The standard matrix of the linear transformation given in the question is
= 1/ 5 [ 1 2 ]
[ 2 4 ]
The direction vector of the given line is , v = ( 1 ,2 ).
So the projection of the line will be,
projection ( x ,x ) = ( (x , y ) . v / v^2 )v
= ( ( x + 2y)/5 ) v
Therefore, the required standard matrix will be ,
1/5 2/5
2/5 4/5
= 1/ 5 [ 1 2 ]
[ 2 4 ]
A matrix is also known as a rectangular array . The elements are arranged in the form of rows and tables forming a table . Arrays are an important part of both mathematical and computational applications.
The data in a conputer is stored in the form of an array . We can perform various operations on matrix like addition, subtraction , multiplication or division.
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Alice makes porridge from milk and oats.
The ratio of milk to oats is 1:2
What proportion of Alice's porridge is milk?
Anyone can help ASAP
Answer:
1 milk and 2 oats
Step-by-step explanation:
milk to oats show that milk is first followed by oats and since 1 is first it is 1 milk and 2 oats
During one particular sales day, 75% of the store's customers paid with credit cards. If there were 60 customers that day, how many used a credit card? A. 15 B. 30 C. 45 D. 50 HINT Method 1: Set up a proportion and cross multiply. Method 2: Convert the
45 people used credit card on that particular day , this could be found out using simplified multiplication.
What is proportion?
A quantitative relation is an ordered try of numbers a and b, written a / b wherever b doesn't equal zero.
A proportion is Associate in Nursing equation within which 2 ratios ar set up to one another.
Main body:
We have been given that during one particular sales day, 75% of the store's customers paid with credit cards. There were 60 customers that day.
To find the number of people, who used credit card, we will find 75% of 60.
The number of people who used credit card = (75 / 100 )* 60
The number of people who used credit card = 0.75 *60
The number of people who used credit card = 45
Therefore, 45 people used credit card on that particular day.
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How do you write an exponential decay model?
The exponential decay formula is f(x) = abx, where b stands for the decay factor. The decay rate in the exponential decay function is specified as a decimal.
What does the exponential decay formula actually mean?At regular intervals, the sum steadily declines by a specified percentage. This decline in growth is calculated using the exponential decay formula. The general form of f(x) is f(x) = a (1 - r)x. Where, a = The starting point, decay rate = r, x = length of time.
Do we require a calculator for exponential growth and decay?When we need to make rapid calculations in a generic way, the exponential growth and decay calculator comes in handy. However, you should not use it frequently as it may slow down your ability to answer issues through math. To improve your comprehension, you must practice word problems with exponential growth and decay on paper.
The exponential decay formula is f(x) = abx, where b stands for the decay factor. The decay rate in the exponential decay function is specified as a decimal. A percentage is used to represent the degradation rate. Simply decreasing the percent and dividing it by 100 yields the decimal equivalent. The decay factor b = 1-r can therefore be calculated.
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Maya said farewell to her favorite uncle as he boarded a plane for Paris. That night she dreamed about an airplane that ran into a thunderstorm and crashed into a mountain, killing everyone onboard. When she woke up, she learned that her uncle’s plane had encountered violent turbulence on the way to Paris and that several passengers had been injured on the flight. She concluded that this series of events (E) is very strong evidence that she has the ability to see distant things using only her mind (H).
Maya thinks that E is strong evidence for H. Assuming she has updated properly given her probability assignments, what does this mean about her assignments to P( E | ~H ) and P( E | H )? For each of these values, how might you challenge her assignment? (Don’t focus on P( H ) and P( ~H ).)
The likelihood of this question will be determined as P( E | ~H)=1 - P(E|H).
For independent events the probability P( E | H ) is calculated as:
P( E | H ) = P( E ) * P( E and H)
P( E and H) = P(E) * P(H).
Since the event E has already happened and is obvious, if P(E | H)>P(E | H) then the event E is dependent on the mind of maya, but if P(E | H)>P(E | H) then the event E is not dependent on the mind of maya.
In our situation, P(E | H), which means that the plane crushing is independent of Maya's thoughts, is the probability that will suit this argument.
Since it is illogical to claim that Maya can perceive far-off objects with her mind, the likelihood of this question will be determined as P( E | ~H ) = 1 - P( E | H ).
For independent events the probability P( E | H ) is calculated as
P( E | H ) = P( E ) * P( E and H)
P( E and H) = P(E) * P(H).
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use the sketch below to decide if congruence can be proved, and if so, which method would prove the congruence.
