Answers
Let's first understand what's relative here, it refers to Point of reference , the point, in respect to which other's position are to be considered, which here is O, the Origin with coordinates (0,0) as we are talking about two-dimensional reference frame. What position vector means? Say, we have the point of Reference X, and we've the position vector of Y with respect to X, then it can be written as [tex]{\overrightarrow{XY}}[/tex]. Now, using this simple rule we can have,
[tex]{\overrightarrow{OA}=-2\hat{i}+7\hat{j}}[/tex][tex]{\overrightarrow{OB}=2\hat{i}-\hat{j}}[/tex][tex]{\overrightarrow{OC}=6\hat{i}+\lambda \hat{j}}[/tex]Now, let's calculate [tex]{\overrightarrow{AC}}[/tex] firstly;
[tex]{:\implies \overrightarrow{AC}=\overrightarrow{OC}-\overrightarrow{OA}}[/tex]
[tex]{:\implies \overrightarrow{AC}=8\hat{i}+(\lambda -7)\hat{j}}[/tex]
Now, here [tex]{AC}[/tex] just means the the magnitude of the vector [tex{\overrightarow{AC}}[/tex], and we're aware that magnitude of a vector [tex]{\overrightarrow{X}=x\hat{i}+y\hat{j}}[/tex] is given by, [tex]{X=\sqrt{x^{2}+y^{2}}}[/tex], so according to question;
[tex]{:\implies \sqrt{64+(\lambda -7)^{2}}=17}[/tex]
Squaring both sides;
[tex]{:\implies (\lambda -7)^{2}=289-64=225}[/tex]
[tex]{:\implies \lambda -7=\pm 15}[/tex]
[tex]{:\implies \boxed{\underline{\bf{\lambda =22,\:or\:-8}}}}[/tex]
Related Questions
2
1²/
3
in all did Jane study for the two tests?
Last weekend Jane studied 4
x
x
3
A 8-2-201
8-hours
7
3
8- hours
4
B 8
C 911212
с
hours
11
D
8 hours
12
1 of 5
08:14
1
hours for her history final and 4
hours for her math exam. How many hours
4
Ne
Answers
The total number of hours that Jane studied for her two tests were 8 ¹¹ / ₁₂ hours
How to find the number of hours ?To find the number of hours that Jane studied, you first need to convert the hours studied for history and math, from mixed fractions to improper fractions.
4 ² / ₃ hours :
= ( 4 x 3 + 2 ) / 3
= 14 / 3 hours
4 ¹ / ₄ hours :
= ( 4 x 4 + 1 ) / 4
= 17 / 4 hours
Add up both hours by using a common denominator of 12 :
= ( ( ( 12 / 4 ) x 17 ) + ( ( 12 / 3 ) x 14 ) ) / 12
= ( 51 + 56 ) / 12
= 8 ¹¹ / ₁₂ hours
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The full question is:
Last weekend Jane studied 4 2 3 hours for her history final and 4 1 4 hours for her math exam. How many hours in all did Jane study for the two tests?
show that the wave function y=e^(b(x-vt)) is a solution of the linear wave equation (eq. 16.27), where b is a constant
Answers
To show that the wave function y=e^(b(x-vt)) is a solution of the linear wave equation (eq. 16.27), we need to plug the wave function into the equation and see if it satisfies the equation.
The linear wave equation (eq. 16.27) is given by:
∂^2y/∂x^2 = (1/v^2) ∂^2y/∂t^2
Plugging in the wave function y=e^(b(x-vt)) into the equation, we get:
∂^2(e^(b(x-vt)))/∂x^2 = (1/v^2) ∂^2(e^(b(x-vt)))/∂t^2
Taking the second derivative with respect to x, we get:
b^2 e^(b(x-vt)) = (1/v^2) ∂^2(e^(b(x-vt)))/∂t^2
Taking the second derivative with respect to t, we get:
b^2 e^(b(x-vt)) = (1/v^2) b^2 v^2 e^(b(x-vt))
Simplifying, we get:
b^2 e^(b(x-vt)) = b^2 e^(b(x-vt))
This shows that the wave function y=e^(b(x-vt)) satisfies the linear wave equation (eq. 16.27) and is therefore a solution of the equation.
