. use implicit function theorem to verify whether the relation x y 2 cos(x − y) = c defines an implicit solution of the differential equation
Yes, the relation x y 2 cos(x − y) = c defines an implicit solution of the differential equation.
To verify this we can use Implicit Function Theorem. According to the theorem, if a relation f(x,y) = c is given, then if the partial derivative of f(x,y) concerning y is nonzero at the point (x0,y0), there is a unique function y = g(x) such that f(x,g(x)) = c.
In this case, the partial derivative of f(x,y) concerning y is -2 sin(x-y). At the point (x0,y0), this derivative is nonzero, so there exists a unique function y = g(x) such that f(x,g(x)) = c. This implies that the given relation does indeed define an implicit solution of the differential equation.
To learn more about the differential equation, visit:
brainly.com/question/16663279
#SPJ4
PLEASE HELP ME WITH THESE QUESTIONS IM SO DESPERATE
WILL GIVE BRAINLIEST
Answer:
11.55m², 181.12mm²,11ft,
Step-by-step explanation:
Simplify the expression.
and multiply A=1/2bh
PROOF Complete the proof.
Given BC AD, BCLDC, ADL DC
Prove ABCD is a rectangle.
A
B
D
C
In algebra, a number exists even equal to itself according to the reflexive property of equality. The equality's reflexive quality. If a is a number, then. a = a.
What is meant by Reflexive Property?In algebra, a number is always equal to itself according to the reflexive property of equality. The equality's reflexive quality. If a is a number, then. a = a.
2. AD = BC due to the congruence of a rectangle's opposite sides.
3. Due to the reflexive property of congruence, DC=DC, each segment is identical to itself.
4. ADC and BCD are right angles since any rectangle's internal angles are right angles (Definition of rectangle).
5. Since they form right angles and all right angles are congruent, ADC=BCD.
6. ADC and BCD are congruent because they have two congruent sides (AD with BC and DC with DC) and a congruent angle between them: Side Angle Postulate Side Congruence Postulate (SAS Congruence Postulate).
7. AC must match BD because Congruent Parts in Congruent Triangles must match (CPCTC).
Statement Reason
1. Rectangle ABCD Given
2. AD=BC Opposite sides of a rectangle are congruent
3. DC=DC Reflexive Property of Congruence
4. <ADC and <BCD are Definition of rectangle
right angles
5. <ADC=<BCD All right angles are congruent
6. ∆ADC=∆BCD SAS Congruence Postulate
7. AC=BD CPCTC
To learn more about Reflexive Property refer to:
https://brainly.com/question/8741371
#SPJ1
Find the indicated measure.
Using the inscribed angle theorem:
7. m<A = 79°
8. m<B = 90°
9. m(BC) = 152°
What is the Inscribed Angle Theorem?The Inscribed Angle Theorem states that if two chords of a circle intersect, the measure of the inscribed angle formed by the two chords is equal to half the measure of the central angle that subtends the same arc as the inscribed angle.
Applying the inscribed angle theorem, we have:
7. m<A = 1/2(158)
m<A = 79°
8. m<B = 1/2(180)
m<B = 90°
9. m(BC) = 2(76)
m(BC) = 152°
Learn more about the inscribed angle theorem on:
https://brainly.com/question/3538263
#SPJ1
two telephone calls come into a switchboard at random times in a fixed one-hour period. assume that the calls are made independently of one another. (a) what is the probability that the calls are made in the first quarter hour? 1/16 correct: your answer is correct. (b) what is the probability that the calls are made within six minutes of each other? (round your answer to four decimal places.)
The probability of two calls to be made in first quarter = 15/60 * (15/60) = 1/16
Probability of a call to happen within 6 minutes within each other is 6/60 = 1/10 = 0.1
What is Probability ?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
A statistical function known as a probability distribution explains all the potential values and probabilities for a random variable within a certain range.
The uniform probability distribution is a distribution composed by two bounds, given by a and b, in which each possible outcome within these two bounds is equally as likely.
The probability that a call is made in the first quarter is 15/60
Now the probability of two calls to be made in first quarter = 15/60 * (15/60) = 1/16
Probability of a call to happen within 6 minutes within each other is 6/60 = 1/10 = 0.1
To learn more about Probability refer to :
https://brainly.com/question/29483317
#SPJ4
a sample of n = 9 scores has a variance of s2 = 18. if the scores were a population, what value would be obtained for the population variance?