Yes, the proof of congruence of two triangles ∆ABC ≅ ∆GHF is possible.
The convergence method which proves this congruence is SSS(side-side-side) congruence.
We have given the sketch of two triangles as seen above. We have to prove ∆ABC ≅ ∆GHF
Now , AB = √(-7+7)² + 5² = 5 in triangle ABC and FG = 5 in triangle FGH,
so, AB ≅ FG
Because AC = 3 in triangle ABC and FH = 3 in triangle FGH,
so, AC ≅ FH
To find the lengths of BC and GH , we can use distance formula.
Length of BC :
BC = √[(x₂ - x₁)² + (y₂ - y₁)²]
(x₁, y₁) = B(-7, 0) and (x₂, y₂) = C(-4, 5).
BC = √[(-4 + 7)² + (5 - 0)²]
= √[32 + 52]
= √[9 + 25]
= √34
Length of GH :
GH = √[(x₂ - x₁)² + (y₂ - y₁)²]
(x₁, y₁) = G(1, 2) and (x₂, y₂) = H(6, 5).
GH = √[(6 - 1)² + (5 - 2)²]
= √[52 + 32]
= √[25 + 9]
= √34
Conclusion :because BC = √34 and GH = √34,
=>BC ≅ GH
All the three sides of one triangle is congruent to the corresponding sides of other triangle.
By SSS congruence postulate,
ΔABC ≅ ΔFGH
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What is 50% of 86? Show your work.
Answer:
43 Is half
Step-by-step explanation:
86/2=43
I need you to promise me you will do good on the homework
This table shows the input and output values for an exponential function f(x) . What is the ratio of outputs for any two inputs that are one value apart? 4 12 18 2 x −3 −2 −1 0 1 2 3 f(x) 1256 164 116 14 1 4 16
The ratio of outputs for any two inputs that are one value apart 2 .
What is ratio?A ratio is an ordered pair of numbers a and b, written a / b. where b is not zero. A ratio is an equation that equates two ratios. For example, if you have one boy and her three girls, the ratio can be written as: 1:3 (3 girls for 1 boy). A ratio is the comparison of the two numbers by division.
Taking the first two outputs, or the -1/8 and -1/4, we can divide not the second one by the first one to find the
ratio:
-1/4-1/8
When dividing fractions, we multiply by the reciprocal:
-1/4x-8/1
To multiply fractions, multiply straight across:
(-1x-8)/(4x1) 8/4=2
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based on the results the pharmacist obtained from her hypothesis test and the following results, conclude whether to reject or not reject h0.
Since, Z(0)>Z(0.1) that is 3.07>1.28. So reject H(0). So the option 1 and 3 is correct.
In the given question,
H(0): μ=18 ; H(a): μ>18
x = 19.1
Conclude whether to reject or not reject H(0), and interpret the results.
σ = 1.6
α = 0.1 (significance level) .
The test statistic is
Z(0) = {x-μ(0)}/(σ/√n)
Z(0)= (19.1-18)/16/√20
Z(0) = 3.07
The critical value is Z(0.1) = 1.28.
As we can see that;
Z(0)>Z(0.1) that is
3.07>1.28
So reject H(0).
So the option 1 and 3 is correct.
Reject H(0), the test statistic Z(0)=3.07 is Z(0)=3.07 is greater than the critical value Z(α)=1.28, for a right-tailed test therefore there is NOT enough evidence to reject H(0) that the mean number of likes is not equal to 18 mg per generic anti-histamine dose.
And
The test statistic falls within the rejection region.
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The right question is:
Select two responses below.
Select all that apply:
(1) Reject H(0). The test statistic Z(0)=3.07 is greater than the critical value Z(α)=1.28, for a right-tailed test therefore there is NOT enough evidence to reject H(0) that the mean number of likes is not equal to 18 mg per generic anti-histamine dose.
(2) Fail to reject H(0). The test statistic Z(0)=3.07 is greater than the critical value Z(α)=1.28, for a right-tailed test therefore there is NOT enough evidence to reject H(0) that the mean number of likes is not equal to 18 mg per generic anti-histamine dose.
(3) The test statistic falls within the rejection region.
(4) The test statistics is NOT in the rejection region.
Adrian hopes that his new training methods have improved his batting average. Before starting his new regimen, he was batting 0.250 in a random sample of 52 at bats. For a random sample of 25 at bats since changing his training techniques, his batting average is 0.480. Determine if there is sufficient evidence to say that his batting average has improved at the 0.10 level of significance. Let the results before starting the new regimen be Population 1 and let the results after the training be Population 2.
