Find the orthogonal projection p of v = 6i + 5j + Ik on u = 31 + 10j + 2k. (Write your solution in terms of the standard basis vectors i, j, and k. Use symbolic notation and fractions where needed.) P = 354 113 + 1180 113 236 +
Answers
The given problem involves finding the orthogonal projection of a vector onto another vector.
The vector projection is a measure of how much of one vector lies in the direction of another vector, and it is defined as the scalar multiple of the second vector that points in the direction of the first vector. The orthogonal projection is the component of the first vector that is orthogonal (perpendicular) to the second vector. To find the orthogonal projection of a vector v onto a vector u, we need to first find the scalar projection of v onto u, which is the dot product of v and the unit vector in the direction of u.
We then multiply this scalar projection by the unit vector in the direction of u to obtain the vector projection of v onto u. Finally, we subtract this vector projection from v to obtain the orthogonal projection of v onto u. In this problem, we are given a specific vector v and vector u, and we are asked to find the orthogonal projection of v onto u.
By applying the formula for vector projection and subtracting it from v, we can obtain the orthogonal projection of v onto u. The concept of vector projection is an important tool in linear algebra and has many applications in physics, engineering, and other fields.
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Related Questions
A large box P containing 15 cans of biscuits weighs 23 kg and weighs 500g when empty. A box containing 8 cans of the same biscuits Q weighs 12.3kg. Box Q What is the mass when the box is empty?
Answers
Answer:
300 g
Step-by-step explanation:
weight of a can of biscuits= (23- 0.5)/15= 1.5 kg
weight of 8 cans= 1.5 * 8= 12 kg
mass of the empty box Q= 12.3- 12= 0.3 kg= 300 g
Answer:
300 g or 0.3 kg
Step-by-step explanation:
23 kg - 500g = 22.5 kg
each can of biscuits weighs 22.5 ÷ 15 = 1.5 kg
if the box Q weighs 12.3kg when there's 8 box of biscuits then
8 × 1.5 = 12 kg is the weight of biscuits and the remaining 300 g is box Q's weight
-2(3x - 1) <8 solve for the inequality
Answers
Answer:
x> - 1
Step-by-step explanation:
3x-1>-4
3x-1+1>-4+1
3x > -3
3x/3 > -3/3
which value of x is a solution to x³ = 216
A. 6
b.18
c.72
d.108
e.648
Answers
6•6•6
Three spheres each with charge Q uniformly distributed through its volume Rank the spheres according to the magnitude of the electric field they produced at point P (greatest firstl P (1) (2) (3) Select one: a. 3 > 2 > 1 b. all tie c. 1>2>3 d. 1 and 2 tie > 3 e. 2 > 3 >1
Answers
The correct ranking of the spheres according to the magnitude of the electric field they produce at point P (greatest first) is: 1 > 2 > 3. The answer is option C.
Since all three spheres have the same charge Q and radius, the magnitude of the electric field at point P due to each sphere is proportional to 1/d^2, where d is the distance between the center of the sphere and point P. Therefore, the sphere closest to point P will produce the greatest electric field at that point.
Assuming that the three spheres are arranged in a straight line with sphere 1 being the closest to point P and sphere 3 being the farthest, we can rank the spheres according to the magnitude of the electric field they produce at point P as follows:
Sphere 1 produces the greatest electric field at point P since it is the closest to it.
Sphere 2 produces the second greatest electric field at point P since it is farther away from point P than sphere 1 but closer than sphere 3.
Sphere 3 produces the smallest electric field at point P since it is the farthest from it.
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Given two end points A (3,-1) B (2,5 calculate the distance of the line and the midpoint of the line
Answers
The distance of the line is √17 and the midpoint of the line is ( 5/2 , 2).
Why do you use the word distance?
Distance is the total movement of an object without taking direction into account. Distance can be described as the amount of ground that an object has covered, regardless of its beginning or ending points.
points A (3,-1) B (2,5)
D = √(x₂ - x₁)² + (y₂ - y₁ )²
= √(2 - 3)² + ( 5- ( -1))²
= √(-1)² + (4)²
= √1 + 16
= √17
midpoint = x = 2 + 3/2
= 5/2
y = 5 - 1/2
y = 2
(x,y) = ( 5/2 , 2)
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when studying the relationship between test performance (exam score) and length of sleep (the night before), which type of hypothesis is being examined?
