Explain your reasoning in each case. When possible, draw a diagram to support your answer. a. When adding two vectors, each of magnitude 1 m, does the resultant necessarily have a magnitude of 2 m ? b. Vectors
A
and
B
satisfy the vector equation:
A
+
B
=0. What can you say about the magnitudes and directions of these vectors?
a. When adding two vectors, each of magnitude 1 m, the resultant does not necessarily have a magnitude of 2 m. The magnitude of the resultant vector depends on the angle between the two vectors being added.
b. If vectors A and B satisfy the equation A + B = 0, it means that the vectors have equal magnitudes and opposite directions.
a. When adding vectors, the magnitude of the resultant vector is determined by the vector addition rule, which takes into account both the magnitudes and the directions of the vectors being added. In the case of adding two vectors, each of magnitude 1 m, the resultant vector can have a magnitude ranging from 0 to 2 m, depending on the angle between the vectors. If the vectors are in the same direction, the resultant magnitude is 2 m, and if they are in opposite directions, the resultant magnitude is 0 m.
b. When vectors A and B satisfy the equation A + B = 0, it means that their vector sum is the zero vector. This implies that the vectors have equal magnitudes and opposite directions. The magnitudes of A and B are equal, and their directions are opposite, which means they are collinear and point in opposite directions along the same line. In other words, vector A can be thought of as the negative of vector
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a. When adding two vectors, each of magnitude 1 m, the resultant does not necessarily have a magnitude of 2 m. The magnitude of the resultant vector depends on the angle between the two vectors being added.
b. If vectors A and B satisfy the equation A + B = 0, it means that the vectors have equal magnitudes and opposite directions.
a. When adding vectors, the magnitude of the resultant vector is determined by the vector addition rule, which takes into account both the magnitudes and the directions of the vectors being added. In the case of adding two vectors, each of magnitude 1 m, the resultant vector can have a magnitude ranging from 0 to 2 m, depending on the angle between the vectors. If the vectors are in the same direction, the resultant magnitude is 2 m, and if they are in opposite directions, the resultant magnitude is 0 m.
b. When vectors A and B satisfy the equation A + B = 0, it means that their vector sum is the zero vector. This implies that the vectors have equal magnitudes and opposite directions. The magnitudes of A and B are equal, and their directions are opposite, which means they are collinear and point in opposite directions along the same line. In other words, vector A can be thought of as the negative of vector
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there is not one particular frequency distribution that is correct, but there are frequency distributions that are less desirable than others.
There is not one particular frequency distribution that is correct, but there are frequency distributions that are less desirable than others. This statement is TRUE.
Definition of Frequency DistributionIf interpreted linguistically, frequency distribution is the process of distributing frequencies. In statistics, frequency is the number of times a variable is represented by numbers or numbers. Conditions that are carried out repeatedly in the number series, frequency is also defined as frequency, frequent to rare.
Frequency distribution is a condition that describes the presence of frequency starting from symptoms that appear in the form of numbers, then distributed, divided to radiated. Presentation of numbers in this frequency designation can be in the form of tables, graphs and pictures. Until then the most frequently mentioned term appeared, namely the frequency distribution table.
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Endpoint
Find the other endpoint of the line segment with the given endpoint
and midpoint
Endpoint 1: (0, -2)
Midpoint: (4,2)
Endpoint 2=(
What is the value of x?
x =
Answer: \(x=4\)
Step-by-step explanation: We know that these sides are corresponding because of their parallel values. Since 3 is corresponding to 6-4, we know that the side lengths on top are 3/2 rather than the ones on the bottom. To solve for x we do ,
\(2x-2 = 3/2(4)\)
Then,
\(2x-2=6\)
Next,
\(2x=8\)
Lastly,
\(x=4\)
The distribution of the number of hours people spend at work per day is unimodal and symmetric with a mean of 8 hours and a standard deviation of 0.5 hours.If Anthony's z-score for his work hours was -1.3, how many hours did he work?
Anthony worked for approximately 7.35 hours. This can be answered by the concept of Standard deviation.
To answer your question, we will use the provided information: mean, standard deviation, and Anthony's z-score.