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5. Pilihan ganda5 menit1 ptQ. An equilateral triangle has an altitude of 15 m. What is the perimeter of the triangle? Leave your answer in radical form.Pilihan jawaban30√3 m10√3 m5√3 m30 m
Answers
If an equilateral triangle has an altitude of 15 meters, then the perimeter of the equilateral triangle is 30[tex]\sqrt{3}[/tex] meters
The altitude of the equilateral triangle = 15 meters
The equilateral triangle is the triangle with equal side. The interior angle of the equilateral triangle will be 60 degrees. Number of vertices and edges will be three . The line of symmetry is 3
The altitude of of the equilateral triangle h = [tex]\sqrt{3}[/tex]a /2
Where h is the altitude of the equilateral triangle
a is the side of the equilateral triangle
Then the equation will become
15 = [tex]\sqrt{3}[/tex] a /2
[tex]\sqrt{3}[/tex]a = 15 × 2
Multiply the terms
[tex]\sqrt{3}[/tex]a = 30
Move [tex]\sqrt{3}[/tex] to the right hand side of the equation
a = 30 / [tex]\sqrt{3}[/tex]
a = 10[tex]\sqrt{3}[/tex] meters
The perimeter of the equilateral triangle = 3 × 10[tex]\sqrt{3}[/tex]
= 30[tex]\sqrt{3}[/tex] meters
Therefore, perimeter of the equilateral triangle is 30[tex]\sqrt{3}[/tex]
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Cans of soda are packaged in boxes containing the same number of cans.
There are 36 cans in 4 boxes.
a) How many cans are there in 7 boxes?
b) How many boxes are needed to package 99 cans of soda?
Answers
a)
63 cans in 7 boxes.
b)
11 boxes are needed for 99 cans.
What is a unit rate?It is a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
36 cans in 4 boxes.
This means,
1 box = 36/4 cans
1 box = 9 cans
Multiply 7 on both sides.
7 box = 63 cans ______(1)
1 box = 9 cans
Multiply 11 on both sides.
11 box = 99 cans ______(2)
Now,
From (1) and (2)
a)
63 cans in 7 boxes.
b)
11 boxes are needed for 99 cans.
Thus,
63 cans in 7 boxes.
11 boxes are needed for 99 cans.
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for safety reasons, 5 different alarm systems were installed in the vault containing the safety deposit boxes at a beverly hills bank. each of the 5 systems detects theft with a probability of 0.82 independently of the others. the bank, obviously, is interested in the probability that when a theft occurs, at least one of the 5 systems will detect it. what is the probability that when a theft occurs, at least one of the 5 systems will detect it?
Answers
The probability that when a theft occurs, at least one of the 5 systems will detect it is approximately 0.9997.
How likely something is to occur is known as its probability. We can discuss the probabilities of different outcomes, or how likely they are, whenever we are unsure of how an event will turn out.
We can solve this problem using the complement rule. The probability that none of the 5 systems detect the theft is given by:
(1 - 0.82)^5 = 0.00033124
So the probability that at least one system detects the theft is:
1 - 0.00033124 = 0.99966876
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What is the perimeter of the parallelogram?
A 12
B 15
C 30
D 44
Answers
Answer:
C. P = 30
Step-by-step explanation:
Parallelogram opposite (or parallel) sides are equal,
so:
2x = x + 2
5y - 9 = 2y + 3
For x:
2x = x + 2
2x - x = 2
x = 2
For y:
5y - 9 = 2y + 3
5y - 2y = 3 + 9
3y = 12
y = 4
the smallest sides are equal 2x and x + 2 => 2 * 2 = 4
the biggest sides are equal 5y - 9 and 2y + 3 => 2 * 4 + 3 = 11
P = 2 * (a + b)
P = 2 * (4 + 11)
P = 2 * 15
P = 30
Y=2x+4 y=-x+1
Solve the system using substitution
Answers
The equivalent solution to the equation is (-1, -2)
Solving simultaneous equation using substitution methodGiven the simultaneous equation below:
Y=2x+4
y=-x+1
Since both equations are y expressions, we will equate then to have;
2x+ 4 = -x + 1
2x + x = 1 - 4
3x = -3
x = -1
For the value of y;
y = -x + 1
y = -1-1
y =-2
Hence the solution to the system of equation is (-1, -2)
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If you return an item that has an original price of $180, how much is the restocking fee if the stocking fee is 6%?
