Evaluate I=∫(sinx+9y)dx + (4x+y)dy for the nonclosed path ABCD in the figure.
Close the path by connecting D to A. Then by Green's theorem, the integral over the closed path ABCDA - which I'll just abbreviate C - is
[tex]\displaystyle \oint_C (\sin(x)+9y)\,\mathrm dx + (4x+y)\,\mathrm dy \\\\ = \iint_{\mathrm{int}(C)}\frac{\partial(4x+y)}{\partial x} - \frac{\partial(\sin(x)+9y)}{\partial y}\,\mathrm dx\,\mathrm dy \\\\ = -5\iint_{\mathrm{int}(C)}\mathrm dx\,\mathrm dy[/tex]
(where int(C ) denotes the region interior to the path C )
The remaining double integral is -5 times the area of the trapezoid, which is
[tex]\displaystyle -5\iint_{\mathrm{int}(C)}\mathrm dx\,\mathrm dy = -\frac52\times(12+4)\times4=-160[/tex]
To get the line integral you want, just subtract the integral taken over the path DA. On this line segment, we have x = 0 and dx = 0, so this integral reduces to
[tex]\displaystyle\int_{DA}y\,\mathrm dy = \int_{12}^0y\,\mathrm dy = -\int_0^{12}y\,\mathrm dy = -72[/tex]
Then
[tex]\displaystyle \int_{ABCD} (\sin(x)+9y)\,\mathrm dx + (4x+y)\,\mathrm dy = -160 - (-72) = \boxed{-88}[/tex]
The triangles below are similar (being similar means there is a proportional relationship between the measures of each of the sides). What is the length of ED? (HINT: You can solve this question by using the MATH Ratio Table)
=================================================
Work Shown:
ED/DF = AB/AC
x/24 = 12/16
16x = 24*12
16x = 288
x = 288/16
x = 18
------------
Explanation:
Because the triangles are similar, we can form the proportion shown above. There are many variations of the proportion that can happen, but they all lead to the same result x = 18.
So for instance, another proportion you could solve is ED/AB = DF/AC.
The key is to keep up the same pattern when forming the ratios.
What I mean by that is when I formed ED/DF I divided the vertical side over the horizontal side for triangle EDF. So to form the second fraction, we must do the same division (vertical over horizontal) for triangle ABC.
A train is traveling at a speed of 60 miles per hour. What happens to the number of miles when the number of hours
changes?
Abebe babe
Answer:
It multiplies
Step-by-step explanation:
if the number of hours changes to example to 2 then you multiply 60 by 2 resulting in 120miles in 2 hours
Noise levels at 5 volcanoes were measured in decibels yielding the following data: 127,174,157,120,161 Construct the 98% confidence interval for the mean noise level at such locations. Assume the population is approximately normal. Step 3 of 4 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answer:
The critical value used is T = 3.747.
The 98% confidence interval for the mean noise level at such locations is (108.944, 186.656).
Step-by-step explanation:
Before building the confidence interval, we need to find the sample mean and the sample standard deviation.
Sample mean:
[tex]\overline{x} = \frac{127+174+157+120+161}{5} = 147.8[/tex]
Sample standard deviation:
[tex]s = \sqrt{\frac{(127-147.8)^2+(174-147.8)^2+(157-147.8)^2+(120-147.8)^2+(161-147.8)^2}{4}} = 23.188[/tex]
Confidence interval:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 5 - 1 = 4
98% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 4 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.98}{2} = 0.99[/tex]. So we have T = 3.747, which is the critical value used.
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 3.747\frac{23.188}{\sqrt{5}} = 38.856[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 147.8 - 38.856 = 108.944
The upper end of the interval is the sample mean added to M. So it is 147.8 + 38.856 = 186.656.
The 98% confidence interval for the mean noise level at such locations is (108.944, 186.656).
The theoretical mean of a distribution is also known as its ______________.
Answer:
skewness
Step-by-step explanation:
Average.
The average of a set of observations is the most important and useful measure of statistics and is a position measure, as it shows the positions of the numbers to which it refers. The average value is involved in several types of statistics and is examined in almost all statistical distributions. It is generally defined as the sum of the observations by their number. That is, it is the mathematical operation of finding the "mean distance" between two or more numbers.
Learn more about averages in https://brainly.com/question/22390452
If there is a die that has 12 sides, that are numbered 1 to 12, what is the probability that she will roll either a 3 or a 9
Answer:
2/12 = 1/6
Step-by-step explanation:
To find the probability of something with an equal chance of each outcome, we can apply the formula (number of favorable outcomes)/(number of total outcomes). Because there is an equal chance for each side of the die to be landed on, we can apply this.
