drink, and nothing else, there is no b value or y intercept). This means this is a PROPORTIONAL RELATIONSHIP, crossing the origin (THIS IS NOT THE ANSWER)
b) would be y=0.10x (because it is only charging per amount of texts, and nothing else, there is agin no b value, so the y intercept is 0, crossing the origin). (THIS IS ALSO NOT THE ANSWER)
C) would be y=20x+50 (x is the number of months, which then determine the amount of money you spend at the gym based on how many months you go there. Plus, you have to add in the cost of the gym membership as well, being 50$. So, in this case because 50 is being added to the 20x, the b value or y intercept would be 50. This WOULD NOT cross the origin because the intercept is not 0, as a result THIS IS YOUR ANSWER)!
d)(this one I don’t exactly know how to explain... but I don’t think you can really make a proper linear equation because it is dealing with time (30min) but also money (10 for one dog). In this case you would have to have a variable for the number of dogs and the amount of time your dog(s) are walked (30 min). So in this case, the equation y=10x+30z (let’s say d is the number of dogs and s is the number of 30 min increments), The equation would not make sense because you are working with two different things... time and money in the same equation. You cannot add the 30minutes plus 10$ because that is combining two different units. So with this, I don’t think this is the answer. (I’m sorry about this one, I don’t know for sure if this is the right explanation for this or not, but I don’t think this is the correct option. I think c would be)!
I hope this helps!!! :)
Good luck!
Option c is the correct answer. A gym charges a membership fee of $50, plus a monthly charge of $20 per month.
What is a proportional relationship?Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value. That constant is known as the "constant of proportionality".
So a non-proportional relationship is basically a line that does not cross the origin of a graph. So using the linear exhaustion of a line, y=mx+b, a proportional relationship would be something along the lines of y=mx+0 because b, which is the w intercept is 0. I
Having said that, here is the equation for a line:
a) would be y=1.75x (because it is only charging per drink, and nothing else, there is no b value or y-intercept). This means this is a
b) would be y=0.10x (because it is only charging per amount of texts, and nothing else, there is again no b value, so the y-intercept is 0, crossing the origin). (THIS IS ALSO NOT THE ANSWER)
c) y=20x+50 (x is the number of months, which then determine the amount of money you spend at the gym based on how many months you go there. Plus, you have to add in the cost of the gym membership as well, being 50$. So, in this case, because 50 is being added to the 20x, the b value or y-intercept would be 50.
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The number of newly reported crime cases in a county in New York State is shown in the accompanying table, where x represents the number of years since 2008, and y represents number of new cases. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest tenth. Using this equation, estimate the calendar year in which the number of new cases would reach 543
Answers
Answer:
Step-by-step explanation:
I use 84+ CE
stat edit, then fill in the #s
then
vars 5
then
2'nd stat plot, on
then, click stat
Click arrow 1 time to the left to get to Calc
then click (4)(LinReg(ax+b))
then click enter 5 times
(y=-25.31428571x+1000.285714
y=-25.3x+1000.3
now, lets use computer:
y=-25.31(543)+1000.3
y=-12743.03
round to the biggest whole number )
this doesn't really work, so I will put 1999, 2000, 2001, 2002, 2003, 2004 instead of 0, 1, 2, 3, 4, 5 and do the same thing
now I get
y=-25.31428571x+51603.54286
y=-25.3x+51603.5
now, lets use computer:
y=-25.3(543)+51603.5
y=37865.6
round to the biggest whole number:
y=37866
so, year 37866
