for the vectors u=3,−3 and v=3,−1, express u as the sum u=p n, where p is parallel to v and n is orthogonal to v.
Answers
The vectors u=3,-3 and v=3,-1 can be expressed in the form u=pn where p is parallel to v and n is orthogonal to v. The orthogonal vector n is obtained by finding the projection of u onto the orthogonal complement of v. In order to find p, the projection of u onto v is required. We can use the formula to find the orthogonal projection of a vector w onto a vector v:
projvw=w⋅v/||v||^2v
where ||v|| is the magnitude of v.
To find the projection of u onto v, we have:
projvu=u⋅v/||v||^2v
= (3*-3 + -3*-1) / (3^2 + -1^2) (3, -1)
= -12/10 (3,-1)
= (-18/5, 6/5)
This is the parallel component of u. To find the orthogonal component, we subtract the parallel component from u:
n=u−p
=(3,-3)−(-18/5,6/5)
=(15/5, -15/5)−(-18/5,6/5)
=(33/5,-21/5)
Therefore, we can express u as the sum u=pn where p=(-18/5,6/5) is parallel to v and n=(33/5,-21/5) is orthogonal to v.
In summary, the process of expressing a vector u as the sum of a parallel and orthogonal vector involves finding the projection of u onto the parallel vector, and the orthogonal projection of u onto the orthogonal vector. The parallel vector is obtained by scaling the original vector by the dot product of u and v divided by the squared magnitude of v. The orthogonal vector is obtained by subtracting the parallel vector from the original vector.
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Related Questions
If U And V Are Orthogonal, What Is The Magnitude Of U Times V?
Answers
If U and V are orthogonal then the magnitude of U times V will be U.V = 0 or |UxV| = uv.
U and V are two orthogonal vectors.
since the angle between them is θ = 90⁰
let u and v be the magnitudes of the vectors U and V respectively.
so first dot-product: If two non-zero vectors are orthogonal than the dot product of these vectors will be zero. Dot product of two vectors is expressed by:
U.V = uv cosθ
since these vectors are orthogonal so,
U.V = uv cos90⁰ = 0
And Cross-product: Magnitude Cross product of two orthogonal vectors will be equal to product of magnitude of these vectors.
|UxV| = uv sin θ
|UxV| = uv sin 90⁰ = uv
Therefore, U.V = 0, |UxV| = uv.
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???? Help asap pls. ……
Answers
The expression equivalent to (3x²z⁻³)² is 9x⁴z⁻⁶.
What is meant by the term indices/index?In mathematics, an index (indices) is indeed the power or exponent raised to a number or variable. A constant is a value that cannot be altered. An index can be assigned to a number or a variable. A variable's index (or constant) is a value raised to a power of the variable. The indices are also referred to as powers or exponents.For the given question;
The expression is given as;
= (3x²z⁻³)²
Squaring each term individually.
= (3)²(x²)²(z⁻³)²
As the property of the index, the power will be multiplied.
= 9x⁴z⁻⁶.
Thus, the expression equivalent obtained for the given expression (3x²z⁻³)² is 9x⁴z⁻⁶.
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PLS HELP WILL GIVE BRAINLIEST ALMOST DUE
Which equation could represent the line of best fit for the temperatures based on the altitudes?
Answers
Answer:
\(y = - \frac{7}{5} x + 59\)
The average weight of the top 5 fish at a fishing tournament was 14.2 pounds. Some of the weights of the
fish are shown in the table.
Top 5 Fish
Caught by Weight (lb)
Wayne S.
?
Carla P.
15.4
Deb N.
14.5
Vincente R.
13.1
Armin G.
12.3
What was the weight of the heaviest fish?
The weight of the heaviest fish was
Ib.
Answers
Answer:
\( \frac{15,4+14,5+13,1+12,3 + x}{5} = 14.2\)
\( \frac{55.3 + x}{5} = 14.2 \\ \)
\(11.06 + \frac{x}{5} = 14.2\)
\( \frac{x}{5} = 3.14\)
\( \frac{x}{5} = 3.14\)
\(x = 3.14 \times 5 = 15.7\)
the heaviest fish was 15.7
I hope it is right
F(x)=6+3x Fund the value of F(5) for the function
Answers
Answer:
F(5)= 21
Step-by-step explanation:
Plug in the 5 for x...
