The integral is path-independent if we can find a scalar function f such that grad(f ) = A. This requires
[tex]\dfrac{\partial f}{\partial x}=2x-y[/tex]
[tex]\dfrac{\partial f}{\partial y}=x+y[/tex]
Take the first PDE and integrate both sides with respect to x to get
[tex]f(x,y)=x^2-xy+g(y)[/tex]
where g is assumed to be a function of y alone. Differentiating this with respect to x gives
[tex]\dfrac{\partial f}{\partial y}=-x+\dfrac{\mathrm dg}{\mathrm dy}=x+y\implies\dfrac{\mathrm dg}{\mathrm dy}=2x+y[/tex]
which would mean g is *not* a function of only y, but also x, contradicting our assumption. So the integral is path-dependent.
Parameterize the unit circle (call it C) by the vector function,
[tex]\mathbf r(t)=\cos t\,\mathbf i+\sin t\,\mathbf j[/tex]
with t between 0 and 2π.
Note that this parameterization takes C to have counter-clockwise orientation; if we compute the line integral of A over C, we can multiply the result by -1 to get the value of the integral in the opposite, clockwise direction.
Then
[tex]\mathrm d\mathbf r=-\sin t\,\mathbf i+\cos t\,\mathbf j[/tex]
and the (counter-clockwise) integral over C is
[tex]\displaystyle\int_C\mathbf A\cdot\mathrm d\mathbf r[/tex]
[tex]\displaystyle=\int_0^{2\pi}((2\cos t-\sin t)\,\mathbf i+(\cos t+\sin t)\,\mathbf j)\cdot(-\sin t\,\mathbf i+\cos t\,\mathbf j)\,\mathrm dt[/tex]
[tex]\displaystyle=\int_0^{2\pi}1-\sin t\cos t\,\mathrm dt=2\pi[/tex]
and so the integral in the direction we want is -2π.
By the way, that the integral doesn't have a value of 0 is more evidence of the fact that the integral is path-dependent.
is sin 30 = 0.5, then sin-1 0.5 =30
Answer:
yes
Step-by-step explanation:
sin 30 = 0.5
sin-1 = 30
What’s the correct answer for this question?
Answer:
C
Step-by-step explanation:
PG = GO
2(4x-3)-8=4+2x
8x-6-8=4+2x
8x-14=4+2x
8x-2x=4+14
6x=18
Dividing both sides by 6
x = 3
Answer:
x = 3
Step-by-step explanation:
Since the chords are congruent then they are equidistant from the centre, thus
PG = GO , substitute values
2(4x - 3) - 8 = 4 + 2x ← distribute and simplify left side
8x - 6 - 8 = 4 + 2x
8x - 14 = 4 + 2x ( subtract 2x from both sides )
6x - 14 = 4 ( add 14 to both sides )
6x = 18 ( divide both sides by 6 )
x = 3
What’s the correct answer for this question?
Answer:
C
Step-by-step explanation:
Slope Formula is used from 2-5
Which is
Slope Formula = Rise/Run
Slope Formula = y₂-y₁/x₂-x₁
Jose constructed Triangle DCE, where m∠D = 103° and m∠C = 22°. Remy constructed triangle PQT, where m∠Q = 22°, and m∠T = 55°. Are the two triangles similar to one another? *
Yes, because two pairs of corresponding angles in the triangles are congruent.
No, because none of the corresponding pairs of angles in the triangles are congruent.
No, because 103 + 22 ≠ 22 + 55.
There is not enough information to determine if the two triangles are similar to one another.
Answer:
The missing angle in Jose's triangle is 180 - 103 - 22 = 55° and since both triangles have two congruent pairs of corresponding angles the answer is yes.
Answer:
Yes
Step-by-step explanation:
They are similar by angle-angle similarly theorem
In two triangles, if two pairs of corresponding angles are congruent, then the triangles are similar . (Note that if two pairs of corresponding angles are congruent, then it can be shown that all three pairs of corresponding angles are congruent, by the Angle Sum Theorem.)
A tent is an example of a____a0____a1.