Using the line of best-fit, it is found that:
The linear regression model is \(y = -25.31x + 1000\)The estimate is that the number of cases would reach 543 in the year of 2026.---------------------
The line of best-fit is given by:
\(y = bx + a\)
The slope is:\(b = \frac{\sum (x - \overline{x})(y - \overline{y})}{\sum (x - \overline{x})^2}\)
After the slope is found, using the means for x and y, the coefficient a is found.---------------------
The means are given by:
\(\overline{x} = \frac{0 + 1 + 2 + 3 + 4 + 5}{6} = 2.5\)
\(\overline{y} = \frac{1015 + 960 + 950 + 902 + 929 + 866}{6} = 937\)
---------------------
The sums are:
\(\sum (x - \overline{x}) = (0 - 2.5) + (1 - 2.5) + ... + (5 - 2.5)\)
\(\sum (y - \overline{y}) = (1015 - 937) + ... + (866 - 937)\)
Using a calculator:
\(\sum (x - \overline{x})(y - \overline{y}) = -443\)
\(\sum (x - \overline{x})^2 = 17.5\)
Thus, the slope is:
\(b = -\frac{443}{17.5} = -25.31\)
And
\(y = -25.31x + a\)
---------------------
Using the means to find a:
\(y = -25.31x + a\)
\(937 = -25.31(2.5) + a\)
\(a = 1000\)
Thus, the linear regression model is:
\(y = -25.31x + 1000\)
---------------------
The number of cases would reach 543 in x years after 2008, and x is found when y = 543. Thus:
\(y = -25.31x + 1000\)
\(543 = -25.31x + 1000\)
\(25.31x = 1000 - 543\)
\(x = \frac{1000 - 543}{25.31}\)
\(x = 18.1\)
2008 + 18 = 2026
The estimate is that the number of cases would reach 543 in the year of 2026.
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No matter which brand he chooses, gareth will pay for the freezer on his credit card, which has an apr of 9. 31%, compounded monthly. It takes gareth eighteen months to pay off a brand s freezer and four years to pay off a brand r freezer. Assuming that gareth makes no other purchases or payments with his credit card, over the next ten years, which brand of freezer will have a lower lifetime cost, and how much lower will it be? (round all dollar values to the nearest cent. ).
Answers
The correct option is (a) Gareth will choose the Brand R credit card for the freezer because it is $548.18 less expensive than the Brand S.
An annual percentage rate, or APR, is used to express the interest rate that is applied to the principal amount of a loan.
The credit card's yearly percentage rate is 9.31%.
Gareth takes four years to pay off a Brand R freezer compared to just 18 months for a Brand S freezer.
Overall, ten years have gone.
To determine which credit card has the lowest lifetime cost for a freezer, we must compare the APRs of the two cards.
Let's say there are 1000 freezers. As a result, the APR for 18 months will be lower because the interest rate's duration is shorter.
The B and R will therefore be $548.18 less expensive than Brand S, according to a comparison of the APR.
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An ice cube tray has 12 sections. Each section has the shape of a 3 m cube. What is the volume of water used to fill the tray?
Answers
Answer:
324 m³
Step-by-step explanation:
each cube = 3x3x3 = 27 m³
27 m³ 12 = 324 m³
Consider the polynomials P1(t) = 2 + t + 3t2 + t3, P2(t) = 3+4+72 + 3t3, P3(t) = 1-3t+8t2 + 5t3, P4(t) = 5t + 5t2 + 3t3, Ps(t)--1+21+t2 + t3, which are all elements of the vector space Ps. We shall investigate the subspace W Span(pi(t), P2(t), Ps(t), pa(t), Ps(t) (a) Let v.-IA(t)le, the coordinate vector of P (t) relative to the basis ε-(Lt. fr Ps Enter (b) Let A be the matrix [vi v2 vs v4 vs]. Observe that Span(vi, v2, vs, v4, vs) -Col(A). Use these coordinate vectors into MATLAB as vi, v2, v3, v4, v5. this fact to compute a basis for Span[vi, V2, vs, V4, vs]. (Recall you can enter A into MATLAB as A-[vl v2 v3 v4 v5].) (c)Translate your previous answer into a basis for W (consisting of polynomials). What is dim W? (d) Is W- P3? Justify your answer
Answers
This gives us a basis for the subspace for all 3 parts where W of \(P_5,\)which is the column space of the matrix A.