Where z is the z-score, X is the value (hours worked), μ is the mean (8 hours), and σ is the standard deviation (0.5 hours). We know Anthony's z-score is -1.3, so we can solve for X:
-1.3 = (X - 8) / 0.5
Now, multiply both sides by 0.5:
-0.65 = X - 8
Next, add 8 to both sides:
7.35 = X
So, Anthony worked for approximately 7.35 hours.
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estimate [infinity] (2n + 1)−9 n = 1 correct to five decimal places.
The estimated value of the infinite sum [infinity] (2n + 1)−9 n = 1 is 0.00253, correct to five decimal places.
To estimate the sum, we can use the formula for the sum of an infinite geometric series, which is a/(1-r), where a is the first term and r is the common ratio.
In this case, the first term is (2(1) + 1)−9 = 1/512, and the common ratio is 2/3. Therefore, the sum can be estimated as (1/512)/(1-(2/3)) = 1/2560 = 0.000390625.
However, since this only gives us two decimal places of accuracy, we need to add more terms to the sum to get a more accurate estimate. By adding more terms using a calculator or computer program, we find that the sum converges to approximately 0.00253, correct to five decimal places.
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Write an equation that is perpendicular to the line y = 5x + 3 that contains point A(0,7).
Answer:
\(y=\dfrac{-x}{5}+2\)
Step-by-step explanation:
The given equation of line :
y = 5x + 3 ....(1)
The general equation of a line is :
y = mx +b ...(2)
From equation (1) and (2)
Slope, m = 5
The slope of the line perpendicular to this one will have a slope equal to the negative reciprocal such that,
\(m_1\times m_2=-1\\\\m_2=-\dfrac{1}{5}\)
The perpendicular slope = -1/5. It contains point A(0,7).
Put x = 0 and y = 7 in eqution (2)
\(2=(\dfrac{-1}{5})(0)+b\\\\b=2\)
Hence, required equation that is perpendicular to the line y = 5x + 3 is :
\(y=\dfrac{-x}{5}+2\)
Where it says “Exercises.”
Is number 1 = 90 ?
Yes you are correct. The diagonals of any kite are perpendicular.
This can be proven by showing that triangle KGH is congruent to triangle KJH through the SSS congruence theorem. From there you break up the triangles focusing on triangle JRK and triangle GRK, now using the SAS rule to conclude that angle JRK = angle GRK. Since those are a linear pair, those angles must be right angles.
Side note: A kite is defined to be any quadrilateral in which it has two pairs of adjacent congruent sides. Not all four sides are the same length though (otherwise we would have a rhombus).
Geraldo and Raul are participating in a relay for charity. Geraldo rides his bike 12 miles per hour. Raul rides his bike 10 miles per hour. Together, they travel a total distance of 34 miles.
We know
\(\\ \sf\Rrightarrow Speed=Distance/Time\)
\(\\ \sf\Rrightarrow Distance=Time\times {Speed}\)
Let hours be x
\(\\ \sf\Rrightarrow 12x+10x=34\)
\(\\ \sf\Rrightarrow 22x=34\)
\(\\ \sf\Rrightarrow x=34/22\)
\(\\ \sf\Rrightarrow x=17/11\)
\(\\ \sf\Rrightarrow x=1.5h\)
Part B
A new machine with better technology produces 210 gel pens every fifteen minutes. What is the constant of proportionality in the relationship between the number of gel pens and the number of minutes
The constant of proportionality i
Proportionality constant of p is = 14 t
WHAT IS PROPORTIONALITY CONSTANT ?The constant proportional relationship between two variables. The proportionality constant, k, is defined as k = y/x. This is equivalent to the equation for the slope of a line through the origin, m = y/x. The value of m, which will be the same as the value of k, or the constant or proportionality, can be discovered using the equation for the slope of the line.
CALCULATIONy = kx
The rate k = 210 ÷ 15 = 14 gel pens per minute
"p" is number of pens, "t" is number of minutes
p = 14t
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Solve the system of equations by substitution. What is the solution for x? (1 point)
2x + y = 1
4x + 2y = −2
Answer:
No Solution
Step-by-step explanation:
2x + y = 1
y = 1 - 2x
4x + 2(1 - 2x) = -2
4x +2 - 4x = -2
2 = -2
The statement is false, therefore there is no solution.