F(5)=6+3(5)
F(5)=6+15
F(5)=21
Step-by-step explanation:
F(5) = 6 +(3 ×5)
= 6 + 15 = 21
Peter has 22 coins, all dimes and quarters whose total value is $4.30 how many of each coin does he have PLEASE HELP!!!!!
Answers
Answer:
8 dimes and 14 quarters.
Step-by-step explanation:
d and q are the number of dimes and quarters, respectively.
"22 coins, all dimes and quarters"
d+q = 22
d = 22-q
"total value is $4.30"
0.10d + 0.25q = 4.30
substitution
0.10(22-q) + 0.25q = 4.30
2.2 + 0.15q = 4.30
q = 14
d = 22-q = 8
8 dimes and 14 quarters.
[−1 3/5⋅(−6)]⋅(−3 3/4)⋅10
Answers
Answer:
The answer will be -300
Step-by-step explanation:
Doing this in a calculator, it will give you -300
ABC is a triangle. P is a point on BC such that BP:PC=3:2 and Q is a point on AB such that AQ:QB=1:2. Line AP and CQ intercept at R. Find AR:RP and CR:RQ.
Answers
In triangle ABC, where P is a point on BC such that BP:PC = 3:2 and Q is a point on AB such that AQ:QB = 1:2, we can determine the ratios AR:RP and CR:RQ. The ratio AR:RP is 4:1, and the ratio CR:RQ is 3:2
Given:
BP:PC = 3:2 and AQ:QB = 1:2
Let's assign variables:
Let BP = 3x and PC = 2x
Let AQ = y and QB = 2y
Using the given ratios, we can determine the lengths of AP and QC:
AP = AQ + QP = y + 2y = 3y
QC = BC - QB = BP + PC - QB = 3x + 2x - 2y = 5x - 2y
By applying the intercept theorem, we know that AP/PB = CR/RQ. Substituting the values, we get:
3y/(3x) = CR/(5x - 2y)
Simplifying the equation:
y/x = CR/(5x - 2y)
From the given ratios, we have AQ:QB = 1:2, which means y/x = 1/2. Solving for y/x in the equation above, we find:
1/2 = CR/(5x - 2y)
To find the values of CR and RQ, we can express them in terms of y and x:
CR = (1/2)(5x - 2y) = 5/2x - y
RQ = 2y
Now we can determine the ratios:
AR:RP = AP:PB = 3y:3x = y:x = 1:1/3 = 4:1 (since x = 3y)
CR:RQ = CR:2y = (5/2x - y):2y = (5/2)(1/3) - 1 = 5/6 - 1 = 3/6 = 1:2
Therefore, in triangle ABC, AR:RP = 4:1 and CR:RQ = 3:2.
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calculate 41% 0f 51kg
Answers
51 x 0.41 = 20.91
Answer:
20.91kg
Step-by-step explanation:
Amount = .41 * 51 = 20.91kg
Determine the probability of precipitation (PoP) using the formula below and the following
PoP = (C * A) * 100 percent
Where C is the confidence that precipitation will occurs somewhere in the forecasted area, and A equals the percentage of the area that will receive measured precipitation if it occurs.
a. A forecaster expresses confidence that there is an 80 percent chance of precipitation in the forecasted area, and it is expected to produce measurable precipitation over 90 percent of the area.
b. A forecaster expresses confidence that there is a 20 percent chance of precipitation in the forecasted area, and it is expected to produce measurable precipitation over 10 percent of the area.
Answers
The correct answer is a) the probability of precipitation is 72%. and b) the probability of precipitation is 2%.
The given formula to determine the probability of precipitation (PoP) is PoP = (C * A) * 100 percent where C represents the confidence that precipitation will occur somewhere in the forecasted area and A represents the percentage of the area that will receive measured precipitation if it occurs.
(a) If a forecaster expresses confidence that there is an 80% chance of precipitation in the forecasted area, and it is expected to produce measurable precipitation over 90% of the area, then the probability of precipitation is given as follows: PoP = (C * A) * 100 per cent C = 80%A = 90%PoP = (80% * 90%) * 100%
PoP = 72%.
Therefore, the probability of precipitation is 72%.