Answers
The restocking fee for an item with an original price of $180 and a restocking fee of 6% is $10.80.
A restocking fee is a fee that is charged when a customer returns an item, usually to cover the costs associated with processing the return and getting the item back in a sellable condition. The fee is typically calculated as a percentage of the original price of the item.
In this problem, we are given that the restocking fee is 6% and the original price of the item is $180. To find the restocking fee, we can use the formula:
Restocking fee = (Percentage fee / 100) x Original price
In this case, the percentage fee is 6% or 0.06 (since 6% is equivalent to 6/100). The original price is $180. Substituting these values into the formula gives:
Restocking fee = (0.06) x $180
Restocking fee = $10.80
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Calculate the volume of this cylinder, giving your answer to 1 decimal point
Answers
The volume of the cylinder is approximately 1413.7 cubic centimeters.
The formula for the volume of a cylinder is V = πr²h, where r is the radius of the base and h is the height or length of the cylinder.
Since the base of the cylinder has a diameter of 9cm, the radius is half of that, or r = 4.5cm.
The length of the cylinder is given as 20cm.
Therefore, the volume of the cylinder is:
V = πr²h
= π(4.5)²(20)
= 1413.72 cubic centimeters (rounded to 1 decimal place)
Thus, the volume of the cylinder is approximately 1413.7 cubic centimeters.
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Complete question:
Calculate the volume of this cylinder. give your answer to 1 decimal place. Base is 9cm. Length is 20cm.
Fill in the missing numbers to complete the linear equation that gives the rule for this table.
x y
3 91
4 89
5 87
6 85
Answers
The linear equation for the given coordinate points is y=-2x+97.
What is the equation of a line?The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
From the given table, the coordinate points are (3, 91) and (4, 89).
Here, slope (m)= (89-91)/(4-3)
m= -2
Substitute m=-2 and (x, y)=(3, 91) in y=mx+c, we get
91=-2(3)+c
91=-6+c
c=97
So, the equation is y=-2x+97
Therefore, the linear equation is y=-2x+97.
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Harvey has some 1 bills and some 5 in all he has 6 bills worth 22 let x be the number of 1 bills and let y be the number of 5 bills write a system of equations to represent the information and use substitution
Answers
x + y = 6 (the number of 1 bills plus the number of 5 bills is 6)
1x + 5y = 22 (the total amount of money is 22)
We can use substitution to solve for one of the variables in terms of the other and then substitute that expression back into one of the equations to find the other variable.
From the first equation, we can solve for y in terms of x:
y = 6 - x
Substituting this expression for y into the second equation, we have:
1x + 5(6 - x) = 22
Expanding the right side:
1x + 30 - 5x = 22
Combining like terms:
-4x + 30 = 22
Subtracting 30 from both sides:
-4x = -8
Dividing both sides by -4:
x = 2
So, there are 2 one dollar bills. To find the number of 5 dollar bills, we can substitute x = 2 back into the equation we derived for y:
y = 6 - x = 6 - 2 = 4
So, there are 4 five dollar bills.
scientists are modeling the spread of a hypothetical virus. in their computer model, there are currently 392 people infected, and the virus is spreading at a rate of 11% each day. how many people will be infected in 3 days? if necessary, round your answer to the nearest whole number.
Answers
According to the model, around 521 people will be infected in three days.
A unitary method is a mathematical technique where we use ratios and proportions to find the value of an unknown quantity.
Let's start by breaking down the problem. We know that there are currently 392 people infected and the virus is spreading at a rate of 11% each day. This means that for every 100 people, 11 people are getting infected. To calculate how many people will be infected in three days, we need to use a unitary method.
To do this, we need to calculate the total increase in the number of infected people over three days. Since the virus is spreading at a rate of 11% each day, the total increase over three days will be 33% (11% x 3). We can then use this percentage increase to calculate the total number of people infected in three days.