Value 02 = 16 represents the population variance.
What is meant by value?The value describes the value of each digit in relation to its position in the number. The place value and face value of the digit are multiplied to arrive at the answer. Value equals Place Value minus Face Value. Value is concerned with how much something is worth, whether in monetary terms or in terms of significance. It can mean "identify how much something is worth" like a reward valued at $200 or it can indicate "hold something in high esteem" like "I value our friendship."The occurrence of two complete sets of tens gives the number 24 its place value of two.To learn more about value, refer to:
https://brainly.com/question/843074
#SPJ4
greatest common factor for 90 and 80
Answer:
10
Step-by-step explanation:
The GCF of 80 and 90 is 10.
: Can you find any relation between the number of ide, edge and
vertice in each hape? What i the relation? What i the formula and what i it known a?
The relation between the number of ide, edge, and vertice in each shape Euler’s Formula for Polyhedron.
Polyhedron Euler's Formula
One of the most significant mathematical theorems, the Euler theorem is named Leonhard Euler and is widely recognized as such.
The link between a polyhedron's face, vertex, and edge counts is stated in the theorem.
F + V = E + 2 is the formula for Euler's equation, where F is the number of faces, V is the number of vertices, and E is the number of edges.
According to Euler's formula, many solid shapes have a number of faces plus vertices plus vertices minus vertices equal to two.
Know more about Euler’s Formula for Polyhedron
https://brainly.com/question/27782111
#SPJ4
A charitable organization in Oxford i hoting a black tie benefit for charity and the organization member hope to bring in at leat $1,200 tandard ticket are available for 21 each wherea vip ticket are offered for 43 a piece
To reach the goal of $1,200, the organization needs to sell at least 28 standard tickets (1,200 / 42 = 28.57) or 28 VIP tickets (1,200 / 43 = 27.91). They can also combine the sales of standard and VIP tickets to reach the goal.
The charitable organization is hosting a black-tie benefit event and aims to raise at least $1,200 through ticket sales.
The standard tickets are priced at $21 each, while the VIP tickets are priced at $43 each.
To reach the goal of $1,200, the organization needs to sell a minimum of 28 standard tickets ($1,200 / $21 = 57.14).
However, if they only sell VIP tickets, they will need to sell at least 28 VIP tickets ($1,200 / $43 = 27.91).
Finally, they can also achieve their goal by selling a combination of standard and VIP tickets.
For example, they can sell 20 standard tickets and 8 VIP tickets, which would result in a total of 20 * $21 + 8 * $43 = $840 + $344 = $1,184, reaching their goal of $1,200.
In conclusion, the charitable organization has multiple options to reach their goal of $1,200 through ticket sales for their black-tie benefit event.
To know more about Calculations
https://brainly.com/question/26046491
#SPJ4
Use the distributive property to write an expression that is equivalent to 5(- 2x - 3)
Answer: -10x - 15
Step-by-step explanation:
The distributive property is used when you multiply a number over an addition or subtraction problem.
5 x (-2x - 3)
Step 1
Take 5 and multiply it by -2x
5 x -2x = -10x
Step 2
Take 5 and multiply it by - 3
5 x - 3 = -15
Step 3
Put the entire problem together.
5 x (-2x - 3) = -10x - 15
Simplify 3/7 =7^1/3.
The cube root of a cube of the number is the same number for any number. Thus, option A is the answer.
In the given question,
[tex]\sqrt[3]{7} = 7^{1/3} \\[/tex]
We have to prove L.H.S = R.H.S
Let's take R.H.S
= [tex]7^{1/3}\\[/tex]
Taking a cube for this,
[tex]= (7^{1/3} )^{3}[/tex]
We can separate this into three terms.
[tex]= 7^{1/3} . 7^{1/3} . 7^{1/3}[/tex]
We know that [tex]x^{n}. x^{m} = x^{n+m}[/tex]
Then,
[tex]= 7^{1/3 + 1/3 +1/3} \\= 7^{3/3}\\ = 7[/tex]
From L.H.S
We have to take cube root,
[tex](\sqrt[3]{7})^{3} \\= 7[/tex]
Hence, L.H.S = R.H.S, and it is verified.
To learn more about the cube roots,
https://brainly.com/question/15968618
You roll a 6-sided die two times. What is the probability of rolling a number less than 4 and then rolling a number greater than 3? Write your answer as a percentage%.