(b) If a forecaster expresses confidence that there is a 20% chance of precipitation in the forecasted area, and it is expected to produce measurable precipitation over 10% of the area, then the probability of precipitation is given as follows: PoP = (C * A) * 100 per cent C = 20%A = 10%PoP = (20% * 10%) * 100%PoP = 2%
Therefore, the probability of precipitation is 2%.
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When a chocolate bar is cut in half its density is: a) doubled b) unchanged c) halved
Answers
The correct answer is b) unchanged. Cutting a chocolate bar in half does not affect its density.
When a chocolate bar is cut in half, its density remains unchanged. Density is a physical property of a substance that is determined by its mass per unit volume. When the chocolate bar is cut in half, the mass is also divided into two equal parts, resulting in a reduction of the volume by half as well. Since both the numerator and denominator in the density formula change proportionally, the density remains the same.
For example, if the density of a chocolate bar is 1 gram per cubic centimeter, cutting it in half would result in two smaller bars, each with half the volume and half the mass. The density of each of the new bars would still be 1 gram per cubic centimeter, even though they are smaller in size.
Therefore, the correct answer is b) unchanged. Cutting a chocolate bar in half does not affect its density.
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Could someone please help me? Thank you and explain the work because I don’t get this
Answers
Answer:
5.59 times per second.
Step-by-step explanation:
Direct variation is in the form:
\(y=kx\)
Where k is the constant of variation.
Inverse variation is in the form:
\(\displaystyle y=\frac{k}{x}\)
In the given problem, the frequency of a vibrating guitar string varies inversely as its length. In other words, using f for frequency and l for length:
\(\displaystyle f=\frac{k}{\ell}\)
We can solve for the constant of variation. We know that the frequency f is 4.3 when the length is 0.65 meters long. Thus:
\(\displaystyle 4.3=\frac{k}{0.65}\)
Solve for k:
\(k=4.3(0.65)=2.795\)
So, our equation becomes:
\(\displaystyle f=\frac{2.795}{\ell}\)
Then when the length is 0.5 meters, the frequency will be:
\(\displaystyle f=\frac{2.795}{.5}=5.59\text{ times per second.}\)
How many solutions does the equation 6x-10=2(3x+8) have?
No Solution
One Solution
Infinitely Many Solutions
Answers
Answer:
No solution
Step-by-step explanation:
As 6x on lhs and 2×3x on the rhs are equal and cancel each other
A car drove 10/45 miles in 0.4 hours. How fast was the car traveling in miles per hour?
Answers
Answer:
1.2 hours equal to 30mph
Step-by-step explanation:
Pls mark brainliest
hey please!! Thank you <33
Answers
Answer:
h÷2
Step-by-step explanation:
\(2\:gallons =1\:hour\\2 \: gallons = h \:hours\\2h = 2\\\frac{h}{2} = \frac{2}{2}\)
is f(x)=x+1/x+2 a function? Explain.
Answers
The equation represented as f(x) = x + 1/x + 2 is a function
How to determine if the equation is a functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = x + 1/x + 2
The above equation is a rational equation whose numerator and denominator are linear functions
Equations with these properties are always functions
This is so because their x values do not have multiple y values
Hence, the equation f(x) = x + 1/x + 2 is a function
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The mean lifetime of a tire is 48 months with a standard deviation of 7. If 147 tires are sampled, what is the probability that the mean of the sample would be greater than 48.83 months
Answers
To find the probability that the mean of the sample would be greater than 48.83 months, we will use the central limit theorem.
We will first find the z-score for the given values using the formula: `z = (x - μ) / (σ / √n)` where `x` is the sample mean, `μ` is the population mean, `σ` is the population standard deviation and `n` is the sample size.
Then we will find the probability using a standard normal distribution table.
Given,The mean lifetime of a tire, μ = 48 monthsStandard deviation of the lifetime of a tire, σ = 7Sample size, n = 147Sample mean, x = 48.83 months
We need to find the probability that the mean of the sample would be greater than 48.83 months.
Using the formula for z-score,z = (x - μ) / (σ / √n)z = (48.83 - 48) / (7 / √147)z = 0.83 / 0.577 = 1.44
Using a standard normal distribution table, the probability corresponding to a z-score of 1.44 is 0.9251.Approximately, the probability that the mean of the sample would be greater than 48.83 months is 0.9251.
Summary: The probability that the mean of the sample would be greater than 48.83 months is 0.9251.