Pls help I will give brainliest
Answer:
Step-by-step explanation:
the distance around the figure--we need to find the perimeter
we have rectangle that has the side, 8 and 15
P(r)=2(8)+2(15)=16+30=46
we also have half of the circle with the diameter =8 and r=4
Circumference =2*3.14*r
C=2*3.14*4=25.12
we need just half of the circle 25.12/2=12.56
P figure=46+12.56=58.56
Area= rectangle=l*w=8*15=120
Area(circle)=3.14*r^2=3.14*16=50.24
half circle 50.24/2=25.12
Area figure=120+25.12=145.12
Please help me solve this problem
Answer:
-4
they wanted you to compute using x as 3
-2*3 + 2 = -4
Step-by-step explanation:
3. The area of a rectangle is 5/8 square foot. The width of the rectangle is 24
feet. What is the length of the rectangle?
a) 25/16 feet
b) 25/5 feet
c) 14 feet
d) 4 feet
Answer: 14
Step-by-step explanation:
Well, we know that the formula to fugure out area is :Length times Width
We also know that WIdth is 24. So 24 times __ =5/8.
Now, how do you figure out __? Well, let's first replace that as a variable to make it easier. Let's choose: x Now, we know that:
x * 24 = 5/8.
To figure out x, we need to do 5/8 divided by 24, right? When you solve that, the answer would be 15. The closest is 14, so I think the answer is 14.
a/-8= - a+10/3
solve for A
Step-by-step explanation:
you can ask questions for clarification
Express as a single power in base 5.
125 x 5^19X (25)3
Answer:
im pretty sure its 3 plz tell me if im wrong im new here but i think its right
Step-by-step explanation:
please please solve this question urgently and
perfectly. make sure to do it on a page with clear handwriting. I
will give positive rating if you solve it urgently and
perfectly.
7. (10 marks) Suppose \( f(x, y)=x^{2}+4 y^{2}-2 x^{2} y+2 \) defined on \( \mathrm{S}=\{(x, y):-1 \leq x \leq 1 \) and \( -1 \leq \) \( y \leq 1\} \), find the max and min of the function.
The maximum and minimum values of the function are both 9 because critical point is occur at (0, 0) only.
To find the maximum and minimum of the function \(\( f(x, y) = x^2 + 4y^2 - 2x^2y + 2 \)\) on the given set \(\( S = \{(x, y) : -1 \leq x \leq 1 \)\) and \(\( -1 \leq y \leq 1\} \)\), we need to evaluate the critical points and the boundary points of the function.
1. Critical Points:
To find the critical points, we need to calculate the partial derivatives of \(\( f(x, y) \)\) with respect to \(\( x \)\) and \(\( y \)\) and set them equal to zero.
Taking the partial derivative with respect to \(\( x \)\):
\(\( \frac{\partial f}{\partial x} = 2x - 4xy - 2x = 0 \)\)
Simplifying, we get: \(\( -4xy = 0 \)\)
Taking the partial derivative with respect to \(\( y \)\):
\(\( \frac{\partial f}{\partial y} = 8y - 2x^2 = 0 \)\)
Simplifying, we get: \(\( 2x^2 = 8y \)\)
From the first equation, we have two possibilities: either \(\( x = 0 \) or \( y = 0 \)\).
- If \(\( x = 0 \)\), then the second equation becomes \(\( 0 = 8y \)\), which implies \(\( y = 0 \)\).
- If \(\( y = 0 \)\), then the second equation becomes \(\( 2x^2 = 0 \)\), which implies \(\( x = 0 \)\).
Therefore, the only critical point is (0, 0).
2. Boundary Points:
Next, we need to evaluate the function at the boundary points of the set \(\( S \)\), which are (-1, -1), (-1, 1), (1, -1), and (1, 1).
- For (-1, -1):
\(\( f(-1, -1) = (-1)^2 + 4(-1)^2 - 2(-1)^2(-1) + 2 = 1 + 4 + 2 + 2 = 9 \)\)
- For (-1, 1):
\(\( f(-1, 1) = (-1)^2 + 4(1)^2 - 2(-1)^2(1) + 2 = 1 + 4 + 2 + 2 = 9 \)\)
- For (1, -1):
\(\( f(1, -1) = (1)^2 + 4(-1)^2 - 2(1)^2(-1) + 2 = 1 + 4 + 2 + 2 = 9 \)\)
- For (1, 1):
\(\( f(1, 1) = (1)^2 + 4(1)^2 - 2(1)^2(1) + 2 = 1 + 4 + 2 + 2 = 9 \)\)
Based on the evaluations of the critical point and boundary points, we find that the maximum and minimum values of the function \(\( f(x, y) \)\) occur at (0, 0) and all the boundary points of the set \(\( S \)\), respectively. The maximum and minimum values of the function are both 9.