Answer:
triangular prism
Step-by-step explanation:
A triangular prism has 3 rectangular sides and 2 triangles as the base
The answer is : Triangular, Prism
Have a great day!
God bless you!
Answer fast i have timer
Answer:
k is equal to 42
Step-by-step explanation:
What is the best interpretation of V(4)=64
I assume the normal function is V(x)=y
So if we plug it in, we know that at x=4, the y value of the function is 64.
Fill in missing information to make the equality true:
(... +2a)2 = … +12ab2+4a2.
Answer:
I suppose it should be
6b² and (6b²)²
or
6b² and 36[tex]b^{4}[/tex]
Step-by-step explanation:
(a+b)² = a² + 2ab + b²
therefore
(6b²+2a)² = (6b²)² + 12ab² + 4a²
The missing information to make the equality true are 3b² and (3b²)². This can be obtained by using the algebraic identity (x+y)² =x² + 2xy + y².
Find the missing information:Let the missing information be p and p²
Then the given equation will be: (p+2a)² =p² + 12ab² + 4a²
The algebraic identities is (x+y)² =x² +2xy+y²
Comparing the given equation with the algebra formula we get
y=2a
2xy =12ab² ⇒2x(2a) = 12 ab² ⇒ x = 3b²
Therefore the given equation will be
(3b²+2a)² = (3b²)²+12ab²+4a²
Hence the missing information to make the equality true are 3b² and (3b²)².
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Identify the measure of arc BD.
A. 51
B. 72
C. 105
D. 129
Answer:
Option (D). 129°
Step-by-step explanation:
In the figure attached,
AB and CD are the diameters intersecting at the center of the circle F.
Central angle AFC = 129°
m([tex]\widehat{AC}[/tex]) = 129°
m(∠AFD) = 180° - (m∠AFC)
= 180° - (129)°
= 51°
Since m∠AFD = m∠BFC = 51° [Vertical angles]
Therefore, [tex]m(\widehat{AD})=m(\widehat{BC})=51[/tex]
Now, [tex]m(\widehat{BC})+m(\widehat{BD})[/tex] = 180°
51° + [tex]m(\widehat{BD})[/tex] = 180°
[tex]m(\widehat{BD})[/tex] = 180° - 51°
[tex]m(\widehat{BD})[/tex] = 129°
Therefore, Option (D) will be the answer.
Simplify: StartRoot 64 r Superscript 8 Baseline EndRoot
Answer:
8r^4
Step-by-step explanation:
[tex]\sqrt{64r^8} =\sqrt{(8r^4)^2}=\boxed{8r^4}[/tex]
Answer:
8r^4
Step-by-step explanation:
Write this number in standard form 6,000,000+9000,000+80,000+9,000+500+80+2
Answer:
15089582 = 1.5089582 x 10^7
Step-by-step explanation:
6,000,000+9000,000+80,000+9,000+500+80+2 = 15089582
15089582 = 1.5089582 x 10^7
A bag has 8 red tiles and 2 green tiles. In a charity carnival game, you pay $5 to randomly pull a tile from the bag. The payout for pulling a red tile is $1 and the payout for pulling a green tile is $10. Which of the followig are true or false.
a. The expected payoff per game for the charity is $2.20.
b. In 20 games, the charity can expect to make $44.
c. In 30 games, the charity can expect to make $120.
d. In 5 games, the player can expect to lose $11.
Answer:
B:True
Step-by-step explanation:
B is true as a bag of 8 red tiles and 2 green tiles you pay 5 per tile meaning in twenty games you pay $100(50 per bag) and the total amount you win back is $56(28 per bag) so the equation would be $100 - $56= $44 profit to the charity
Hence only statement 1 is correct,∴The expected payoff per game for the charity is $2.20.
What is payoff?Money provided to someone as a bribe, reward, or when they leave a position. As a result, a mathematical function representing the award awarded to a single player at the game's conclusion has been developed.
How to Solve?Given a bag of tiles containing 8 red tiles, 2 green tiles.