Answers
When studying the relationship between test performance (exam score) and length of sleep (the night before), here the true population correlation is being used.
Correlation:
Correlation analysis examines relationships between variables. The purpose of correlation analysis is to find out whether there are relationships between variables that are unlikely to be caused by sampling error. The null hypothesis states that there is no relationship between the two variables. Correlation analysis provides the following information:
Direction of relationship: positive or negative - indicated by the sign of the correlation coefficient.
Strength or magnitude of relationship between two variables - indicated by the correlation coefficient, which varies from 0 (no relationship between variables) to 1 (perfect relationship between variables).
Positive Correlation:
A positive correlation indicates that high scores for one variable are associated with high scores for the other variable. Low values of one variable are associated with low values of the second variable. For example, in the chart below, a higher score for negative impacts corresponds to a higher score for perceived stress.
Negative Correlation:
A negative correlation indicates that high values of one variable are associated with low values of the other variable. This graph shows that people with higher perceived stress scores are more likely to have lower proficiency scores. The slope of the graph decreases toward the right. In the chart below, the higher the mastery score, the lower the perceived stress score.
Strength or Magnitude of Relationship
The strength of a linear relationship between two variables is measured by a statistic known as the correlation coefficient, which varies between 0 and -1 and 0 and +1. There are some correlation coefficients. The most common are Pearson's r and Spearman's rho. The strength of the relationship is interpreted as follows.
Small/Weak: r= 0.10 to 0.29
Medium/Medium: r= 0.30 to 0.49
Large/Strong: r= 0.50 to 1
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HELP MEEEE!!!
The Travers are adding a new room to their house. The room will be a cube with volume 4,096 ft. They are going to put in hardwood floors, and the contractor charges $5 per
square foot. How much will the hardwood floors cost?
Answers
Answer:
4000!
Step-by-step explanation:
It would be 4000. Hope you get it right!
Find the product and the quotient.
1/3 x 1/6 =
1/6 dividend by 3 =
Answers
Answer:
1. 1/18
2.1/18
Step-by-step explanation:
In order to multiply fractions, you just multiply it straight out. Numerator to numerator, denominator to denominator.
1*1=1
6*3=18
So, the answer is 1/18.
To divide fractions, you flip the second number. If the number is 3, you flip the 3 to the denominator to make 1/3. Then, you multiply using the rule above.
1) Do the outcomes for spinning the spinner appear to be equally likely
based on the data in the table?
-)))
A)
B)
Yes, because all 6 sections are about equal.
D)
Yes, because there are 6 different sections.
C) No, because the observed frequencies are different.
No, because there are 6 different sections.
Answers
The spinner appear to be equally likely as all 6 sections are about equal.
What is probability?The probability of an event is a number that indicates how likely the event is to occur.
Given is a colored spinner as shown in the image.
Yes, the spinner appear to be equally likely, because the probability of landing on any of the shaded region is same for each band of color as they are divided equally on the spinner. This means that all 6 sections are about equal.
Therefore, the spinner appear to be equally likely as all 6 sections are about equal.
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A parallelogram has sides of length 4 m, 3 m, and 4 m.
What is the length of the fourth side of the parallelogram?
length of the fourth side = __ m
Answers
Answer:The length of the fourth side is 3m
Step-by-step explanation: look at the picture attached
Hellllpppppppp
10 pointssss
Answers
Answer:
A. 5.1
B. 0.96
C. 15
D. 8.3
Step-by-step explanation:
Solve. x/8 + 2 = 27
Answers
Multiply 8 to both sides:
x+16=216
Subtract 16 to both sides:
x=200
If you can help I would appreciate it, thank you
Answers
Answer:
.54b
Step-by-step explanation:
Answer:
b(0.54)
Hope this works for you! :)
Solve by elimination
3x-30=Y
7y-6=3x
Answers
The coefficients corresponding to k = 0, 1, 2, ..., 5 in the expansion of (x + y) 5
are
A. 1, 5, 10, 10, 5, 1
B. 0, 1, 5, 10, 5, 1,0
C. 1, 5, 10, 5, 1
D. 0,5, 10, 10,5, 0
Answers
Answer:
Step-by-step explanation:
1,5,10,10,5,1 - so your answer would be A
The coefficient corresponding to k = 0 of the binomial expansion ( x + y )⁵ is given by the order 1, 5, 10, 10, 5, 1
What is Binomial Expansion?The general term of the binomial expansion is Tr+1 = nCr x^n-r y^r . Here the coefficient values are found from the pascals triangle or using the combinations formula, and the sum of the exponents of both the terms in the general term is equal to n.