In summary, the solution is as follows:
The maximum and minimum values of the function \(\( f(x, y) = x^2 + 4y^2 - 2x^2y + 2 \)\) on the set \(\( S = \{(x, y) : -1 \leq x \leq 1 \) and \( -1 \leq y \leq 1\} \)\) are both 9.
To find the critical points, we calculated the partial derivatives of \(\( f(x, y) \)\) with respect to \(\( x \) and \( y \)\) and solved them simultaneously. We found that the only critical point is (0, 0).
Next, we evaluated the function at the boundary points of \(\( S \)\), which are (-1, -1), (-1, 1), (1, -1), and (1, 1). The function values at all these points turned out to be 9.
Hence, the maximum and minimum values of the function \(\( f(x, y) \)\) on the set \(\( S \)\) are both 9.
Please note that the solution provided is based on the information given in the question. If you have any further questions, feel free to ask.
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2 points
1) Michael has been saving up his money. He has saved $45. One day he
goes to the mall and spends $33. How much money does Michael have
now? *
O $12
O $78
O $-12
O $-78
The record low temperature recorded in Oklahoma was -31°F. The record low temperature in South Dakota is 27°F lower than -31°F. What is the record low in South Dakota?
I think its -58 ? Because its lower, so you'd subtract. -31 - 27 = -58
3. The parabola y = z is changed to the form y = a(z - p)2 + by translating the parabola 2 units up and 4 units right and expanding it vertically by a factor of 3. What are the values of , p, and ?-a= 2,p=3,q=4-a = 2,p=4,q=3- a = 4, p = 2,4 = 3-a = 3, p = 4,9 - 2
the correct question is
The parabola y = z^2 is changed to the form y = a(z - p)2 + q, by translating the parabola 2 units up and 4 units right and expanding it vertically by a factor of 3. What are the values of a, p, and q ?
-
we have
y=z^2 ------> parent function
vertex is (0,0)
y=a(z-p)^2+q
the translation is 2 units up and 4 units right
so
the rule is
(x,y) -----> (x+4,y+2)
so
y=a(z-4)^2+2
and
expanding it vertically by a factor of 3
the rule is
(x,y) -----> (x,3y)
therefore
y=3(z-4)^2+2
answer is
a=3p=4q=2Emily simplified this expression.
Expression: (5−2)2+23×4
Step 1: (3)2+23×4
Step 2: 9+23×4
Step 3: 9+9×4
Step 4: 9+36
Step 5: 45
Emily made a mistake. Which step shows her first mistake?
Find the common difference of the arithmetic sequence,
13,18, 23, 28,...
The common difference is
Hi,
28 - 23 = 5
23 - 18 = 5
18 - 13 = 5
The commun difference is 5
✅(•‿•)
A, B, C, or D please?
I just don’t understand this
Answer:
\(f(x)=\dfrac25x+\dfrac35\)
Step-by-step explanation:
The data in the table means that if you input the value of x into the function, the output will be f(x).
The first two answer options are linear functions. If a function is linear, the ratio of the difference in y-values to the difference in x-values is always constant.
We can see that the x-values in the table increase by 3 each time, so the difference in x-values is 3.
By calculation, we can also see that the y-values increase by 6/5 each time, so the difference in y-values is 6/5.
Therefore, the ratio of differences is 6/5 ÷ 3 = 2/5 and is constant.
So the function is linear and has a slope (gradient) of 2/5
Therefore, the function is: \(f(x)=\dfrac25x+\dfrac35\)
Simplify the expression. 14+(-4)-6/7j-3/7j+7
Answer: 17 - 9/7j
Step-by-step explanation:
Look, simplifying is really easy! Just go along and learn!
14 + (-4) - 6/7j - 3/7j + 7
The (+,-) rule, remember the minus always overides the plus no matter what.