Probability of drawing a red tile =1/8
Probability of drawing a green tile =1/2
If red tile is pulled payout is $1 else $10
Payout=
payout for 1 game= $1*8/10+$10*2/10-$5=2.20
payout in 20 games =$1*10*8/10+$10*10*2/10-$5*20=-72
payout for 30 games=$1*15*8/10+$10*15*2/10-$5*30=0
payout in 5 games=$1*5*8/10+10*5*2/10-$5*5=$25
Hence only statement 1 is correct, ∴The expected payoff per game for the charity is $2.20.
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Solve each system by elimination
-9x -4y=2
7x +4y = -6
Answer:
cộng vế theo vế ta đc :
-2x=-4<=>x=2
thay x=2 vào 1 trong 2 ptrình ta đc: y=-5
Identify the type of claim in each research question below.
For many years "working full-time" was 40 hours per week. A business researcher gathers data on the hours that corporate employees work each week. She wants to determine if corporations now require a longer work week.
Group of answer choices
a.Testing a claim about a single population proportion.
b.Testing a claim about a single population mean.
c.Testing a claim about two population proportions.
dTesting a claim about two population means.
Answer:
b.Testing a claim about a single population mean.
Step-by-step explanation:
Hello!
The researcher wants to test the claim that corporation employees work more than 40 hours per week.
The variable of interest is "The number of hours a corporate employee works per week"
The parameter of study, for her to make a valid conclusion about the weekly working hours of the population of corporation employees is the population mean μ.
If the claim is correct, she would expect the population mean of weekly hours the corporate employees work to be greater than 40.
This is an example of a single population mean test.
what are the factors of x^2+4x+3x?
Answer:
x(x+7)
Step-by-step explanation:
x^2+4x+3x
Combine like terms
x^2+7x
Factor out an x
x(x+7)
Answer:
[tex]x(x + 7)[/tex]
Step-by-step explanation:
[tex] {x}^{2} + 4x + 3x[/tex]
Combine like terms
[tex] {x}^{2} + 7x[/tex]
Factoring
[tex]x(x + 7)[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Which values of a,b,and c correctly represent the answer in simplest form 7/9 divied by 4/9 =
Answer:
[tex]7/4[/tex]
Solution:
[tex]\frac{7}{9} /\frac{4}{9}[/tex]
Reciprocal.
[tex]7/9(9/4)[/tex]
Multiply.
[tex]\frac{63}{36}[/tex]
Simplify
[tex]\frac{7}{4}[/tex]
Which equation represents the linear function that is shown on the graph below?
y = one-half x + 4
y = one-half x minus 2
y = 4 x minus 2
y = negative 2 x + 4
Answer:
A=(4,0) and B = (6,1)
We can find the slope with this formula:
[tex]m =\frac{y_2 -y_1}{x_2 -x_1}[/tex]
And replacing we got:
[tex] m= \frac{1-0}{6-4}= \frac{1}{2}[/tex]
Now we can find the y intercept using one of the points like this:
[tex] 0 = \frac{1}{2} *4 +b[/tex]
And then b would be:
[tex] b = -2[/tex]
And the equation would be given by:
[tex] y= \frac{1}{2}x -2[/tex]
And the best option is:
y = one-half x minus 2
Step-by-step explanation:
In order to find the equation for the line we can use two points and let's take:
A=(4,0) and B = (6,1)
We can find the slope with this formula:
[tex]m =\frac{y_2 -y_1}{x_2 -x_1}[/tex]
And replacing we got:
[tex] m= \frac{1-0}{6-4}= \frac{1}{2}[/tex]
Now we can find the y intercept using one of the points like this:
[tex] 0 = \frac{1}{2} *4 +b[/tex]
And then b would be:
[tex] b = -2[/tex]
And the equation would be given by:
[tex] y= \frac{1}{2}x -2[/tex]
And the best option is:
y = one-half x minus 2
Answer:
C
Step-by-step explanation:
hope this helps!
Two cyclists, 55 miles apart, start riding toward each other at the same time. One cycles 5 miles per hour faster than the other, and they meet after 5 hours of riding.
a. Write an equation using the information as it is given above that can be solved to answer this problem. Use the variable r to represent the speed of the slower cyclist.
b. What are the speeds of the two cyclists?