To find the total number of people infected in three days, we can use the following formula:
Total infected = current infected + (current infected x percentage increase)
Plugging in the values from the problem, we get:
Total infected = 392 + (392 x 0.33)
Total infected = 392 + 129.36
Total infected ≈ 521
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Identify the function shown in this graph. PLEASEEE.
Answers
The function shown in this graph is y = x + 4
How to determine the function shown in this graphFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we can see a straight line
This means that the graph is a linear function
This can be represented as
y = mx + c
From the graph, we have
c = 4 (because the graph intersects the y-axis at y = 4)
m = 1 (because a unit change in x gives a unit change in y)
So, we have
y = x + 4
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Emma was ranked 54th in his graduating class of 296 students. At what percentile is Emma’s ranking?
Answers
Answer: 54 is 18.24% of 296
Step-by-step explanation:
54:296*100 =
(54*100):296 =
5400:296 = 18.24
Now we have: 54 is what percent of 296 = 18.24
Question: 54 is what percent of 296?
Percentage solution with steps:
Step 1: We make the assumption that 296 is 100% since it is our output value.
Step 2: We next represent the value we seek with x
Step 3: From step 1, it follows that 100% = 296
Step 4: In the same vein, x% = 54
Step 5: This gives us a pair of simple equations:
100% = 296 (1)
x% = 54 (2)
Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS (left-hand side) of both equations have the same unit (%); we have
100% over x% = 296 over 54
Step 7: Taking the inverse (or reciprocal) of both sides yields
x% over 100% = 54 over 196
x=18.54
Which word best describes the degree of overlap between the two data sets?
A.
high
B.
moderate
C.
low
D.
none
Answers
The word that best describes the degree of overlap between the two data sets is C. low
What is the meaning of data overlap ?In statistics, data overlap refers to the situation where two or more groups being compared have some individuals or data points that have similar or identical values. When this happens, it can make it more difficult to accurately distinguish between the groups and to draw meaningful conclusions from the data.
From the given data, we can see that one data set is positively skewed while the other is negative. This shows that the data overlap is quite low.
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1 Triunghiul dreptunghic ABC, A = 90°, este înscris într-un cerc de rază 13 cm.
Ştiind că AC = 10 cm, calculați:
a perimetrul și aria triunghiului;
b distanțele de la centrul cercului la laturile AB şi AC.
Answers
i don't speak that language so i don't know what your saying. im sorry
The perimeter of a rectangle is 30 inches. The width of the rectangle is two-thirds of its
length, as shown.
What are the length and the width of the rectangle? Check your solution.
Answers
Answer:
The length is [tex]9[/tex] inches and the width is [tex]30[/tex] inches.
Step-by-step explanation:
The perimeter of the rectangle is [tex]2x + \frac{4x}{3} = 30[/tex]. We multiply [tex]3[/tex] by both sides which will give us [tex]6x + 4x = 90[/tex]. Adding, we have [tex]10x = 90[/tex]. Dividing [tex]10[/tex] by both sides will give us [tex]x = 9[/tex]. The length of the rectangle is [tex]9[/tex], and the width is [tex]\frac23 \cdot 9 = 6.[/tex] Checking our answer, we have [tex]6 + 6 + 9 + 9 = 30.[/tex] Therefore, the length of the rectangle is [tex]\boxed{9 \text{ inches}}[/tex] and the width of the rectangle is [tex]\boxed{30 \text{ inches}}[/tex].
Hope that helps!
joint and/or inverse variation. show you solution.
Answers
The force is 80,000 Dynes.
What is joint variation?We know that when we talk about the joint variation then we have a lot of variables that are being altered at the same time and this is what we are going to work on in the questions that we have here.
We are told that;
C α mr/t^2
Then;
C = kmr/t^2
k = Ct^2/mr
k = 6000 * 2^2/6 * 10
k = 400
Then, to find C;
C = 400 * 18 * 100/3^2
C = 80,000 Dynes
\
Hence, we can see from the calculation that the centrifugal force that is required is 80,000 Dynes.