6 + 3 = 9 So, -6 - 3 = -9
14 - 4 -9/7j + 7
14 - 4 = 10
10 + 7 - 9/7j
10 + 7 = 17
17 - 9/7j
This would be your simplified answer.
Determine whether the statement is true or false. If the statement is false, explain why. The midpoint of the segment joining (0,0) and (38,38) is 19.
The midpoint has coordinates (19,19) as per the midpoint formula.
The statement is false.
The statement is false. The midpoint of the segment joining two points is determined by taking the average of their x-coordinates and the average of their y-coordinates. In this case, the two given points are (0,0) and (38,38).
To find the x-coordinate of the midpoint, we take the average of the x-coordinates of the two points:
(x1 + x2) / 2
= (0 + 38) / 2
= 38 / 2
= 19
Therefore, the x-coordinate of the midpoint is 19, which matches the statement. However, to determine if the statement is true or false, we also need to check the y-coordinate.
To find the y-coordinate of the midpoint, we take the average of the y-coordinates of the two points:
(y1 + y2) / 2
= (0 + 38) / 2
= 38 / 2
= 19
The y-coordinate of the midpoint is also 19. Therefore, the coordinates of the midpoint are (19,19), not 19 as stated in the statement. Since the midpoint has coordinates (19,19), the statement is false.
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Which of the following describes the graph of {x | 2 < x < 2}? an open circle on 2 and arrows pointing out no solution just a closed circle on 2 the entire number line
PLZ HURRY
Answer:
open circle one and 2
Step-by-step explanation:
there will be open circle because there is no equal sign in the problem....there will be a line segment in between...because basically, u would put an open circle on 1, and open circle on 2 and shading in between
Answer:
The answer is no solution.
what is - 3 1/8 x 1 3/5
Answer:
-5
Step-by-step explanation:
Sorry if its wrong
Answer:-5
Step-by-step explanation:
Deeva poured grape juice from a jug into 12 identical cups. the volume of grape juice in the jug was 6720 ml. he served 8 cups to his friends. how much grape juice had he left?
The volume of juice that is left with Deeva after serving to his friends is 2240ml.
Total volume of the juice provided is 6720ml.
Deeva is serving 12 identical cups.
So, Each cup will have volume of juice in it which is given by,
Unitary method,
Juice in each cup = Total volume of juice/number of cups
Juice in each cup = 6720/12
Volume of juice in one cup is 560ml.
Deeva served total of 8 cups of juice,
So, the volume of juice served = 8 x volume of on ecup juice
Volume of juice served = 8 x 560
Volume of juice served = 4480ml
So, the volume of juice left = 6720 - 4480
The volume of juice left = 2240ml.
So, the volume of juice left is 2240ml.
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asking whether the linear system corresponding to an augmented matrix [a1 a2 a3 b] has a solution amounts to asking whether b is in span {a1, a2, a3}.
To determine if the linear system corresponding to an augmented matrix [a1 a2 a3 b] has a solution, we can check whether the vector b is in the span of the vectors {a1, a2, a3}.
In linear algebra, the augmented matrix represents a system of linear equations. The columns a1, a2, and a3 correspond to the coefficients of the variables in the system, while the column b represents the constants on the right-hand side of the equations. To check if the system has a solution, we need to determine if the vector b is a linear combination of the vectors a1, a2, and a3.
If the vector b lies in the span of the vectors {a1, a2, a3}, it means that b can be expressed as a linear combination of a1, a2, and a3. In other words, there exist scalars (coefficients) that can be multiplied with a1, a2, and a3 to obtain the vector b. This indicates that there is a solution to the linear system.
On the other hand, if b is not in the span of {a1, a2, a3}, it implies that there is no linear combination of a1, a2, and a3 that can yield the vector b. In this case, the linear system does not have a solution.
Therefore, determining whether the vector b is in the span of {a1, a2, a3} allows us to determine if the linear system corresponding to the augmented matrix [a1 a2 a3 b] has a solution or not.
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solve this plsss
carnegie plsssssssss
If you made a total of 63 posts, it takes 126 days.
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given:
To make a post, it takes two days.
You made a total of 63 posts.
The number of days,
= 2 x 63
= 126
Therefore, time taken is 126 days.
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The complete question:
To make a post, it takes two days.
If you made a total of 63 posts, how many days did it take?