On a 12 sided die, there are 12 sides. Two of those sides are 3 and 9. Therefore, there are two favorable outcomes (3 and 9). There are 12 sides to choose from, so there are 12 total outcomes, making the probability 2/12 = 1/6
I’m so bad at this pls-
Answer:
[tex]5 \sqrt{2} [/tex]
Step-by-step explanation:
[tex] \sqrt{5} \times \sqrt{10} \\ = \sqrt{5} \times \sqrt[]{5} \times \sqrt{2} \\ = 5\sqrt{2} [/tex]
Hope it is helpful....Simplify 7a – 11b + 4ab – 6a + 5b.
find the x – intercepts of the graph of the function f(x) = x2 – 2x + 1
A) (1,0)
B) (-1,0)
C) (0,-1)
D) (0,1)
PLEASE HELP ME ITS URGENT , WILL MARK AS BRAINLIEST!!!
Answer:
[tex]\boxed{\sf A) ( 1,0) }[/tex]
Step-by-step explanation:
A quadratic function is given to us and we need to find the x Intercept of the graph of the given function . The function is ,
[tex]\sf \implies f(x) = x^2 -2x + 1 [/tex]
For finding the x intercept , equate the given function with 0, we have ;
[tex]\sf \implies x^2 -2x + 1 = 0 [/tex]
Split the middle term ,
[tex]\sf \implies x^2-x-x+1=0[/tex]
Take out common terms ,
[tex]\sf \implies x( x -1) -1( x -1) = 0[/tex]
Take out (x - 1 )as common ,
[tex]\sf \implies (x - 1 )(x-1) = 0[/tex]
Equate with 0 ,
[tex]\sf \implies x = 1,1 [/tex]
Therefore the root of the function is 1. Hence the x Intercept is (1,0)
Hence the x Intercept is (1,0) .
Step-by-step explanation:
x² - 2x + 1 = 0
x² - (x + x) + 1 = 0
x² - x - x + 1 = 0
x(x - 1) - 1(x - 1) = 0
(x - 1)(x - 1) = 0
x = 1
Hence,
Option A
8P + 2 > 3P - 15
solve for p
Answer: p >-17/5
Step-by-step explanation:
Answer:
P = [tex]\frac{-17}{5}[/tex]
Step-by-step explanation:
Substract 3P from both sides:
5P + 2 > - 15
Subtract 2 from both sides:
5P > -17
Divide both sides by 5:
P = [tex]\frac{-17}{5}[/tex]
There are three separate, equal-size boxes, and inside each box there are four separate small boxes, and inside each of the small boxes there are three even smaller boxes. how many boxes are there all together?
Answer:
There are 51 boxes all together.
Step-by-step explanation:
Since there are three separate, equal-size boxes, and inside each box there are four separate small boxes, and inside each of the small boxes there are three even smaller boxes, to determine how many boxes are there all together, the following calculation must be done:
3 + 3 x 4 + 3 x 4 x 3 = X
3 + 12 + 36 = X
51 = X
Therefore, there are 51 boxes all together.
the sum of the digits of a two digit number is 5. If nine is subtracted from the number it will equal the reversed number. FIND THE EQUATION!! PLEASE!
Answer:
D
Step-by-step explanation:
Using the Time Series Data for the US Nuclear Electric Power Production, calculate the exponential smoothing forecasts for 2005 through 2010 using alpha equals 0.2. Find the forecast error for each time period. If there is n
Answer:
????????????
I don't know
Perimeter (numerical)
Answer:
270 m
Step-by-step explanation:
Add up all the sides
P = 19 +18.8+18.8 +18.8+18.8+40.8+19+40.8+18.8+18.8+18.8+18.8
P = 270 m
Do number 7 plz finding QR
Answer:
QR = sqrt(147)
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2 + b^2 = c^2
7^2 + QR^2 = 14^2
49 + QR^2 = 196
QR^2 = 196-49
QR^2 = 147
Taking the square root of each side
QR = sqrt(147)
find the constant of variation k for the direct variation. 4x = -y
Answer:
k = - 4
Step-by-step explanation:
The equation representing direct variation is
y = kx ← k is the constant of variation
Given
4x = - y ( multiply both sides by - 1 )
- 4x = y , that is
y = - 4x ← in standard form
with k = - 4
Which number can be written on the line to make the inequality true?
3.91 < ___ < 4.23 < 4.44
a) 3.7
b) 3.9
c) 4.1
d) 4.3
Answer:
[tex]3.7[/tex]
Step-by-step explanation:
[tex]3.9 < 3.7[/tex]
Answer:
answer is A
3.7
Step-by-step explanation:
Write the equation of a line in slope-intercept form that has a slope of 3/4 and passes through the point (-4, 1).
y equals 0.75 x plus 4
y equals 4 x plus 0.75
y equals minus 4 x plus 1
y equals 0.75 x plus 1
Answer:
y = 3/4 x + 4
y equals 0.75 x plus 4
Step-by-step explanation:
y = 3/4 x + b
1 = 3/4 (-4) + b
1 = -3 + b
b = 4
Answer:
A) y equals 0.75 x plus 4Step-by-step explanation:
Another way to solve this to use the point-slope form:
y - y₁ = m(x - x₁)Substitute the values of m, x₁, y₁ and convert this into slope-intercept form:
y - 1 = 3/4(x - (-4))y - 1 = 3/4x + 3y = 3/4x + 4y = 0.75x + 4Correct choice is A
Find the following images in width and circumference
Step-by-step explanation:
hey guys how do you put a picture like you did ?