Step 1 of 3 :
State the null and alternative hypotheses for the test. Fill in the blank below.
H0Ha: p1=p2: p1⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯p2
According to the manufacturer's claim, we build an hypothesis test, find the test statistic and the p-value relative to this test statistic.
The value of the test statistic is z = 1.65.
The p-value of the test is of 0.0495 > 0.02, which means that there is not sufficient evidence to say that his batting average has improved at the 0.02 level of significance.
Average of 0.48 in 25 at bats,
Test if there was improvement:
At the null hypothesis :
[tex]H_0 : P_1 - P_2 = 0[/tex]
At the alternative hypothesis:
[tex]H_1 : P_1 - P_2 > 0[/tex]
The p-value of the test is the probability of finding a difference of at least 0.19, which is 1 subtracted by the p-value of z = 1.65.
Looking at the z-table, z = 1.65 has a p-value of 0.9505.
1 - 0.9505 = 0.0495.
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The slope of a line is -6. The line goes through the point (7.-14). Write the equation of the line in point-slope form.
Answer:
Step-by-step explanation:
(7, -14)
y - y1 = m(x - x1)
y - (-14) = -6(x - 7) = y + 14 = -6(x - 7)
Standard Form
y + 14 = -6x + 42
y = -6x + 28
I need to know the answer. Please. :')
The inequality we want to write is:
100 + W*50 ≥ 1800
And its graph can be seen in the image at the end.
How to write and graph the inequality?We know that you start the game with 100 points and you get 50 extra for each word you make.
So, if you make W words, the total number of points that you get is:
100 + W*50
And that must be equal to or larger than 1,800, so we can writ the inequality:
100 + W*50 ≥ 1800
To solve it, we can isolate W.
100 + W*50 ≥ 1800
W*50 ≥ 1800 - 100
W ≥ 1700/50
W ≥ 34
So the number line is a point on W = 34 and a line that extends to the right, like the one below.
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6 2/3+ 3 3/4 solve pls help me solve it
Answer: 10.4166
Step-by-step explanation:
6 2/3= (18+2)/3= 20/3
3 3/4= (12+3)/4=15/4
6 2/3 + 3 3/4=(20/3)+(15/4)
=125/12
=10.4166
Answer:
[tex]10\frac{5}{12}[/tex]
Step-by-step explanation:
[tex]\sf6\frac{2}{3} +3\frac{3}{4}[/tex]
First, write the above fractions as improper fractions.
[tex]\sf\frac{20}{3} +\frac{15}{4}[/tex]
To solve the fractions you have to make the denominators of the fractions the same.
For that, we have to multiply both the numerator and denominator of the fractions (20/3) by 4 and (15/4) by 3.
Let us solve it now.
[tex]\sf\frac{20}{3} +\frac{15}{4}\\\\\sf\frac{20*4}{3*4} +\frac{15*3}{4*3}\\\\\frac{80}{12}+\frac{45}{12}\\\\\frac{125}{12}[/tex]
And now let us write the answer as a mixed number.
[tex]10\frac{5}{12}[/tex]
if the angle between two vectors is represented by , tell if the following angles would mean the vectors are orthogonal, parallel or neither.
If the angle between two vectors is represented by theta and it is equal to zero or 180 degrees then the following angles would mean the vectors are parallel .
Given :
if the angle between two vectors is represented by , tell if the following angles would mean the vectors are orthogonal, parallel or neither.
if two vectors points are given then find the dot product of vectors if the result is equal to zero then the two vectors are orthogonal vectors .
If they were parallel the angle would be 0 or 180 degrees, therefore, the two vectors are not parallel.
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please help, screenshot is here:
[tex]Answer:\ cos(\theta_1)=\boxed{-\frac{40}{41} }[/tex]
Step-by-step explanation:
[tex]\displaystyle\\sin(\theta_1)=\frac{9}{41}\ \ \ \ \ \ 90^0 < \theta_1 < 180^0\ \ \ \ \ \ \ cos(\theta_1)=?\\\\sin^2(\theta_1)+cos^2(\theta_1)=1\\\\cos^2(\theta_1)=1-sin^2(\theta_1)\\\\cos^2(\theta_1)=1-(\frac{9}{41})^2\\\\cos^2(\theta_1)=1-\frac{81}{1681} \\\\cos^2(\theta_1)=\frac{1(1681)-81}{1681} \\\\cos^2(\theta_1)=\frac{1600}{1681} \\\\[/tex]
Extract the square root of both parts of the equation:
[tex]\displaystyle\\\cos(\theta_1)=б\sqrt{\frac{1600}{1681} } \\\\\cos(\theta_1)=б\sqrt{\frac{40^2}{41^2} } \\\\\cos(\theta_1)=б\sqrt{(\frac{40}{41})^2 } \\\\\cos(\theta_1)=б\frac{40}{41}[/tex]
[tex]\displaystyle\\Since\ 90^0 < \theta_1 < 180^0, \\\\ therefore\ cos(\theta_1)=-\frac{40}{41}[/tex]
In which cases of the following lengths of sides of a triangle, is it possible to
draw a triangle?