Answer:
r = 6 mph and f = 11 mph
Step-by-step explanation:
Representations:
1) speed of faster cyclist: f = r + 5
2) speed of slower cyclist: r
Distances covered:
(r + 5)(5 hr) + r(5) = 55 mi (total distance covered)
Then 5r + 25 + 5r = 55, or, after reducing this equation:
r + 5 + r = 11, or
2r = 6
Then r = 6 mph and f = 11 mph
A total of 4.8 percent of the prime time viewing audience watched shows on ABC, 6.7 percent watched shows on CBS, 5.2 percent on Fox, 5.8 percent on NBC, 1.7 percent on Warner Brothers, and 1.9 percent on UPN. A total of 73.9 percent of the audience watched shows on other cable networks, such as CNN and ESPN. What will be the prime time viewing percentage of the pie chart for the following data? (Only consider the viewers watching non-cable news.) (Round your answers to 2 decimal places.)
Prime time viewing
ABC %
CBS %
Fox %
NBC %
Warner %
UPN %
Answer:
Prime time viewing
ABC % = 18.39%
CBS % = 25.67%
Fox % = 19.92%
NBC % = 22.22%
Warner % = 6.51%
UPN % = 7.28%
Step-by-step explanation:
We have to calculate the percentage of prime time viewing for each of the non-cable networks.
We know that 73.9% of the audience watched shows on cable networks. That left us with 26.1% of the audience for the non-cable networks.
[tex]\text{Cable\%}=1-0.739=0.261=26.1\%[/tex]
Then, if we use a pie chart only for the non-cable networks, we have to calculate the proportion of each network relative to the non-cable audience.
We can calculate that as:
[tex]\text{ABC}=0.048/0.261=0.1839=18.39\%\\\\\text{CBS}=0.067/0.261=0.2567=25.67\%\\\\\text{Fox}=0.052/0.261=0.1992=19.92\%\\\\\text{NBC}=0.058/0.261=0.2222=22.22\%\\\\\text{Warner}=0.017/0.261=0.0651=6.51\%\\\\\text{UPN}=0.019/0.261=0.0728=7.28\%\\\\[/tex]
complete this sentence in a triangle the angle with the greatest measure is always opposite the
Answer:
longest side
Step-by-step explanation:
In a triangle the angle with the greatest measure is always opposite the longest side.
what is archieves meaning
Answer:
the meaning is "a collection of historical documents or records providing information about a place, institution, or group of people."
Step-by-step explanation:
hope this helped and plz mark me as brainliest!
Answer:
a collection of historical documents or records providing information about a place, institution, or group of people
Step-by-step explanation:
According to Eurostat, 55.2% of households in Italy have one child, the highest percentage in the Euro zone. A random sample of 160 Italian households was selected. The standard error of the proportion is ________.
Answer:
0.04
Step-by-step explanation:
In this case we must use the following formula to be able to find the standard error, which would be the square root, of the probability for its complement divided by the population:
SE= [tex]\sqrt{\frac{p *(1-p)}{n} } \\[/tex]
Now, knowing that p = 0.552 and n = 160 we replace and we are left with:
SE = [tex]\sqrt{\frac{0.552 *(1-0.552)}{160} } \\[/tex]
SE = [tex]\sqrt{0.00154}[/tex]
SE = 0.039
Which means that the standard error of the proportion is 0.04
Please answer this correctly
Answer:
V =113.04 cm^3
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h
V = 3.14 (3)^2 4
V = 3.14 *9*4
V =113.04 cm^3
Answer:
Step-by-step explanation:
3*3.14
9.42*9.42
88.7364*4
354.9456 rounded to
355
The wattle thickness (in millimeters) of 15 randomly selected chickens was measured before and after treatment with phytohemagglutinin (PHA). Does treatment with PHA increase wattle thickness
Answer:
Step-by-step explanation:
The question is incomplete. The complete question is:
The wattle thickness (in milimeters) of 15 randomly selected chickens was measured before and after treatment with PHA. Does treatment wih PHA increase wattle thickness?