Answer:
Step-by-step explanation:
3/6
In 2015, the per capita consumption of bottled water in the United States was reported to be 36.2 gallons. Assume that the per capita consumption of bottled water in the U.S. is approximately normally-distributed with a standard deviation of 10 gallons.
Find the Z-score of someone who consumed 26.2 gallons of water. Using the Empirical Rule, what is the approximate probability that someone in the United States consumed less than 26.2 gallons of water, what is the approximate probability that someone in the United States consumed between 26.2 and 36.2 gallons of water, and what is the approximate probability that someone in the United States consumed between 26.2 and 46.2 gallons of water?
The required probabilities = 0.16
The required probabilities = 0.68
What is z-score?The Z-score quantifies the discrepancy between a given value and the standard deviation. The Z-score, also known as the standard score, indicates how many standard deviations a specific data point deviates from the mean. In essence, standard deviation represents the degree of variability present in a particular data collection.
As given that,
μ = 36.2
σ = 10
As per empirical Rule:
μ± σ = 36.2 ±10 = 26.2, 46.2 = 68%
μ± 2σ = 36.2 ±20 = 16.2, 56.2 = 95%
μ ± 3σ = 36.2 ±30 = 6.2, 66.2 = 99.7%
less than 26.2:
13.5% + 2.35% + 0.15% = 0.16
between 26.2 and 36.2:
68% = 0.68
The required probabilities = 0.16
The required probabilities = 0.68
To know more about probabilities refer to:
https://brainly.com/question/24756209
#SPJ4
Research On effects of poor scale Interpration in maths
The effects of poor scale interpretation in maths are discussed below.
What are the effects of poor scale Interpretation in maths?Poor scale interpretation in mathematics can have significant effects on various areas of life and work that require the use of mathematical concepts and skills. Some of the consequences of poor scale interpretation are:
1. Inaccurate Results: Poor interpretation of scales on graphs, charts, and other mathematical representations can lead to incorrect conclusions and decisions based on the resulting data.
2. Miscommunication: Poor scale interpretation can result in misinterpretation of information and lead to miscommunication between individuals and groups.
3. Ineffective Problem Solving: Poor scale interpretation can hinder the ability to solve mathematical problems effectively, resulting in incorrect solutions and wasted time and resources.
4. Limited Career Opportunities: Poor scale interpretation skills can limit career opportunities in fields that require mathematical proficiency, such as engineering, finance, and technology.
5. Low Confidence and Motivation: Poor scale interpretation skills can lead to frustration and low confidence in mathematics, causing students and individuals to lose interest in the subject.
To avoid the negative effects of poor scale interpretation, it is important to receive proper mathematical education and training, and to continually practice and improve one's mathematical skills. Additionally, seeking help and guidance from teachers and mentors can be beneficial in improving one's scale interpretation skills.
Learn more about poor scale interpretation on:
brainly.com/question/27178197
#SPJ1
anderson and addison leave from the same restaurant and the same time, traveling in opposite directions. if anderson travels 15 mph and addison travels 6 mph, how long until they are 126 miles apart?
After 6 hours, Anderson and Addison will be 126 miles apart.
Let's call the time they have been traveling "t" (in hours).
Anderson will have traveled 15t miles and Addison will have traveled 6t miles. The total distance between them is 15t + 6t = 21t miles.
We know that they need to be 126 miles apart, so we can set up the equation:
21t = 126
Now we can solve for t:
t = 126 / 21
t = 6
So after 6 hours, they both will be 126 miles apart.
You can learn more about distance at
https://brainly.com/question/26550516
#SPJ4
$122.62-$lal
5.) On February 3rd, Cardi B borrowed $17,500.00 at 6.5% exact interest to buy a new car. She had to pay back
a maturity value of $17,873.97 to pay off the loan. On what day did Cardi pay back the loan?
has a 10.3% ordinary
The day that Cardi B paid back the loan is given as follows:
June 3rd.
How to obtain the balance using simple interest?The balance of an account after t years, using simple interest, that is, a single compounding per year, is given by the equation presented as follows:
A(t) = P(1 + rt).
In which the parameters of the equation are explained as follows:
P is the value of the initial deposit.r is the interest rate, as a decimal.The parameter values for this problem are given as follows:
A = 17873.97, P = 17500, r = 0.065.