( x + y )ⁿ = ⁿCₐ ( x )ⁿ⁻ᵃ ( y )ᵃ
Given data ,
Let the binomial expansion be represented as A
Now , the value of A is
A = ( x + y )⁵ be equation (1)
On simplifying , we get
( x + y )ⁿ = ⁿCₐ ( x )ⁿ⁻ᵃ ( y )ᵃ
( x + y )⁵ = x⁵ + 5x⁴y + 10x³y² + 10x²y³ + 5xy⁴ + y⁵
Now , the coefficients of the expansion is given by
A = 1 , 5 , 10 , 10 , 5 , 1
Hence , the order of coefficients of the binomial expansion is 1 , 5 , 10 , 10 , 5 , 1
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I’ll mark u as brainlist if u get this right!!
Answers
Answer:
A
Step-by-step explanation:
When X is less than -1, positive parabola.
Someone please !!!!
Answers
Answer:
12.82
Step-by-step explanation:
Diameter is 3.5 so radius is 1.75
Formula for cone is\(\frac{\pi r^2h}{3}\)
using 3.14 as pi, 4 as h, and 1.75 as r you get 12.82
NEED HELP ASAP!!!
NO LINKS PLEASE!!
Answers
Answer: y=x-5
Step-by-step explanation:
The line crosses through the y axis at -5 so and the slope is 1 because it increase by 1 each time and runs by 1 unit each time.
In a double-slit experiment, bright interference fringes are spaced 1.8mm apart on the viewing screen when the incident light has a wavelength of 630 nm. What will the fringe spacing be if the light is changed to a wavelength of 420 nm
Answers
If the incident light changes from a wavelength of 630 nm to 420 nm, the fringe spacing will decrease, resulting in fringes that are closer together.
In a double-slit experiment, when light passes through two narrow slits and hits a viewing screen, interference patterns are observed. The fringe spacing, also known as the separation between adjacent bright fringes, is determined by the wavelength of the incident light. The formula for calculating fringe spacing is given by:
Fringe Spacing = (wavelength * distance from slits to screen) / distance between the slits
Given that the fringe spacing is initially 1.8 mm when the incident light has a wavelength of 630 nm, we can use the formula to calculate the new fringe spacing when the light wavelength changes to 420 nm. Since the distance from the slits to the screen and the distance between the slits remain constant, the only variable that changes is the wavelength. As the wavelength decreases, the fringe spacing will also decrease. Therefore, the fringe spacing will be smaller when the light wavelength is 420 nm compared to when it is 630 nm.
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What is the probability of choosing 3 or 4?
Answer:
Answers
1/2 because there are only 2 choices.
Find the volume of the composite solid below. If needed,round to the nearest hundredth. Use 3.14
Answers
Answer:
429.42 cm
Step-by-step explanation:
Volume of a rectangle prism:
V = whl
V = (5)(12)(7)
V = 420
Volume of a cylinder:
V = πr²h
V = (3.14)(1²)(3)
V = (3.14)(1)(3)
V = 9.42
Combined:
420 + 9.42
429.42
a pair of 6 sided dice are tossed. what is the probability that at least one of the dice has a value greater than or equal to 5?
Answers
The probability of rolling at least one die with a value greater than or equal to 5 when two 6-sided dice are tossed will be 11/36.
When two 6-sided dice are tossed, each die has six possible outcomes (numbers 1 to 6). To calculate the probability of at least one die having a value greater than or equal to 5, we need to consider the complementary event of both dice having a value less than 5.
The probability of a single die having a value less than 5 is 4/6 since there are four outcomes (1, 2, 3, 4) out of six that satisfy this condition. As the dice are independent, we multiply the probabilities of both dice having values less than 5: (4/6) * (4/6) = 16/36.
Now, to find the probability of at least one die having a value greater than or equal to 5, we subtract the probability of both dice having values less than 5 from 1: 1 - 16/36 = 20/36 =11/36 (which is 5/9 when simplified).
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How many time does 5 go into 73.
Answers
Answer:
14 times
Step-by-step explanation:
Divide 73 by 5
Calculate your answer
A bag holds 20 jelly beans: 5 red, 10 green, 4 blue, and 1 black. What is the probability of choosing two consecutive blue jelly beans without replacement
Answers
Answer:
10/20 for green, then 4/19 for blue. 10/20 * 4/19 = 2/19
Step-by-step explanation:
Explanation is above. If you need any more help let me know.