Chicken Number // Pretreatment // Posttreatment
1 // 1.05 // 3.48
2 // 1.01 // 5.02
3 // 0.78 // 5.37
4 // 0.98 // 5.45
5 // 0.81 // 5.37
6 // 0.95 // 3.92
7 // 1.00 // 6.54
8 // 0.83 // 3.42
9 // 0.78 // 3.72
10 // 1.05 // 3.25
11 // 1.04 // 3.66
12 // 1.03 // 3.12
13 // 0.95 // 4.22
14 // 1.46 // 2.53
15 // 0.78 // 4.39
Solution:
Corresponding wattle thickness before and after treatment form matched pairs.
The data for the test are the differences between the wattle thickness at pretreatment and posttreatment.
μd = wattle thickness at pretreatment minus wattle thickness at posttreatment
Pretreatment. Posttreatment diff
1.05 3.48 -2.43
1.01 5.02 -4.01
0.78 5.37 -4.59
0.98 5.45 -4.47
0.81 5.37 -4.56
0.95 3.92 -2.97
1 6.54 -5.54
0.83 3.42 -2.59
0.78 3.72 -2.94
1.05 3.25 -2.2
1.04 3.66 -2.62
1.03 3.12 -2.09
0.95 4.22 -3.27
1.46 2.53 -1.07
0.78 4.39 -3.61
Sample mean, xd
= (-2.43 - 4.01 - 4.59 - 4.47 - 4.56 - 2.97 - 5.54 - 2.59 - 2.94 - 2.2 - 2.62 - 2.09 - 3.27 - 1.07 - 3.61)/15 = - 3.264
xd = - 3.264
Standard deviation = √(summation(x - mean)²/n
n = 15
Summation(x - mean)² = (- 2.43 + 3.264)^2 + (-4.01 - 3.264)^2 + (-4.59 - 3.264)^2+ (-4.47 - 3.264)^2 + (-4.56 - 3.264)^2 + (-2.97 - 3.264)^2 + (-5.54 - 3.264)^2 + (-2.59 - 3.264)^2 + (-2.94 - 3.264)^2 + (-2.2 - 3.264)^2 + (-2.62 - 3.264)^2 + (-2.09 - 3.264)^2 + (-3.27 - 3.264)^2 + (-1.07 - 3.264)^2 + (-3.61 - 3.264)^2 = 627.32444
Standard deviation = √(627.32444/15
sd = 6.47
For the null hypothesis
H0: μd ≥ 0
For the alternative hypothesis
H1: μd < 0
1) The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 15 - 1 = 14
The formula for determining the test statistic is
t = (xd - μd)/(sd/√n)
t = (- 3.264 - 0)/(6.47/√15)
t = - 1.95
We would determine the probability value by using the t test calculator.
p = 0.036
Assume alpha = 0.05
Since alpha, 0.05 > than the p value, 0.036, then we would reject the null hypothesis. Therefore, we can conclude that at a significance level of 5%, treatment with PHA increase wattle thickness
If the p-value for a hypothesis test is 0.027 and the chosen level of significance is a=0.05, then the correct conclusion is to
Answer:
[tex] p_v = 0.027[/tex]
And for this case we have a significance level [tex] \alpha=0.05[/tex] and then:
[tex] p_v <\alpha[/tex]
So then we have enough evidence to reject the null hypothesis. And we can conclude in favor the alternative hypothesis.
Step-by-step explanation:
For this case we have the following hypothesis:
[tex]Null hypothesis: p =p_o[/tex]
[tex]Alternative hypothesis: p \neq p_o[/tex]
And for this case we got the following hypothesis:
[tex] p_v = 0.027[/tex]
And for this case we have a significance level [tex] \alpha=0.05[/tex] and then:
[tex] p_v <\alpha[/tex]
So then we have enough evidence to reject the null hypothesis. And we can conclude in favor the alternative hypothesis.