(а) 3 cm, 4 cm, 7cm (b) 2 cm, 3 cm, 7 cm c)2.5cm, 1.8cm, 4cm
By using Euclidean geometry, the set of side lengths 2.5 cm, 1.8 cm, 4 cm can form a triangle.
what is triangle inequality?The sum of the lengths of any two sides must be greater than the length of the third side.
a + b ≥ c
What is triangle?A triangle is a three-sided polygon with three straight sides. It is a basic geometric shape that is found in many areas of mathematics and geometry.
Using this rule, we can determine which of the given sets of side lengths can form a triangle:
(a) 3 cm, 4 cm, 7 cm: It is not possible to form a triangle with these side lengths, because the sum of the lengths of the first two sides (3 cm + 4 cm = 7 cm) is equal to the length of the third side.
(b) 2 cm, 3 cm, 7 cm: It is not possible to form a triangle with these side lengths, because the sum of the lengths of the first two sides (2 cm + 3 cm = 5 cm) is less than the length of the third side.
(c) 2.5 cm, 1.8 cm, 4 cm: It is possible to form a triangle with these side lengths, because the sum of the lengths of the first two sides (2.5 cm + 1.8 cm = 4.3 cm) is greater than the length of the third side.
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The ratio of dye to pounds of clothing is constant. A worker develops the chart below to show the amount of dye needed for different amounts of clothing.
Clothes Dyeing
Weight of clothing (pounds)
Cups of dye
21 3
42 9
84 12
105 15
For which weight of clothing is the ratio of weight to dye different from the other ratios?
21 pounds
42 pounds
84 pounds
105 pounds
42 pounds has a weight of clothing to weight to dye different from the other ratios
How to determine for which weight of clothing is the ratio of weight to dye different from the other ratios?Ratio is used to compare two or more quantities. It is used to indicate how big or small a quantity is when compared to another
The ratio weight of clothing to the weight of dye will be:
For 21 and 3:
21:3 = 7: 1
For 42 and 9:
42:9 = 14: 3
For 84 and 12:
84:12 = 7: 1
For 105 and 15:
105:15 = 7: 1
Thus, 42 pounds is different from the other ratios
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Lin is paid $90 for 5 hours of work. She used the table to calculate how much she would be paid at this rate for 8 hours of work
Answer: $144
Step-by-step explanation: To find the price she gets paid for 1 hr we need to divide the money by the hours. So, 90 / 5 = 18.
So, now we know she gets paid 18 dollars an hour. So, we need to find out how much she earns in 8 hrs. So, we would simply multiply the 18 by the 8, to get $144.
A major department store chain is interested in estimating the average amount its credit card customers spent on their first visit to the chain’s new store in the mall. Fifteen credit card accounts were randomly sampled and analyzed with the following results: x-bar = $50.50 and s2 = 400 . Assuming the distribution of the amount spent on their first visit is approximately normal, what is the shape of the sampling distribution of the sample mean that will be used to create the desired confidence interval for \mu ?
a) Approximately normal with a mean of $50.50
b) A standard normal distribution
c) A t distribution with 15 degrees of freedom
d) A t distribution with 14 degrees of freedom
The value of the standard deviation does not change and remains the same.
Given, a retired statistic professor has recorded final exam results for decades. the mean final exam score for the population of a student is 82.4 with a standard deviation of 6.5.
The mean μ = 82.4
The standard deviation σ = √[ ((x - μ)2 + (y - μ)2 + (z - μ)2)/3 ]
we have to find the variance,
We now add a constant k to each data value and calculate the new mean μ'.
μ' = ((x + k) + (y + k) + (z + k)) / 3 = (x + y + z) / 3 + 3k/3 = μ + k
We now calculate the new mean standard deviation σ'.