Hence the time in years is obtained as follows:
17873.97 = 17500(1 + 0.065t)
1 + 0.065t = 17873.97/17500
1 + 0.065t = 1.02136971429
t = (1.02136971429 - 1)/0.065
t = 0.32876483523
A year is composed by 365 days, hence the time in days is given as follows:
0.32876483523 x 365 = 120 days.
120 days after February 3rd is June 3rd.
More can be learned about simple interest at https://brainly.com/question/20690803
#SPJ1
Solve by graphing
4x - 4y = 22
y = -5.5
The system of equations has a unique solution. The solution is (0,-5.5).
What is the system of equations?
A system of equations in algebra consists of two or more equations and looks for common answers to the equations. "A set of equations satisfied by the same set of variables is called a system of linear equations."
According to the discussion above, a system of equations is a collection of equations that aim to find a common solution for all of the variables.
The system of equations is
4x - 4y = 22 ....(i)
y = -5.5 ...(ii)
Putting x = 0 in 4x - 4y = 22:
4 × 0 - 4y = 22
- 4y = 22
y = -5.5
Putting x = 1 in 4x - 4y = 22:
4 × 1 - 4y = 22
- 4y = 18
y = -4.5
The points on equation (i) are (0,-5.5) and (1, -4.5).
The points on the line y = -5.5 are (-3,-5.5), (2,-5.5).
Plot the points and join them.
The intersection point is the solution of the system of equations.
The solution is x = 0 and y = -5.5
To learn more about the graphing solutions, click on the below link:
https://brainly.com/question/13677313
#SPJ1
Help me because why is math so hard now
Answer:
Step-by-step explanation:
The answer will be the third one because 2/3 * (3/10 X 1) is the same as 2/3 already being multiplied to 3/10.
If you use a calculator and put 2/3 * (3/10 X 1), you will get 0.2 and if you put (2/3 * 3/10) x 1 you will also 0.2.
So (2/3 * 3/10) x 1 is equal to 2/3 * (3/10 X 1)
Lat week, Toby bought 11 book and 8 movie for a total of $207. Today, Toby bought 16 book and 9 movie for a total of $280. Auming neither item ha changed in price, what i the cot of a book in dollar?
Last week, Toby bought 11 book and 8 movie for a total of $207. Today, Toby bought 16 book and 9 movie for a total of $280 the cost of book is 13$.
Toby bought 11 book and 8 movie for a total of $207 so,
11B + 8M = 207
Today, Toby bought 16 book and 9 movie for a total of $280 so,
16B + 9M = 280
Solving equations simultaneously we get,
11B + 8M = 207
16B + 9M = 280
99B = 1863
B = $13
So, the cost of a book in dollar is $13.
Cost price is the complete sum of money that a manufacturer must spend to create a specific good or render a specific service.
Lear more about Cost related problem :
https://brainly.com/question/12912968
#SPJ4
Water flows at a speed of 20 cm/s along a rectangular channel into a lake. The width of the channel is 15 cm, the depth of the water is 2.5 cm. Calculate the amount of water that flows from the channel into the lake in 1 hour. Give your answer in litres.
Answer is 2.7 million liters/hour
What is speed?
Speed tells us how fast something or someone is travelling.
The flow rate of water can be calculated as the cross-sectional area of the channel multiplied by the speed of the water.
The cross-sectional area of the channel can be calculated as width x depth = 15 cm x 2.5 cm = 37.5 cm^2
The flow rate of water can be calculated as 37.5 cm^2 x 20 cm/s = 750 cm^3/s
To convert this to liters, we need to multiply by 1000 to convert cubic centimeters to cubic centimeters:
750 cm^3/s x (1000 cm^3/L) = 750 L/s
Finally, to find the amount of water that flows into the lake in 1 hour, we need to multiply the flow rate by the number of seconds in an hour:
750 L/s x (3600 s/hr) = 2700000 L/hr = 2.7 million liters/hour.
Learn more about multiplied here : brainly.com/question/1076137
#SPJ1
72% it goes down by 20% what is the original price of the jacket
Answer:
4x/5
Step-by-step explanation:
the price of the jacket before goes down = x
20/100*x = x/5
the original price of the jacket= x-(x/5) = 4x/5
An iterative formula is shown below.
Xn+1 = 3/4xn-1
Work out the values of x2, x3 and x4, starting
with x1 = 2.
