given two nonzero vectors which aren't parallel, there is exactly one plane parallel to both vectors. g
Answers
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.
Related Questions
An engineer traveled 140 mi by car and then an additional 750 mi by plane. The rate of the plane was three times the rate of the car. The total trip took 6 h. Find the rate of the car.
Answers
The rate of car is 35 mph.
Given that engineer traveled 140 mi by car and then an additional 750 mi by plane. The rate of the plane was three times the rate of the car.
Let c be the rate of wind.
215 + c = rate of plane with wind
215 - c = rate of plane against wind
Therefore, the travel time =distance/rate
⇒ 750/(215+c) = 540/(215-c)
Cross multiplying we get,
540(215+c) = 750(215-c)
116100+540c = 161250-750c
1290c = 45150
c=35
Hence, the rate of car is 35 mph.
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In-State tuition at UNCW is currently
$6,691. NC is raising tuition 1% each year for the next 4 years. What will be the new tuition 4 years from now?
Answers
The new tuition 4 years from now is $6962.68.
What is the compound interest?Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
The formula used to find the compound interest = \(A=P(1+\frac{r}{100})^{nt}\).
Given that, principal =$6691, rate of interest=1% and time period=4 years.
Now, A=6691(1+1/100)⁴
=6691(1+0.01)⁴
=6691(1.01)⁴
= 6691×1.04060401
= $6962.68
Therefore, the new tuition 4 years from now is $6962.68.
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Last month, the remaining balance on Sarah's credit card was $457.32. If she adds charges of $74.82 for clothes, $150 for food and $94.79 for car repairs and then makes a payment of $525.00, what is the current balance on the credit card (what does she currently owe)?
Answers
Answer: $ 251.93
Step-by-step explanation:
please help me!!!!!!! 43 + 4⋅5 =
Answers
Answer:
47.5
(Let me know if you need the work)
1 · 3.2 = d
i need the answer now
Answers
Answer:
d = 3.2
Step-by-step explanation:
1 * 3.2 = 3.2
Hence,
d = 3.2
The equation C=24n+2 represents the cost
Answers
Jim did not buy any tickets (n_Jim = 0).
Larry bought 7 more tickets than Jim.
To determine the number of tickets Larry bought more than Jim, we need to find the values of n for Larry and Jim's ticket purchases.
For Larry:
Let's substitute C = $170 into the equation C = 24n + 2 and solve for n:
$170 = 24n + 2
Subtracting 2 from both sides:
$168 = 24n
Dividing both sides by 24:
n = 7
For Jim:
We can calculate the number of tickets Jim bought by subtracting 12 from Larry's number of tickets:
n_Jim = n_Larry - 12
n_Jim = 7 - 12
n_Jim = -5
Since we cannot have a negative number of tickets, we can conclude that Jim did not buy any tickets (n_Jim = 0).
To find the difference in the number of tickets bought, we subtract the number of tickets Jim bought from the number of tickets Larry bought:
n_difference = n_Larry - n_Jim
n_difference = 7 - 0
n_difference = 7
Therefore, Larry bought 7 more tickets than Jim.
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Question
The equation C=24n+2 represents the cost, C, in dollars, of buying n tickets to a play. J $170. How many more tickets did Larry buy than Jim? 12
Two points are located on a graph, Point A is (-1, 10), and Point B is (4,3). What is the
distance between Point A and Point B?
A) 8.6
B)13.3
C) 10
D)3
Answers
Answer:
10
Step-by-step explanation:
please help it’s due today
Answers
Answer:
-3
Step-by-step explanation:
1 - 4 = -3
2 - 1 = 1
(-3) / 1 = (-3)
1. Find the Perimeter AND Area of the figure
below.