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The graph represents the amount of money, in thousands, that you make over a
time period of years. According to the graph, what is the original price you invested?
Answers
Answer:
$2,000
Step-by-step explanation:
The initial investment price is given by the y-value where the graph intersects the y-axis
This is at y = 2
Since the scale is in thousands of $, that would mean $2,000 as the original price
omar buys a bag of cookies that contains 5 chocolate chip cookies, 9 peanut butter cookies, 6 sugar cookies and 7 oatmeal cookies. what is the probability that omar randomly selects a sugar cookie from the bag, eats it, then randomly selects an oatmeal cookie? probability
Answers
The probability that Omar randomly selects a sugar cookie from the bag eats it, then randomly selects an oatmeal cookie is 0.06.
Omar buys a bag of cookies that contains,
5 chocolate chip cookies,9 peanut butter cookies, 6 sugar cookies, and 7 oatmeal cookies,
We have to find the probability that Omar randomly selects a sugar cookie from the bag, eats it, then randomly selects an oatmeal cookie
Total number of cookies in bag = 27
the probability that Omar randomly selects a sugar cookie from the bag, eats it, then randomly selects an oatmeal cookie
[tex]=\frac{6}{27}.\frac{7}{26}\\\\=0.0598 =0.06[/tex]
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how quarts are equivalent to 14 liters? Round your answer to the nearest tenth.
Answers
Answer:
14.737
Step-by-step explanation:14 divided by .95 = 14.7368… then rounded to nearest hundred is 14.737
Kurram was born on June 12, 2002, and his brother was born on February 10, 2004. Who is the elder among them and by how many months?
Answers
Answer:
Kurram is elder by 19 months
geometric: you vs serena williams* you are playing serena williams (who has one hand tied behind her back) in tennis. your probability of losing is 98% and thus probability of winning is 2%. you will stop playing after you beat her. what is the probability you win on the 20th game played?
Answers
Probability determines the likelihood of an event occurring: P(A) = f / N. Odds and probability are related but odds depend on the probability. You first need probability before determining the odds of an event occurring.
P(A) = f / N.
probability = 2%/100=0.0002
One of the areas of probability theory is the estimation of the chance of experiments occurring. Using a probability, we can calculate everything from the likelihood of getting heads or tails when flipping a coin to the likelihood of making a research error, for example. It is essential to appreciate the most basic definitions of this branch, such as the formula for computing probabilities in equiprobable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc., in order to properly understand it .Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. Mathematics has incorporated probability to forecast the likelihood of various events.
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I would really appreciate your help. Thank you.
Answers
Answer:
75
Step-by-step explanation:
trust me bro
−2x+y = 0 - −7x+3y = 2
Answers
To solve this system of linear equations, we need to find the values of x and y that make both equations true at the same time. One method to solve this is to use elimination or substitution.
First, let's rearrange the first equation:
y = 2x
Next, we can substitute y = 2x into the second equation:
-7x + 3y = 2
-7x + 3(2x) = 2
-7x + 6x = 2
-x = -2
So, x = 2.
Finally, we can use the first equation to find y:
y = 2x
y = 2 * 2
y = 4
So, the solution to the system of equations is (x, y) = (2, 4).
Martha has a box of assorted chips. There are 2 bags of Doritos, 4 bags of Cheetos, and 5 bags of plain
potato chips.
a. What is the probabilty that Martha will grab a bag of potato chips? Write your answer as an unreduced
fraction & a percent.
b. If Martha grabs a bag of potato chips and takes them to eat with her lunch, what is the probability that her
friend, Jamie, will grab a bag of potato chips out of the box next? Write your answer as an unreduced fraction
& a percent.
c. Is this an independent or dependent event? EXPLAIN.
Answers
a. The probability that Martha will grab a bag of potato chips is 5/11 or 45.45%.
b. The probability that Jamie will grab a bag of potato chips out of the box next is 4/10 or 40%.
c. This is a dependent event because Martha's choice of a bag of potato chips affects the probability of Jamie's choice. If Martha chooses a bag of potato chips, then there are 4 bags of potato chips remaining in the box, so Jamie's probability of choosing a bag of potato chips is 4/10 or 40%. If Martha chooses a bag of Doritos or Cheetos, then there are 5 bags of potato chips remaining in the box, so Jamie's probability of choosing a bag of potato chips is 5/10 or 50%.