Give your answers to 2 d.p.
The value for the following order of the given iterative formula of xₙ + 1 = 3/4 xₙ₋₁ are:
x₂ = 0.5x₃ = - 0.63x₄ = - 1.47Iterative formula is used to process a repeating procedure to produce a series of results
We have an iterative formula of:
xₙ + 1 = 3/4 xₙ₋₁
We know that:
x₁ = 2
Hence:
x₂ + 1 = 3/4 x₁
x₂ + 1 = 3/4 (2)
x₂ + 1 = 3/2
x₂ = 1/2 = 0.5
x₃ + 1 = 3/4 x₂
x₃ + 1 = 3/4 (1/2)
x₃ + 1 = 3/8
x₃ = -5/8 = - 0.63
x₄ + 1 = 3/4 x₃
x₄ + 1 = 3/4 (-5/8)
x₄ + 1 = -15/32
x₄ = - 47/32 = -1.47
Learn more about Iterative Formula here: brainly.com/question/27751920
#SPJ1
15 POINTS! WILL MARK BRAINLIEST
If f(x) and g(x) are inverse functions, use the information shown to find g(x)
f(2x - 10) = x + 1
f(-10) = 1
f(-12) = 0
f(2x - 12) = x
Answer Choices:
g(x) = -12
g(x) = 2x - 10
g(x) = -10
g(x) = 2x - 12
The function g(x) is defined as follows:
g(x) = 2x - 12.
How to obtain the inverse function?The inverse function is obtained exchanging the variables x and y, and then isolating y, thus:
The fact that the variables are exchanged means that the functions are symmetric over the line y = x.
As the lines are symmetric over the line y = x, these following statements regarding the composition of a function with it's inverse is given as follows:
f(g(x)) = x.g(f(x)) = x.We have that f(2x - 12) = x, hence the function g(x) is defined as follows:
g(x) = 2x - 12.
More can be learned about inverse functions at brainly.com/question/3831584
#SPJ1
Categorize these measurements associated with student life according to level: nominal, ordinal, interval, or ratio. (a) Length of time to complete an exam (b) Time of fi rst class (c) Major field of study (d) Course evaluation scale: poor, acceptable, good (e) Score on last exam (based on 100 possible points) (f) Age of student
The measurements associated with student life are categorized as follows: length of time to complete an exam is a ratio, time of first class is an interval, major field of study is nominal, course evaluation scale is ordinal, score on last exam is a ratio, and age of student is a ratio.
(a) Length of time to complete an exam - Ratio: This is measured on a scale of time, and can be expressed as a ratio (i.e. the amount of time spent on the exam divided by the total time allotted for the exam).
(b) Time of first class - Interval: The time of the first class is measured on a scale of minutes, hours, and days, and can be expressed as an interval (i.e. the amount of time between two classes).
(c) Major field of study - Nominal: This is a categorical measurement and can be expressed as a nominal variable (i.e. the student's major field of study is either engineering, business, etc).
(d) Course evaluation scale: poor, acceptable, good - Ordinal: This is a scale of quality and can be expressed as an ordinal variable (i.e. the quality of the course can be rated as poor, acceptable, or good).
(e) Score on last exam (based on 100 possible points) - Ratio: This is measured on a scale of points, and can be expressed as a ratio (i.e. the student's score on the exam divided by the total number of points possible).
(f) Age of student - Ratio: This is measured on a scale of years, and can be expressed as a ratio (i.e. the student's age divided by the total number of years they have been alive).
The measurements associated with student life are categorized as follows: length of time to complete an exam is a ratio, time of first class is an interval, major field of study is nominal, course evaluation scale is ordinal, score on last exam is a ratio, and age of student is a ratio.
Learn more about measurement here:
https://brainly.com/question/29178095
#SPJ4
Please help !,,,!,!,,!,,,meeee long division step by step
What is 65 Inches in Feet?
When 65 inches are converted to feet, the result is 5.41667 feet.