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Ayudame por favor
Help me please
Answers
The full equation is
Y=-1/2x+ 6 1/2
Determine whether the Law of Cosines or the Law of Sines is needed to solve the triangle a = 11, b = 13, c = 7
Answers
Answer:
Step-by-step explanation:
Use the Law of Cosines:
c^2 = a^2 + b^2 - 2ab*cos C becomes
7^2 = 11^2 + 13^2 - 2(11)(13)cos C.
Once you have cos C, and then side c, you can use the Law of Sines to find the other two interior angles.
Find the distance between the points T(13, 1. 6) and V(5. 4, 3. 7). Answer in simplest exact form.
The exact distance between the two points is
Answers
the exact distance between the points T(13, 1.6) and V(5.4, 3.7) is approximately √62.17. This is the simplest exact form of the answer.
To find the distance between two points in a coordinate plane, we can use the distance formula. The distance formula is derived from the Pythagorean theorem and helps us calculate the straight-line distance between two points.
The distance formula is given as:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
Let's find the distance between the points T(13, 1.6) and V(5.4, 3.7):
x₁ = 13
y₁ = 1.6
x₂ = 5.4
y₂ = 3.7
Using the distance formula, we have:
d = √((5.4 - 13)² + (3.7 - 1.6)²)
Simplifying the expression inside the square root:
d = √((-7.6)² + (2.1)²)
Calculating the squares:
d = √(57.76 + 4.41)
Adding the values inside the square root:
d = √(62.17)
Taking the square root:
d ≈ √62.17
Therefore, the exact distance between the points T(13, 1.6) and V(5.4, 3.7) is approximately √62.17. This is the simplest exact form of the answer.
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Which of the following statements does not prove that ABCD is a parallelogram.
Given: A(-4, 7), B(3,0), C(2,-5) and D(-5, 2).
Answers
Answer:
answer A
Step-by-step explanation:
A=(-4,7)
C=(2,-5)
midpoint = U=((-4+2)/2, (7+(-5))/2)=(-1,1))
B=(3,0)
D=(-5,2)
midpoint = V=((3+(-5))/2,(0+2)/2)=( -1,1)
Diagonals have the same middle, the quadrilater is a parallogram.
What is the degree of the polynomial 2x² 5x³ 7x 8?
Answers
Answer:he degree of the polynomial 3x 8 + 4x 3 + 9x + 1 is 8. We know that the polynomial can be classified into polynomial with one variable and polynomial with multiple variables
Step-by-step explanation:
Name 4 points that would form a square with the origin at its center
Answers
The points that would form a square are (2, 2), (2, -2), (-2, 2), (-2, -2)
Naming the points that would form a squareFrom the question, we have the following parameters that can be used in our computation:
Forming a square
As a general rule
A square has equal sides and the angles at the vertices are 90 degrees
Since it must make a point with origin at its center, then the center must be (0, 0)
So, we have the following points (2, 2), (2, -2), (-2, 2), (-2, -2)
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What is 11.3 times 4.3
Answers
Answer:
48.59
Step-by-step explanation:
Answer:
48.59
Step-by-step explanation:
11.3x4.3=48.59
You watch your favorite tv show every night. each episode is 53 minutes long, and you watched 62 episodes. how many days of your life did you spend watching this show? hint: first multiply 53 x 62 to get the total number of minutes that you watch the show, then convert the minutes to days.
Answers
By multiplying the duration of each episode by the number of episodes watched and then converting minutes to days, we find that you spent around 2.285 days of your life watching your favorite TV show.
To calculate the total number of minutes spent watching the show, multiply the duration of each episode (53 minutes) by the number of episodes watched (62). This gives us 3296 minutes.
To convert minutes to days, divide the total number of minutes by the number of minutes in a day (1440 minutes).
3296 minutes / 1440 minutes per day = 2.285 days.
Therefore, you spent approximately 2.285 days of your life watching this show.
In conclusion, by multiplying the duration of each episode by the number of episodes watched and then converting minutes to days, we find that you spent around 2.285 days of your life watching your favorite TV show.
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Henry opens a savings account that has a 4.5% annual interest
rate. After 18 months, he receives $75,000. How much did he invest?
Show all work
Answers
Henry opens a savings account with an annual interest rate of 4.5 percent. After a year, he gets $75,000 in payment. He made a deposit into the savings account of $72,831.68.