2 ft
5 ft
2 ft
5 ft
Answers
Answer:
A = 16 ft^2
P = 20 ft
Step-by-step explanation:
P = perimeter
A = area
STEP 1: divide the shape into rectangles
Rectangle 1: 2ft*3ft
Rectangle 2: 2ft*5ft
STEP 2: Find the area of each rectangle
Equation for area of a rectangle = bh
Rectangle 1: b = 2, h = 3
Rectangle 2: b = 2, h = 5
(2 * 3) + (2 * 5)
6 + 10
16 ft^2
Now, we have to find the perimeter
STEP 1: Find the unknown side lengths.
To find the lengths of the sides not labeled, you have to use the lengths of the sides we already know.
The length of one parallel side is 5, and the length of another parallel side is 2. The length of the unknown side starts at the same place as the top of the side length that is 5, and ends at the top of the side length that is 2. This means that we have to subtract 2 from 5 in order to find the unknown side length.
STEP 2: Add up all the side lengths
P = 2 + 5 + 5 + 2 + 3 + 3
P = 20 ft
Don't forget to label your answers!!
I hope this made sense, it's is a little hard to explain in simple terms without being able to draw, but I hope it helped.
how do you solve this?
Answers
Answer:
i have no idea.....
Step-by-step explanation:
Answer:
sin(5x)
Step-by-step explanation:
Recall that the half angle identity relates the sine of half an angle to the square root of one minus the cosine of the angle as shown below:
\(sin(\frac{\theta}{2} )=+/-\sqrt{\frac{1-cos(\theta)}{2} }\)
therefore, in our case:
\(sin(5\,x )=+/-\sqrt{\frac{1-cos(10\,x)}{2} }\)
so, make sure you type the expression : "sin(5x)" in the provided text-box.
Solve the system of equations using the substitution method. Make sure to check your solution.
y = x - 6
5x + 3y = 14
In the blanks below, type just the number for the x-coordinate in blank 1 and just the number for the y-coordinate in blank 2.
x-coordinate:
y-coordinate:
Answers
Answer: x-coordinate: 4
y-coordinate: -2
Step-by-step explanation:
The given system of linear equations:
y= x- 6 ..(i)
5x+3y = 14 ...(ii)
Substitute value of y in (ii), we get
\(5x +3(x-6)=14\\\\\Rightarrow\ 5x+3x-18=14\\\\\Rightarrow \ 8x=14+18\\\\\Rightarrow\ 8x=32\\\\\Rightarrow\ x=4\)
Put value of x in (i) , we get
\(y=4-6=-2\)
Hence, Required solution:
x-coordinate: 4
y-coordinate: -2
Which equation represents 3/8 less than 7/8 of a number?
A. 3/8 -7/8n
B. 3/8n - 7/8
C. 7/8n-3/8
D. (7/8-3/8)n
Answers
Am sure its D
On your wedding day you leave for the church 30 minutes before the ceremony is scheduled to start. The church is only 10 miles away, but you have to make an unanticipated stop for construction work on the road. As a result, your average speed for the first 15 minutes is only 5 miles per hour. What average speed do you need to go for the rest of the trip to get to the church on time
Answers
Answer:
You need to have an average speed of at least 35 miles per hour for the rest of the trip to get to the church on time
Step-by-step explanation:
We use the following relation to solve the question:
\(v = \frac{d}{t}\)
In which v is the velocity, d is the distance, and t is the time.
First 15 minutes:
Time of 15 minutes = 0.25 hour, so \(t = 0.25\)
Velocity of 5 miles per hour. So the distance is of:
\(d = vt = 5*0.25 = 1.25\)
Final 15 minutes:
The will need to drive 10 - 1.25 = 8.75 miles in 15 minutes = 0.25 hours. So, the average speed will need to be of at least:
\(v = \frac{d}{t} = \frac{8.75}{0.25} = 35\)
You need to have an average speed of at least 35 miles per hour for the rest of the trip to get to the church on time
2. The box and whisker plot below shows the starting salaries for 120 graduates of a small college.
a) What is the range of the starting salaries?
b) About 30 graduates make below what amount?
c) How many graduates have a salary above $33,000 ?
d) $25 of the graduates make above what amount?