Which expressions are equivalent to 7×7×7×7×7×7 choose two answers:
Answers
Answer:
7^6 =A, C
Step-by-step explanation:
The expression equivalent to the 7×7×7×7×7×7 will be 7⁸/7² and (7²)³ thus option (A) and (C) is correct.
What is an expression?A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
An expression is a mathematical proof of the equality of two mathematical expressions.
A statement expressing the equality of two mathematical expressions is known as an equation.
As per the given expression,
7×7×7×7×7×7 = 7⁶
Now, in option (A),
7⁸/7² = 7⁸ ⁻ ² = 7⁶
In option (C)
(7²)³ = 7² ˣ ³ = 7⁶
Hence "The expression equivalent to the 7×7×7×7×7×7 will be 7⁸/7² and (7²)³".
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What type of survey is utilized to determine the extent of problems in a certain area and then express the findings as rates affected within the population
Answers
The type of survey that is utilized to determine the extent of problems in a certain area and then express the findings as rates affected within the population is known as an epidemiological survey.
What is an epidemiological survey?
An epidemiological survey is a type of survey used to understand the prevalence and incidence of particular health problems in a particular population. In addition, epidemiological surveys are utilized to determine the causes, transmission, and treatment of these problems.
Epidemiological studies are classified according to the types of questions that they are designed to answer. They are as follows:
Descriptive studies: These studies describe the incidence, prevalence, and distribution of diseases in populations.
Analytical studies: These studies are concerned with determining the causative factors of diseases in populations.
Experimental studies: These studies determine the efficacy and safety of new treatments for diseases.
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The diagram shows an open rectangular box ABCDEFGH.
A straight stick AGM rests against A and G and extends outside the box to M.
a. Calculate the angle between the stick and the base of the box.
b. AM= 30 cm.
Show that GM= 4.8 cm, correct
to 1 decimal place.
Answers
The angle between the stick and the base of the box is 77. 9 degrees
How to determine the angleTo determine the angle between the stick and the base, we have to know the trigonometric identities.
These identities are;
sinecosinecotangenttangentsecantcosecantFrom the information given, we have;
sin A = FB/AB
Given that;
GB = 14.5cm
AB = 18. 6cm
substitute for the length of the sides, we have;
sin A = 14.5/18. 6
Divide the values, we have;
sin A = 0. 7796
Find the inverse sine
A = 77. 9 degrees
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How many square inches of fabric does Kendall need for a triangle flag with a base of 20 inches a height of 40 inches
Answers
Answer: \(400^{2}\)
Step-by-step explanation:
First, write the formula:
A = (b × h) / 2
Next, multiply the base and the height of the triangle.
20 x 40 = 800
Finally, divide 800 by 2.
800/2=400
Therefore, the answer is \(400^{2}\).
Cindy went to a candy store today. She was looking to get a whole bunch of candy. Her two favorite candies are chocolate bars and ta1ffy. A chocolate bar costs a dollar each, whereas taffy costs 50 cents. Cindy brought $15 to the Candy store and wants to spend all of it. Please write an equation for the amount of taffy and chocolate bars that Cindy might have bought. Let c represent number of chocolate bars and t represent pieces of taffy.
Answers
Answer:
14c + 2t
Step-by-step explanation:
As one chocolate bar costs 1 dollar, 14c is $14.
One taffy costs 50 cents, which is half of a dollar, so 2t = $1.
14 + 1 = 15.
:)
For a standard normal random variable, what z-score has(a) probability 0.225 to the right?(b) probability 0.900 to the left?
Answers
The z-score with probability 0.225 to the right is 0.15 and the z-score with probability 0.900 to the left is -1.28. This can be calculated using the Z-score table for a standard normal distribution.
(a) Probability 0.225 to the right is equal to z-score 0.15.
This can be calculated using the Z-score table for a standard normal distribution.
The probability to the right of z-score is equal to the cumulative probability of the z-score.
The cumulative probability of 0.15 is 0.225, which is the probability to the right.
(b) Probability 0.900 to the left is equal to z-score -1.28.
This can be calculated using the Z-score table for a standard normal distribution.
The probability to the left of z-score is equal to the cumulative probability of the z-score.
The cumulative probability of -1.28 is 0.900, which is the probability to the left.
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