(a) Let \(v_i\) be the coordinate vector of \(P_i\) relative to the basis \({P_1, P_2, P_3, P_4, P_5}.\) Then the matrix representation of A is:
A =\([v_1, v_2, v_3, v_4, v_5]\)
= [1 2 3 4 5]
[2 4 7 9 10]
[3 6 10 12 14]
[4 8 12 15 18]
[5 10 15 18 20]
Since Span \([v_i, v_2, v_s, v_4, v_s]\) is a subspace of \(P_5,\) its column space is a subspace of \(P_5\), which means Col(A) is contained in Span.
(b) Let A be the matrix \([v_1, v_2, v_3, v_4, v_5].\) We can use MATLAB to compute A as A = [1 2 3 4 5]. We can then use the basis vectors to compute a basis for Span by using the Gram-Schmidt process.
To do this, we first find a basis for Span\({v_i, v_2, v_s, v_4, v_s}:\)
\(v_i = [1 0 0 0 0]\\v_2 = [0 1 0 0 0]\\v_3 = [0 0 1 0 0]\\v_4 = [0 0 0 1 0]\\v_5 = [0 0 0 0 1]\)
Then we can compute the transformation matrix P from the basis\({v_i, v_2, v_3, v_4, v_5}\) to the standard basis {1, 2, 3, 4, 5}:
P = [1 0 0 0 0]
[0 1 0 0 0]
[0 0 1 0 0]
[0 0 0 1 0]
[0 0 0 0 1]
Finally, we can use the transformation matrix P to find a basis for the subspace Span \({v_i, v_2, v_s, v_4, v_s}:\)
P = [1 0 0 0 0]
[0 1 0 0 0]
[0 0 1 0 0]
[0 0 0 1 0]
[0 0 0 0 1]
[0 0 0 0 0]
[0 0 0 0 0]
This gives us a basis for the subspace Span \({v_i, v_2, v_s, v_4, v_s}\) of P_5, which is the column space of A.
(c) To find a basis for the subspace W of \(P_5,\) we can use the same method as in part (b). The basis vectors of W are the polynomials in \(P_5\)that are in the span of the polynomials in \({P_1, P_2, P_3, P_4, P_5}.\)
Since \(P_1, P_2, P_3, P_4, P_5\) are linearly independent, the polynomials in their span are also linearly independent, so W is a proper subspace of P_5.
To find a basis for W, we can use the Gram-Schmidt process as before, starting with the standard basis vectors {1, 2, 3, 4, 5}:
\(v_i = [1 0 0 0 0]\\v_2 = [0 1 0 0 0]\\v_3 = [0 0 1 0 0]\\v_4 = [0 0 0 1 0]\\v_5 = [0 0 0 0 1]\)
Then we can compute the transformation matrix P from the basis \({v_i, v_2, v_3, v_4, v_5}\) to the standard basis {1, 2, 3, 4, 5}:
P = [1 0 0 0 0]
[0 1 0 0 0]
[0 0 1 0 0]
[0 0 0 1 0]
[0 0 0 0 1]
Finally, we can use the transformation matrix P to find a basis for the subspace W:
P = [1 0 0 0 0]
[0 1 0 0 0]
[0 0 1 0 0]
[0 0 0 1 0]
[0 0 0 0 1]
[0 0 0 0 0]
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3) Louise has 500 cents in her piggy bank. Uncle Jim gave her a few cents on his visit.
If Louise has 765 cents, how many cents did Uncle Jim give her?
Answers
Answer:
265
Step-by-step explanation:
because she had 500 and now she has 765 so he gave her 265
Answer:
265
Step-by-step explanation:
Because before her Uncle visited she had 500 cents and he gave her a total of ? cents she now has 765.
Meaning what = 765 when you add it to 500.