σ' = √[ ((x + k - μ')2 +(y + k - μ')2+(z + k - μ')2)/3 ]
Note that x + k - μ' = x + k - μ - k = x - μ
also y + k - μ' = y + k - μ - k = y - μ and z + k - μ' = z + k - μ - k = z - μ
Therefore σ' = √[ ((x - μ)2 +(y - μ)2+(z - μ)2)/3 ] = σ
If we add the same constant k to all data values included in a data set, we obtain a new data set whose mean is the mean of the original data set PLUS k. The standard deviation does not change.
Hence, the standard deviation does not change.
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6 -9x = 5x -10x + 2 solve for x
everything else being equal, explain why you usually would prefer an unbiased estimator to a biased estimator.
Everything else is being equal, but we prefer an unbiased estimator mostly compare to a biased estimator because a biased estimator may be used for a variety of reasons, such as the difficulty of computing an unbiased estimator (as in the case of estimating standard deviation).
The fact that a biased estimator may be unbiased with respect to different measures, and the fact that an unbiased estimator does not exist without further assumptions about a population. Thus, it's miles scientifically now no longer accurate to apply a biased estimator for a parameter while there may be an independent estimator for it.
Only in unavoidable situation, it's miles cautioned to apply a biased estimator (which need to be consistent) for a parameter while there may be no independent estimator for it. It could be anticipated that a terrific estimator need to bring about an estimate this is near the real cost of the parameter. Because in exercise the parameters are unknown, it isn't always viable to evaluate the estimate with the real cost. Unbiasedness serves as a degree of closeness among an estimator and the parameter.
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question 1.
Gerald purchased 55 paving stones to use in his garden. The graph shows points representing the number of stones left to place at several different times while Gerald is working.
Select from the drop-down menus to complete the equation, in standard form, that represents the relationship between the number of paving stones left to place, y, and the time, x, Gerald has spent working.
The linear equation representing the relationship between the number of paving stones left for Gerald to place, y, and the time, x, Gerald has spent working is 5x + y = 55.
What is the linear equation?A linear equation is always in the form of y = ax + b, where a is the slope and b is the y-intercept.
The slope, a, is given as (y2 - y1)/(x2 - x1).
Data Points:(0, 55), (3, 40), and (7, 20)
Taking (3, 40) and (7, 20), the slope is determined as follows:
7 - 3 = 4
20 - 40 = -20
-20/4
= -5
In standard form, the linear equation is 5x + y = 55.
Thus, based on the linear equation above, we can conclude that the more time Gerald spends playing with the paving stones, the fewer stones he has to place.
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A company manufactures two products, A and B, and each of these products must be processed on two different machines. Product A requires 2 min of work time per unit on machine 1 and 4 min of work time per unit on machine 2. Product B requires 3 min of work time per unit on machine 1 and 1 min of work time per unit on machine 2. Each day 200 min are available on machine 1 and 300 min are available on machine2. To satisfy certain customers, the company must produce at least 8 units per day of product A and at least 10 units per day of product B. If the profit of each unit of product A is Php50 and the profit of each unit of product B is Php60, how many units of each product should be produced daily in order to maximize the company's profits?
The maximum profit is maximized 70 of product A and 20 of product B are produced.
How to calculate the units that maximize the profit?The objective function:
The profit is 50 for each product A and 60 for each product B:
P = 50A + 60B
The machine 1 constraint:
2 minutes for each product A and 3 minutes for each product B; 200 total minutes available:
2A+3B ≤ 200
The machine 2 constraint:
4 minutes for each product A and 1 minute for each product B; 300 total minutes available:
4A+B ≤ 300
The production constraints:
At least 8 of product A and at least 10 of product B:
A ≥ 8
B ≥ 10
2A+3B=200
4A+B=300
4A+6B=400
5B=100
Divide
B = 100 / 5
B=20
Also, A=70
The units are 70 and 20 respectively.
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Sara has agreed to help with her younger sister's science fair experiment. Her sister planted string beans in two pots. She is
using a different fertilizer in each pot to see which one will grow the tallest plant. Currently, plant A is 4 inches tall and
grows 2/3 inch per day, while plant B is 9 inches tall and grows 1/2 inch per day. If the plants continue growing at these rates
in how many days will the two plants be the same height? Which plant will be tallest in six weeks? Write a system of
equations and solve.
Answer: plants are same height in 30 days; Plant A is tallest in 6 weeks
Step-by-step explanation:
x = number of days
4 + (2/3)x = 9 + (1/2)x
(2/3)x - (1/2)x = 9 - 4
(1/6)x = 5
x = 30, number of days for Plant A and Plant B to be same height.