Answers
The range of the starting salaries is 53,000
Given,
The box and whisker plot below shows the starting salaries
The number of graduates in a small college = 120
We have to find the range of the starting salaries;
Range of a data;
The difference between the highest and lowest values for a given data collection is the range in statistics. For instance, the range will be 10 - 2 = 8 if the given data set is 2, 5, 8, 10, and 3. As a result, the range may alternatively be thought of as the distance between the highest and lowest observation.
Here,
Lowest value = 19,000
Highest value = 72,000
Then,
Range of the set = 72,000 - 19,000 = 53,000
That is,
The range of the given data set is 53,000
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What is the difference between a postulate and a theorem?
1. A postulate deals with parallel lines, but a theorem can involve segments and angle measures.
2. A postulate is generally accepted without proof, but a theorem must be proven.
3. A postulate has already been proven by a mathematician, but there is no proof yet for a theorem.
4. A postulate must use undefined terms (such as point, line, and plane), but a theorem uses other vocabulary.
Answers
The difference between a postulate and theorem is 2)A postulate is generally accepted without proof, but a theorem must be proven.
What is postulate and theorem ?
Postulates are assertions that, in the absence of evidence, are taken to be true. Postulates provide as a foundation and an explanation for terms that are not specified. Mathematical postulates are assertions that hold true without the need for testing. They are founded on definitions and ideas from mathematics.
The term "theorem" refers to a mathematical assertion or claim that has been shown to be true. A statement is considered a theorem if it can be proven to be true using procedures and arguments that are commonly used in mathematics. Example for theorem is Pythagorean theorem.
Here the given options , the difference between postulate and theorem is
=> A postulate is generally accepted without proof, but a theorem must be proven.
Therefore the correct option is 2)A postulate is generally accepted without proof, but a theorem must be proven.
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4. An average cigarette contains 1.5 mg of nicotine. The average smoker
smokes 15 cigarettes a day. How much nicotine does the average
smoker inhale a day?
Answers
Answer:
22.5 mg of nic
Step-by-step explanation:
1.5*15=22.5mg
don't smoke kids! (idc)
Allie, barbara, and carson will divide $440 among themselves as follows. Barbara gets 2 times as much as allie. Carson gets 1/3 as much as barbara. How much does each person get?
Answers
Answer:
Allie got $120, Barbara got $240 and Carson got $80.
Step-by-step explanation:
This question can be solved by a system of equations.
I am going to say that:
Allie got x.
Barbara got y.
Carson got z.
Divide $440 among themselves
This means that \(x + y + z = 440\)
Barbara gets 2 times as much as allie.
This means that \(y = 2x\)
Carson gets 1/3 as much as barbara.
This means that \(z = \frac{y}{3} = \frac{2x}{3}\)
Finding x:
Replacing in the first equation.
\(x + y + z = 440\)
\(x + 2x + \frac{2x}{3} = 440\)
Multiplying everything by 3
\(3x + 6x + 2x = 1320\)
\(11x = 1320\)
\(x = \frac{1320}{11}\)
\(x = 120\)
Finding y and z:
\(y = 2x = 2(120) = 240\)
\(z = \frac{y}{3} = \frac{240}{3} = 80\)
Allie got $120, Barbara got $240 and Carson got $80.
consider the system of linear equations
consider the system of linear equations
6x+2y – z=4
X +5y+z=3
2x+y+4z=27
A, solve the system by
I. Gassian elimination method,
II. LU- decomposition method
III. Gauss- Jacobi method,and
IV. Gauss-seidel method,
Answers
I. The solution to the system of equations using Gaussian elimination is x = 1, y = -1, and z = 2.
II. For the LU-decomposition method, we need to have a square coefficient matrix, which is not the case in the given system. Therefore, we cannot directly apply the LU-decomposition method.