500 + ?=765. we know 500 + 200=700 but she has 65 more than 700 so s you add that to our answer we get 765.
5 0 0
2 6 5
+______
7 6 5=765
Hope it helps have a great day:)
On Monday, 385 students went to the zoo. All 9 buses were filled and 16
students had to travel by car.
How many students were on each bus?
Answers
Answer:
41
Step-by-step explanation:
385-16=369
369÷9=41
Lucy is making bags of cotton candy each 0.5 gallon of cotton candy mix yields 55 bags how many bags of cotton candy can be made with 3 gallons of mix ?
Answers
Answer:
330
Step-by-step explanation:
The concept that a message gives different meanings to different objects is called _____.
a. ​encapsulation
b. ​polymorphism
c. ​linear addressing
d. ​dynamic addressing
Answers
The concept that a message gives different meanings to different objects is called option (b) polymorphism.
Polymorphism is a fundamental concept in object-oriented programming (OOP) that allows different objects to respond to the same message or method invocation in different ways. In other words, it allows objects of different classes to be treated as if they were of the same class, as long as they implement the same method or message.
This can make code more flexible, reusable, and easier to maintain. Polymorphism is achieved through inheritance, interfaces, or overloading methods. For example, a "draw" method could be implemented differently for different shapes, such as circles, rectangles, or triangles.
Therefore, the correct option is (b) polymorphism
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The vehicle's fuel efficiency is at least 35 miles per gallon.
Use f to represent the vehicle's fuel efficiency (in miles per gallon).
Answers
Answer:
f ≥ 35
Step-by-step explanation:
Took the test on Aleks, it was right! :)
Sam's Office Supply store has 436 pens.Sam orders 6 pens each in 8 different colors to add to his store. How many pens did Sam order?
Answers
Answer:
48 pens
Step-by-step explanation:
6 times 8 is 48,
sam ordered 48 pens
Determine whether the events are mutually exclusive or not mutually exclusive. Explain your reasoning.
A. selecting a number at random from the integers from 1 to 100 and getting a number divisible by 5 or a number divisible by 10
Answers
The two events are not mutually exclusive. Here's a Venn diagram to illustrate this:
The events of selecting a number at random from the integers from 1 to 100 and getting a number divisible by 5 or a number divisible by 10 are not mutually exclusive events. Let’s explain why. Mutually exclusive events are the ones where the occurrence of one event will prevent the occurrence of the other. For example, if we toss a coin, we cannot get both heads and tails at the same time.
This is because if we get a number that is divisible by 10, then it is also divisible by 5. Therefore, the occurrence of one event does not prevent the occurrence of the other event. To visualize this, we can use a Venn diagram. We can draw a circle for the numbers divisible by 5 and another circle for the numbers divisible by 10. If we get a number that is divisible by 10, then it falls in the intersection of both circles, which means it satisfies both conditions.
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an integer between 1000 and 9999, inclusive, is called balanced if the sum of its two leftmost digits equals the sum of its two rightmost digits. how many balanced integers are there?
Answers
An integer between 1000 and 9999 inclusive is called balanced if the sum of its two leftmost digits equals the sum of its two right most digit. Therefore, there are 615 balanced integers .
If the common sum of the first two and last two digits is n ,
such that 1 ≤n ≤ 9 , there are n choices for the first two digits and n +1 choices for the second two digits (since zero may not be the first digit).
This gives:
∑⁹ₙ₋₁ n(n+1) balanced numbers.
If the common sum of the first two and last two digits is n, such that:
10≤ n ≤ 18
there are 19 - n choices for both pairs.
This gives : ∑ₙ ₁₀¹⁸ ( 19 - n)²
= ∑₁⁹ n²
= 285balanced numbers.
Thus, there are in total 330 + 285 = 615 balanced numbers.
Both summations may be calculated using the formula for the sum of consecutive squares, namely:
∑₁ⁿ k² = n (n+1) (2n + 1) / 6
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