6 wks = 42 days
Plant A in 42 days: 4 + (2/3)(42) = 32 inches
Plant B in 42 days: 9 + (1/2)(42) = 30 inches
Which equation represents a circle that contains the point (-2, 8) and has a center at (4, 0)?
(x - 4)2 + y2 = 100
(x - 4)2 + y2 = 10
x2 + (y - 4)2 = 10
x2 + (y - 4)2 = 100
Convert the ratio of sheep to pigs below to the ratio of pigs to total animals (sheep and pigs) 3:5
Answer:
5:8
Step-by-step explanation:
Which scenario describes a pattern of exponential decay?
A: a backgammon competition has 10 players exiting after each round of games
B: a table tennis club has had 10,9, and 8 new numbers in three years, respectively
C: a billiards organization lost 5%,4%, and 3% of its members in three years, respectively
D: an elimination chess tournament has half the number of players on each successful round
The scenario that describes a pattern of exponential decay is option (D) i.e, an elimination chess tournament has half the number of players on each successful round.
What is Exponential Decay ?
A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. This process can be expressed by the following differential equation,dN/dt = -λNWhere, N is the quantity
λ (lambda) is a positive rate called the exponential decay constant, disintegration constant, rate constant, or transformation constant.
Hence, the answer is option(D) i.e, an elimination chess tournament has half the number of players on each successful round.
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What is the value of the expression 6\ times10+4^36×10+4
3
The value of the expression; 6 × 10 + 4³ as given in the task content is; 124.
What is the value of the expression 6 × 10 + 4³?It follows from the task content that the value of the expression given in the task content; 6 × 10 + 4³ is to be determined.
Hence, the value of the expression can be evaluated using PEMDAS guidelines as follows;
Since the given expression is;
6 × 10 + 4³
Since the exponent, so that we have;
6 × 10 + 64
Next, solve the multiplication, so that we have;
60 + 64
= 124.
On this note, the value of the expression is; 124.
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Q2 Convert the following readings to the unit indicated:
a) 0.05 m=______cm
b)50 gm= ______kg
c)25 mm=______km
a) 1 m = 100 cm.
0.05 m = 0.05×100
= 5 cm
b) 1000 gm = 1kg
50 = 50/1000
= 0.05 kg
c) 1000000 mm = 1 km
25 = 25/1000000
= 0.0000025 km
Hope understands.
Let C be the positively oriented square with vertices (0,0), (1,0), (1,1), (0,1). Use Green's Theorem to evaluate the line integral ∫C7y2xdx+8x2ydy.
The value of line integral is 1/2 .
The interior of the square is the region D = { (x,y) : 0 ≤ x,y ≤1 }. We call L(x,y) = 7y²x, M(x,y) = 8x²y. Since C is positively oriented, Green Theorem states that
[tex]\int\limits^1_0 {L(x,y)} \, dx + M(x,y)dy =\int\limits^1_0 \int\limits^0_1 {(Mx- Ly)} \, dx\, dy[/tex]
Lets calculate the partial derivates of M and L, Mx and Ly. They can be computed by taking the derivate of the respective value, treating the other variable as a constant.
Mx(x,y) = d/dx 8x²y = 16xy
Ly(x,y) = d/dy 7y²x = 14xy
Thus, Mx(x,y) - Ly(x,y) = 2xy, and therefore, the line integral is equal to the double integral
[tex]\int\limits^1_0 \int\limits^0_1 {2xy} \, dx\, dy[/tex]
We can compute the double integral by applying the Barrow's Rule, a primitive of 2xy under the variable x is x²y, thus the double integral can be computed as follows
[tex]\int\limits^1_0 \int\limits^0_1 {2xy} \, dx\, dy = \int\limits^1_0 {x^{2}y \left \{ {{1} \atop {0}} \right. } \, dy =\frac{y^{2} }{2} \left \{ {{1} \atop {0}} \right. } = \frac{1}{2}[/tex]
We conclude that the line integral is 1/2
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Answer: x = 56
Step-by-step explanation:
The angle horizontally adjacent from 73 is also equal to 73 due to the triangle being isosceles (the legs are given as equal). Therefore the other angle in that triangle has to be 180 - (73*2) = 34. This angle is a part of the 90 degree angle that is noted in the figure. The other part of that angle must be 90 - 34 = 56. Since this angle is in another isosceles triangle, the angle horizontally adjacent to it must also be 56. x is equal to this angle by definition of vertical angles, so x = 56.