Here are the steps on how to calculate the amount Henry invested:
Convert the annual interest rate to a monthly rate.
\(\begin{equation}4.5\% \div 12 = 0.375\%\end{equation}\)
Calculate the number of years.
\(\begin{equation}\frac{18 \text{ months}}{12 \text{ months/year}} = 1.5 \text{ years}\end{equation}\)
Use the compound interest formula to calculate the amount Henry invested.
\(\begin{equation}FV = PV * (1 + r)^t\end{equation}\)
where:
FV is the future value ($75,000)
PV is the present value (unknown)
r is the interest rate (0.375%)
t is the number of years (1.5 years)
\(\begin{equation}\$75,000 = PV \cdot (1 + 0.00375)^{1.5}\end{equation}\)
\$75,000 = PV * 1.0297
\(\begin{equation}PV = \frac{\$75,000}{1.0297}\end{equation}\)
PV = \$72,831.68
Therefore, Henry invested \$72,831.68 in the savings account.
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Phil and Meredith work for a book publisher editing mathematics textbooks. Phil has less experience and takes three times as long as Meredith to edit a textbook. Together, it takes them 15 hours to edit a textbook.
How long does it take Phil to edit a textbook if he works alone?
hours
How long does it take Meredith to edit a textbook if she works alone?
Answers
The number of hours taken by Meredith to edit a textbook if she works alone is 20 hours and time taken by Phil alone to edit text book is 60 hours..
Given that, Phil and Meredith work for a book publisher editing mathematics textbooks.
What is time and work?The basic concept of Time and Work is similar to that across all Arithmetic topics, i.e. the concept of Proportionality. Efficiency is inversely proportional to the Time taken when the amount of work done is constant.
Let the time taken by Meredith be x.
Phil has less experience and takes three times as long as Meredith to edit a textbook.
So, time taken by Phil be 3x.
Now, 1/x +1/3x =1/15
⇒ (3+1)/3x =1/15
⇒ 4/3x =1/15
⇒ 4/x =1/5
⇒ x=20 hours
So, time taken by Phil =3x =60 hours
Therefore, the number of hours are 60 hours.
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solve the linear equation 4x-(2x-1)=x+5+x-6
Answers
The linear equation doesn't have a solution.
How to compute the value?The linear equation given is illustrated as: 4x-(2x-1) = x+5+x-6
This will be solved thus:
4x - 2x + 1 = x+5+x-6
4x - 2x + 1 = 2x - 1.
2x + 1 = 2x - 1
Collect like terms
2x - 2x = -1 - 1
0 = -2
This illustrates that the equation doesn't have a solution.
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TEN POINTS!!!!! (41*31)^2 find the equivalent expression
Answers
Answer:
1615441
Step-by-step explanation:
Use BPEMDAS:
Multiply in the parenthesis 1st:
(1271)²
Then exponent:
1615441
Zane is mixing fruit punch in a 36-cup punch bowl for a party. He plans to add
at least 16 cups of fruit juice to the bowl before adding ginger ale.
Identify the graph that represents the amounts of fruit juice and ginger ale he
can use, and then identify a valid solution. (The graph shows the overlapping
solution region only, not the shading for each inequality.)
A. Valid solution: (20, 12)
B. Valid solution: (20,12)
C. Valid solution: (12,16)
D. Valid solution: (12,16)
Answers
Answer:
A (20,12) with the graph shown in example A here.
Step-by-step explanation:
He starts wtih 16 cups of fruit juice (x axis) and can UP TO 12 more of ginger ale, (going up the Y axis 12) for a total of 36. But he can pu in any number between 1-12 of gingerale, so the graph shown in A is correct. Also correct on A P E X.
The graph that represents the amounts of fruit juice and ginger ale he can use is A. Valid solution: (20, 12).
Calculations and ParametersA valid solution to the problem that Zane has about mixing fruit punch and fruit juice is given below:
On graph A, there is a valid solution of (20, 12) and this is because:
Zane began with 16 cups of fruit juice on the x-axis
He can add an additional 12 cups of ginger ale in the y-axis
The total would be 36 cups.
But, based on the fact that he can insert any number from 1-12 range of ginger ale, the graph in option A is correct as it shows the proper range on both the x and y-axis.
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