Which procedure correctly simplifies the expression 2(4x + 3) + (x - 3)?
Answers
To simplify the expression 2(4x + 3) + (x - 3), we need to use the distributive property of multiplication over addition, and then combine like terms.
The expression 2(4x + 3) + (x - 3) contains parentheses and addition and multiplication operations, so we need to follow the order of operations to simplify it. The order of operations is:
1. Simplify any expressions inside parentheses.
2. Evaluate any exponents.
3. Perform multiplication and division, from left to right.
4. Perform addition and subtraction, from left to right.
Let's follow these steps to simplify the expression,
1. Simplify any expressions inside parentheses.
There are two sets of parentheses in the expression: (4x + 3) and (x - 3).
We can use the distributive property of multiplication over addition to eliminate the parentheses:
2(4x + 3) + (x - 3) = 8x + 6 + x - 3
2. Evaluate any exponents,
There are no exponents in the expression.
3. Perform multiplication and division, from left to right.
There is no multiplication or division to perform.
4. Perform addition and subtraction, from left to right.
We can now simplify the expression by combining like terms:
8x + 6 + x - 3 = (8x + x) + (6 - 3) = 9x + 3
Therefore, the simplified expression is 9x + 3.
In summary, the correct procedure to simplify the expression 2(4x + 3) + (x - 3) is to use the distributive property to eliminate the parentheses, and then combine like terms to obtain the simplified expression 9x + 3.
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Nicole james and jenny shared one - third of pizza. What fraction of the the whole pizza did each of them receive
Answers
The fraction of pizza that each of them gets out of the whole pizza is 1/9.
What is meant by a fraction?
The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection. The denominator is the figure that appears below the line. A piece or sector of any quantity is another name for the fraction. Some of the different types of fractions are:
proper fractions, improper fractions, mixed fractions and so on.
Given 1/3rd portion of the pizza is shared by Nicole, James and Jenny.
Let us are assuming they shared the 1/3rd portion equally among themselves.
Then,
1/3 pizza = 3 people
1 person = 1/(3*3) = 1/9
Therefore the fraction of pizza that each person gets out of the whole pizza is 1/9.
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!URGENT HELP! 100 points to any who are willing ^-^
Consider the function f(x) = [tex]2^{x}[/tex]. Find b so that the graphs of each of the functions listed are the same as the graph of function f.
• [tex]g(x) = 4^{bx}[/tex]
• [tex]h(x) = 8^{bx}[/tex]
• [tex]j(x) = (\frac{1}{2}) ^{bx}[/tex]
Side note:
To whom it may concern!
I do deeply appreciate all your help if you did or were willing to help me! Thank you for taking the time out of your day and life to bring aid to my little situation! Bless your kind soul.
Answers
For g(x), we have:
g(x) = 4^bx = (2^2)^bx = 2^(2bx)
Since 2^x = f(x), we can set 2bx = x to find b. Solving for b, we get:
b = 1/2
For h(x), we have:
h(x) = 8^bx = (2^3)^bx = 2^(3bx)
Since 2^x = f(x), we can set 3bx = x to find b. Solving for b, we get:
b = 1/3
For j(x), we have:
j(x) = (1/2)^bx = 2^(-bx)
Since 2^x = f(x), we can set -bx = x to find b. Solving for b, we get:
b = -1
So, for g(x) = 4^bx, b = 1/2; for h(x) = 8^bx, b = 1/3; and for j(x) = (1/2)^bx, b = -1.
Find the value of each variable show proofs
Answers
The sides of the right triangle are as follows:
x = 18 units
y = 15.6 units
How to find the side of a right triangle?A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, let's find the sides of the right triangle using trigonometric ratios
tan 30° = opposite / adjacent
tan 30° = 9 / y
cross multiply
y = 9 / tan 30
y = 15.5884645362
y = 15.6 units
Let's find x
sin 30 = opposite / hypotenuse
sin 30° = 9 / x
x = 9 / 0.5
x = 18 units
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