How do I convert an inch to a foot?To convert 65 inches to feet, divide 65 by 12.We can calculate 65 inches equals 5.41667 feet using a calculator or long division. As a result, 65 inches is equivalent to 5.41667 feet. It is important to note that inches and feet are both length units, so converting between the two involves moving the decimal point in the number two places to the left or right, depending on which unit you are converting to.Divide the number of inches by 12 to convert to feet, because a foot is 12 inches long. Similarly, multiply the number of feet by the number of inches.As a result, 65 inches equals 5.41667 feet, and you can convert inches to feet by dividing the number of inches by 12.To learn more about inches refer to :
brainly.com/question/30403115
#SPJ4
Arnold is drawing another part of his blueprint. He draws a line that is 1/8 an inch and then draws another line next to it that is 14 of an inch. How long is this line Arnold has drawn?Arnold is drawing another part of his blueprint. He draws a line that is 1/8 an inch and then draws another line next to it that is 1/4 of an inch. How long is this line Arnold has drawn?
The length of the new line is twice the length of the old line and total length is given by the equation L = (3/8 ) of an inch
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the length of the old line be A
Now , the value of A = 1/8 of an inch
Let the length of the new line be B
Now , the value of B = 1/4 of an inch
So , the equation will be
The number of times the new line is greater than old line is given by
B / A = x
Substituting the values in the equation , we get
x = ( 1/4 ) / ( 1/8 )
x = 8/4
x = 2 times
So , the total length of the line = A + B
Substituting the values in the equation , we get
The total length of the line L = ( 1/4 ) + ( 1/8 )
The total length of the line L = 3/8 of an inch
Hence , the equation is L = (3/8 ) of an inch
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ1
Suppose that y(t) solves the ordinary differential equation
dy/dt = (4-3Y)/(5+2Y) Y(0)=0 Find d2y/dt2 (0)
To find the second derivative of y(t) at t = 0, we can use the chain rule. We can write the given equation as dy/dt = f(y), where f(y) = (4-3y)/(5+2y).
Then the second derivative of y at t = 0 can be calculated as: d2y/dt2 (0) = f'(y) * dy/dt (0) = f'(0)f(0) = [-3/(5+20)](4-30)/(5+2*0) = -3/5.
A differential equation is an equation that relates one or more unknown functions and their derivatives. It is mainly used in the fields of biology, physics, engineering, economics, and other sciences.
A differential equation states how a rate of change (a "differential") in one variable is related to other variables. For example, the Single Spring simulation involves a differential equation that describes the displacement of a spring in response to a force.
Learn more about differential equation:
https://brainly.com/question/1164377
#SPJ4
Which of the following statements is TRUE about the value of a college degree?
O A high school graduate can expect to earn about the same as a college graduate
• Every college graduate can expect to have a starting salary over $60,000 right after college
• A college graduate can expect to earn, on average, more than a high school graduate over a career
• A college graduate typically earns less than someone with a high school diploma for the first 10 years
Over the course of a career, a college graduate can anticipate making, on average, $60,000 more money than a high school graduate.
what is proportionality ?Links are regarded to as appropriate when they typically have the same ratio. For instance, the trees in an estate and or the number of peaches in a harvest in apples depend on the average number of apples provided by each tree. A linear correlation between two numbers as well as variables is referred to as being proportional in mathematics. When the primary quantity doubles, the other amount also does so. Once one of the variables is reduced to 1/100th of its previous value, the other decreases as well. If two components are proportional, it suggests that if one rises, the other climbs as well, and their correlation is continuous at all values. The diameter and circumference of such a circle are used as an example.
given
The true statement is
starting salary = $60,000
average = $60,000 / 3
= $ 20,000
Over the course of a career, a college graduate can anticipate making, on average, $60,000 more money than a high school graduate.
To know more about proportionality visit:
https://brainly.com/question/29126727
#SPJ1
find a · b. a = 4, 1, 1 3 , b = 8, −3, −9
The dot product of a.b is 20.
What is the dot product?
The dot product (also called scalar product or inner product) of two vectors a and b in a Euclidean space is a scalar value that represents the projection of one vector onto the other and the cosine of the angle between them. The dot product of two vectors a and b is defined as:
a · b = ||a||||b||cos(θ) = a1b1 + a2b2 + ... + anbn
where a = (a1, a2, ..., an) and b = (b1, b2, ..., bn) are the components of the vectors and θ is the angle between the vectors.
Finding a · b:
Given a = (4, 1, 1) and b = (8, -3, -9), we can calculate the dot product as:
a · b = 4 * 8 + 1 * -3 + 1 * -9 = 32 - 3 - 9 = 20
Hence, the dot product of a.b is 20.
To learn more about the dot product, visit:
https://brainly.com/question/26726614
#SPJ4