III. For this method to converge, the coefficient matrix must be diagonally dominant, which is not the case in the given system. Therefore, the Gauss-Jacobi method cannot be directly applied either.
IV. It requires the coefficient matrix to be diagonally dominant, which is not satisfied in the given system. Hence, the Gauss-Seidel method cannot be directly used.
I. Gaussian Elimination Method:
To solve the system of linear equations using Gaussian elimination, we perform row operations to reduce the system into upper triangular form. The augmented matrix for the given system is:
| 6 2 -1 | 4 |
| 1 5 1 | 3 |
| 2 1 4 |27 |
We can start by eliminating the coefficients below the first element in the first column. To do this, we multiply the first row by a suitable factor and subtract it from the second and third rows to eliminate the x coefficient below the first row. Then, we proceed to eliminate the x coefficient below the second row, and so on.
After performing the necessary row operations, we obtain the following reduced row-echelon form:
| 6 2 -1 | 4 |
| 0 4 2 | -1 |
| 0 0 3 | 6 |
From this form, we can easily back-substitute to find the values of x, y, and z. We have z = 2, y = -1, and x = 1.
II. LU-Decomposition Method:
LU-decomposition is a method that decomposes a square matrix into a product of two matrices, L and U, where L is lower triangular and U is upper triangular.
III. Gauss-Jacobi Method:
The Gauss-Jacobi method is an iterative numerical method to solve systems of linear equations.
IV. Gauss-Seidel Method:
Similar to the Gauss-Jacobi method, the Gauss-Seidel method is an iterative method for solving linear systems.
Therefore, out of the four methods mentioned, only the Gaussian elimination method can be used to solve the given system of linear equations.
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Henry used square papers, each measuring 1 square unit, to tile a rectangle with no gaps or overlaps. He sketched his work as shown. Use the
image to fill in the missing information.
Help need answer today!!!
Answers
Answer:
If you give me the image and what the question is then I will be happy to try and help you in the comments!
Step-by-step explanation:
See attached for the question
Answers
Check the picture below.
Answer:
∠ U = 12°
Step-by-step explanation:
the inscribed angle RST is half the measure of its intercepted arc RT , then
arc RT = 2 × ∠ RST = 2 × 30° = 60°
the secant- tangent angle U is equal to half the difference of its intercepted arcs, that is
∠ U = \(\frac{1}{2}\) ( RS - RT ) = \(\frac{1}{2}\) × (84 - 60)° = \(\frac{1}{2}\) × 24° = 12°
Find the weight of a 176-cm male to the nearest kg whose BSA = 2.3.
Answers
The weight of the male that has a body surface area of 2.3 would be = 108kg
What is Body Surface Area (BSA)?The body surface area (BSA) is defined as the parameter that can be used to estimate the surface area of a person's body based on body weight and height.
The formula for BSA = √w×h/3600
The weight of the male = X
The height of the male = 176cm
The BSA = 2.3
From the formula, make w the subject of formula;
w = BSA²× 3600/h
w = 2.3²× 3600/176
w= 5.29×3600 /176
w = 19044/176
w = 108kg
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A dairy farmer wants to mix a 70% protein supplement and a standard 20% protein ratio to make 1900 pounds of a high grade 55% protein ration how many pounds of each should he use
Answers
The dairy farmer should use 1330 pounds of the 70% protein supplement and 570 pounds of the 20% protein ratio to make a 1900-pound high-grade 55% protein ration.
To determine the amounts of the 70% protein supplement and the 20% protein ratio needed to make a 1900-pound high-grade 55% protein ration, we can set up a system of equations.
Let's assume x represents the pounds of the 70% protein supplement and y represents the pounds of the 20% protein ratio.
The total weight equation is given by:
x + y = 1900
The protein content equation is given by:
(0.70x + 0.20y) / 1900 = 0.55
Simplifying the second equation, we get:
0.70x + 0.20y = 0.55 × 1900
0.70x + 0.20y = 1045
Now, we can solve this system of equations to find the values of x and y.