I need help with this
Answer:
D.
Step-by-step explanation:
According to converse of the Pythagorean Theorem, that if the square of the third side (longest side) of a triangle equals the sum of the other two shorter sides, therefore, the triangle formed must be a right triangle.
From the side lengths given, the following satisfies the Pythagorean triple:
5² + 12² = 13².
Therefore, the procedure to use to confirm the converse of the Pythagorean Theorem would be to draw the two shortest side, 5 cm and 12 cm, so that a right angle will be between them. The side measuring 13 cm should therefore fit in to form a right triangle.
construct an angle that bisect 120°
Answer:
just make a 120 angle and divide it by 2, 60.
Which graph represents y = |xl?
A
B
C
D
Answer:
B
Step-by-step explanation:
The equation represented in the question is the parent absolute value question. If you know the different parent functions, then the answer is obvious because absolute value equations always form a V. However, if you do not do this then you can create a table and plugin values. Plugin numbers like 0, -1, and 1 for X and solve for Y. Finally, graph these points and see what graph best fits. If needed you can also plug in more points.
Answer:
B.
Step-by-step explanation:
I got it correct on the warm up
odd number more than 100 are empty,unit,finite,or,infinite
odd numbers more than 100 are infinite.
Use the substitution method to solve the system of equations below.
y = 3x − 2x + 8y = −22
The director of special events for Sun City believed that the amount of money spent on fireworks displays on the 4th of July was predictive of attendance at the Fall Festival held in October. She gathered the following data to test her suspicion.
4th of July ($000) Fall Festival (000)
10.6 8.8
8.5 6.4
12.5 10.8
9.0 10.2
5.5 6.0
12 11.1
8.0 7.5
7.5 8.4
9.0 9.5
10 9.8
7.5 6.6
10 10.1
6.0 6.1
12 11.3
10.5 8.8
Required:
Determine the regression equation. Is the amount spent on fireworks related to attendance at the Fall Festival? Conduct a hypothesis test to determine if there is a problem with autocorrelation.
Answer:
The complete question and its solution in the attached file please find it.
Step-by-step explanation:
I need help with this
Answer:
A.
Step-by-step explanation:
Twust me n' dwont doubt me
A is for apple
And cause A looks like ABC
DWUHHH
Solve this equation for x. Round your answer to the nearest hundredth. 0.77 = log x
Answer:
x ≈ 5.89
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra II
Exponential to Logarithmic: [tex]\displaystyle b^m=x \rightarrow log_bx=m[/tex]Step-by-step explanation:
Step 1: Define
Identify
0.77 = log(x)
Step 2: Solve for x
[Equality Property] Raise both sides to the 10th power: [tex]\displaysytle 10^{0.77} = 10^{logx}[/tex]Simplify: [tex]\displaysytle x = 10^{0.77}[/tex]Evaluate: [tex]\displaysytle x = 5.88844[/tex]Jim took a loan of R30 000 for 18 months at simple interest rate of 12,5% per year. determine the amount that Jim will pay in 18 months
Answer:
36151,82923
Step-by-step explanation:
30000* ( 1+12,5%/12)^18
The odometer on your car shows the total number of miles traveled up to 99,999 miles, after it turns over it starts over at 0. If the odometer shows, 98,654 miles, what will it show after a trip of 3782?
Answer:
2437miles
Step-by-step explanation:
amount left before it starts over = 999999-98654 = 1354
amount it will show = 3782-1354 = 2437
The odometer will show 2437 miles after 3782 miles if the odometer on your car shows the total number of miles traveled up to 99,999 miles, after it turns over it starts over at 0.
What is the distance?Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.
We have:
The odometer on your car shows the total number of miles traveled up to 99,999 miles.
Current reading = 98,654 miles
After 99,999 miles the odometer turns over it and starts over at 0
The differnece = 99999 - 98654 = 1354
After 1354 miles odometer turns over and starts over at 0
Now, take the difference between 3782 and 1354
= 3782 - 1354
= 2437 miles
After 3782 miles the meter will show 2437 miles
Thus, the odometer will show 2437 miles after 3782 miles if the odometer on your car shows the total number of miles traveled up to 99,999 miles, after it turns over it starts over at 0.
Learn more about the distance here:
brainly.com/question/26711747
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Identify which of the following is not equivalent to 234.
Question 1 options:
A)
B)
23−−√4
C)
(214)12
D)
214 x 212
Answer:
A since A is left blank its A