Golf-course designers have become concerned that old courses are becoming obsolete since new technology has given golfers the ability to hit the ball so far. Designers, therefore, have proposed that new golf courses need to be built expecting that the average golfer can hit the ball more than 230 yards on average. A random sample of 177 golfers show that their mean driving distance is 230.7 yards, with a standard deviation of 41.8.
1. Set up the null and alternative hypotheses to test for the designers belief.
a. H0 : µ ≥ 230 versus Ha : µ < 230
b. H0 : µ = 230.7 versus Ha : µ ≠ 230.7
c. H0 : µ ≥ 230.7 versus Ha : µ < 230.7
d. H0 : µ ≤ 230.7 versus Ha : µ > 230.7
e. H0 : µ ≤ 230 versus Ha : µ > 230
2. Find the value of the standardized test statistic.
a. 0.125
b. -0.125
c. 0.223
d. -0.7
e. 0.7
3. Find the P-value for the above mentioned test.
a. 0.8237
b. 0.0228
c. 0.5871
d. 0.4118
e. 0.0871
Answer:
a) e) H0 : µ ≤ 230 versus Ha : µ > 230
b) [tex]t=\frac{230.7-230}{\frac{41.8}{\sqrt{177}}}=0.223[/tex]
c. 0.223
c) [tex]p_v =P(t_{(176)}>0.223)=0.4118[/tex]
d. 0.4118
Step-by-step explanation:
Information given
[tex]\bar X=230.7[/tex] represent the sample mean
[tex]s=41.8[/tex] represent the sample standard deviation
[tex]n=177[/tex] sample size
[tex]\mu_o =230[/tex] represent the value to verify
t would represent the statistic
[tex]p_v[/tex] represent the p value
Part a
We want to verify if the true mean is higher than 230 yards, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 230[/tex]
Alternative hypothesis:[tex]\mu > 230[/tex]
The best option would be:
H0 : µ ≤ 230 versus Ha : µ > 230
Part b
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{230.7-230}{\frac{41.8}{\sqrt{177}}}=0.223[/tex]
Part c
The degrees of freedom are:
[tex]df=n-1=177-1=176[/tex]
The p value would be given by:
[tex]p_v =P(t_{(176)}>0.223)=0.4118[/tex]
d. 0.4118
Please answer this correctly
Answer:
0
Step-by-step explanation:
Since the original: 6 is not either the largest or the smallest, it wouldn't affect the range
The only numbers that can affect the range when replaced are the greatest and the least values: 5 and 9
In 1970, the average length of a major league baseball game was 150 minutes compared to 180 minutes in 2018. Calculate the absolute and relative change in major league baseball game times from 1970 to 2018. Round your answer for relative change to the nearest whole percent.
Answer:
30 min20%Step-by-step explanation:
The absolute change in game length is ...
(180 min) -(150 min) = 30 min . . . . change in game length
__
The relative change is expressed as a fraction of the original game length:
(30 min)/(150 min) × 100% = 20% . . . . relative change in game length
given B(-5 0) reflected across the line y=-2
Answer:
When it is reflected across y=-2, the new location will be at (-5,-4)
Step-by-step explanation:
y=-2 is a horizontal line. The points B(-5,0) is 2 units above that point. So, when reflected, it will move 4 units down, which gives you (-5,-4).
In the chi-square test of association, as the difference between the observed and expected proportions increases... a. the chi-square test statistic increases b. the chi-square critical value increases c. the likelihood of rejecting the null hypothesis increases d. the likelihood of rejecting the null hypothesis decreases e. the chi-square critical value decreases f. the chi-square test statistic decreases
Answer:
Opton A
Step-by-step explanation:
In the chi-square test of association, as the difference between the observed and expected proportions increases, the chi-square test statistic also increases. This is because if the claim made in the null hypothesis is true: the claim that frequency of the observed is equal to that of the expected (Oi = Ei) then, the observed and the expected values are close to each other and the difference Oi − Ei is small for each category and the chisquare test statistic is small.
But when the observed data does not fit to what is expected as of the null hypothesis, the difference between the observed and expected values, Oi − Ei is large producing a large chi square statistic.