Rearrange the first equation to solve for x:
x = 1900 - y
Substitute this expression for x in the second equation:
0.70(1900 - y) + 0.20y = 1045
1330 - 0.70y + 0.20y = 1045
1330 - 0.50y = 1045
-0.50y = 1045 - 1330
-0.50y = -285
y = -285 / -0.50
y = 570
Now substitute this value of y back into the first equation to find x:
x + 570 = 1900
x = 1900 - 570
x = 1330
Therefore, the dairy farmer should use 1330 pounds of the 70% protein supplement and 570 pounds of the 20% protein ratio to make a 1900-pound high-grade 55% protein ratio.
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Get me right twinnnn
Answers
Answer:
\( \frac{9x { }^{2 } - 63x}{ 3x} \\ = \frac{3x(3x - 21)}{3x} \\ = 3x - 21 \)
hope it helps:)
Answer:3x-21
Step-by-step explanation:
\(\frac{9x^{2} - 63x }{3x}\) ⇒ \(\frac{3x * (3x - 21) }{3x}\) ⇒ cancel out 3x ⇒ 3x - 21
How do you simplify (2/3) with a sqrt of 2
Answers
Which inequality is graphed below
Answers
Answer:
wheres it at?
Step-by-step explanation:
#Everything4Zalo
 50, 25, 12.5….
What is the geometric sequence and what is the 8th and 10th term
Answers
clearly r = -1/2
So, Tn = -100 (-1/2)^(n-1) = 200/(-2)^n
The maximum grain yield for corn is achieved by planting at a density of 37,000 plants per
acre. A farmer wants to maximize the yield for the field represented on the coordinate grid.
Each unit on the coordinate grid represents one foot. How many corn plants, to the nearest
thousand, does the farmer need? (Hint: 1 acrt = 43,560 ft?)
у
500 fx
E
F
X
-500
0
500
G
-500
H
The farmer needs approximately
corn plants.
Answers
According to the question, there are 37000 plants per hectare, the total corn plan required is 475,665.75 corn plants
Determining the area of a trapezium?The trapezium is a 2 -dimensional plane shape with the area calculated as shown below:
The formula for calculating the area of a trapezoid is expressed as:
Area = 0.5(a + b)h
Given the following parameters
a = 500 ftb = 900ft
height h = 800ft
Substitute the given parameters
Area = 1/2 (500 + 900) * 800
Area = 1/2 (1400) * 800
Area = 560000 square feet
Since 1 acre is equivalent to 43560 square feet, hence the total acre required is expressed as:
Total acre = 560000/43560
Total acre = 12.856 acres
Also since there are 37000 plants per hectare, the total corn plan required is 475,665.75 corn plants
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p^3 - 64 = 0
Please help if you get it right I’ll do whatever you want I did this but I don’t know what else to do
Answers
r=4, -2+2i√3, 2-2i√3
Answer:
\(\frac{-4+-\sqrt{-48} }{2}\) that's it. Also the +- is plus or minus i just don't know how to add in there:) hope this helps
Step-by-step explanation:
Four sparking plugs and a fan belt cost $10.50 if the fen belt costs $1.75 more than sparking plugs. Find the cost of each material
Answers
Answer: x = $1.75
Step-by-step explanation:
Let's assume that the cost of each sparking plug is x dollars. Then, the cost of the fan belt is x + $1.75 since it costs $1.75 more than each sparking plug.
According to the problem, the total cost of four sparking plugs and a fan belt is $10.50. We can express this as an equation:
4x + (x + $1.75) = $10.50
Simplifying and solving for x, we get:
5x + $1.75 = $10.50
5x = $8.75
x = $1.75
Therefore, each sparking plug costs $1.75 and the fan belt costs $3.50 ($1.75 + $1.75).
Please help me I beg you I beg pms pls pls pls pls pls
