To evaluate the double integral Slo (22 + y^2) LA over the ellipse with equation 112x^2 + 8y^2 = 88, we can use the given transformation x = 18u and y = sqrt(11)v.
First, we need to find the bounds of integration for u and v. Substituting the given equations into the ellipse equation, we get:
112(18u)^2 + 8(sqrt(11)v)^2 = 88
18144u^2 + 88v^2 = 88
204u^2 + v^2 = 1
This gives us the equation of an ellipse with semi-axes of length 1/sqrt(204) and 1/sqrt(88). To find the bounds of integration, we can set u and v equal to these semi-axes:
u = ±1/sqrt(204)
v = ±1/sqrt(88)
We can also use the fact that the ellipse is symmetric about the x and y axes to simplify our calculations. Therefore, we can integrate over the first quadrant and multiply our result by 4.
The double integral becomes:
Slo (22 + y^2) LA = 4 * ∫(0 to 1/sqrt(88)) ∫(0 to 1/sqrt(204)) (22 + 11v^2) * 18 dv du
Simplifying and evaluating the integral, we get:
Slo (22 + y^2) LA = 4 * 18 * (22/3 + 11/2 * (1/sqrt(88))^2) * (1/sqrt(204)) * (1/sqrt(88))
Slo (22 + y^2) LA = 4 * 3 * (22/3 + 11/2 * 1/88) * (1/sqrt(204)) * (1/sqrt(88))
Slo (22 + y^2) LA = 12 * (22/3 + 11/2 * 1/88) * (1/sqrt(204)) * (1/sqrt(88))
Slo (22 + y^2) LA ≈ 3.693
Therefore, the evaluated integral is approximately 3.693.
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A 12 hour circular analogue clock shows 6 o'clock, with the hour hand pointing at 6, and the minute hand pointing at 12. Sometime between 7 and 8 o'clock the hour hand and minute hand are at 180° to each other. At how many minutes past 7 o'clock does this happen?
After 11 minutes, the angle between the hour's hand and the minute hand is 180°.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
A 12 hours roundabout simple clock shows 6 o'clock, with the hour hand pointing at 6, and the moment hand pointing at 12.
The angle between the hour hand and minute hand is 180°. Then the number of minutes is given as,
In each hour, the hour hand rotates 30°. Then in 8 hours, the hour hand rotation is calculated as,
⇒ 30° x 8
⇒ 240°
After 11 minutes the position of the hour hand is given as,
⇒ 240° + (11 / 60) x 30°
⇒ 240° + 5.5°
⇒ 245.5°
The rotation of the minute hand is given as,
⇒ (360° / 60) x 11
⇒ 66°
Then angle between the hour and the minute hand is calculated as,
Angle = 245.5° - 66°
Angle = 179.5°
Angle ≈ 180°
The number of minutes past 7 o'clock will be 11 minutes.
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Prepare a calibration curve by plotting the measured wavenumbers vs. accepted wavenumbers for the seven Hg lines. Fit the data with a linear function and be sure to report the slope and y-intercept with a reasonable number of significant figures. Use the calibration curve to determine the values for the four H emission lines. Calculate the Rydberg constant for hydrogen using these values. Explain how to make all graphs and do all calculations.
theoretical hg values
17264.37
17327.39
18307.39
22938.1
22995.23
24515.88
24705.3
Theoretical H Values
410.1
434
486.1
656.2
To prepare a calibration curve for the Hg lines, plot the measured wavenumbers against the accepted wavenumbers. Fit the data with a linear function to determine the slope and y-intercept. Then, use the calibration curve to determine the values for the four H emission lines and calculate the Rydberg constant for hydrogen using these values.
Step 1:
To create a calibration curve, plot the measured wavenumbers of the Hg lines on the x-axis and the corresponding accepted wavenumbers on the y-axis. Fit the data points with a linear function to obtain the equation of the line. The slope and y-intercept of the linear function represent the calibration parameters.
Step 2:
The calibration curve provides a relationship between the measured wavenumbers and the accepted wavenumbers for the Hg lines. By fitting the data with a linear function, we can determine the slope and y-intercept, which define the linear relationship. These parameters allow us to convert the measured wavenumbers of unknown samples to their corresponding accepted values.
Step 3:
Using the calibration curve, we can determine the values for the four H emission lines by finding their corresponding measured wavenumbers. By substituting these measured wavenumbers into the linear function obtained from the calibration curve, we can calculate the accepted wavenumbers for the H emission lines.
Step 4:
The Rydberg constant for hydrogen can be calculated using the values obtained for the H emission lines. The Rydberg formula relates the wavenumber of a spectral line to the Rydberg constant, the principal quantum numbers of the initial and final energy levels, and the atomic mass. By rearranging the formula and substituting the known values, we can solve for the Rydberg constant.
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Helppppp with this please
Answer:180
Step-by-step explanation:
hope this helps
Answer:
0.8 mm
Step-by-step explanation:
Given that you require the actual size.
The ant has been magnified by 15 X
To find the actual size divide magnified size by 15
actual size = 12 mm ÷ 15 = 0.8 mm
Find the smallest positive integer value of n for which 225n is a multiple of 540.
The smallest positive integer value of n for which 225n is a multiple of 540 is 8.
To determine the smallest positive integer value of n for which 225n is a multiple of 540, we need to find the least common multiple (LCM) of 225 and 540 and then divide it by 225.
To find the LCM of 225 and 540, we can factor both numbers into primes:
225 = 3^2 x 5^2
540 = 2^2 x 3^3 x 5
The LCM will be the product of the highest powers of each prime factor:
LCM = 2^2 x 3^3 x 5^2 = 1800
Now, we divide the LCM by 225:
1800 / 225 = 8
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Simplify 7x²-x²
how to simplify this maths question
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to simplify the expression \(\large\pmb{7x^2-x^2}\).
\(\triangle~\fbox{\bf{KEY:}}\)
Combine like terms! :)That's exactly what we need to do - combine like terms.
So, we subtract:
\(\star~\large\pmb{7x^2-x^2}\)
Which gives us:
\(\star~\large\pmb{6x^2}\)
Hope it helps you out! :D
Ask in comments if any queries arise.
#StudyWithBrainly
~Just a smiley person helping fellow students :)
Please answer this for me
Answer:
According to my calculations the answer would be C or B
Step-by-step explanation:
Unless I did it incorrectly
Answer:
C
Step-by-step explanation:
30 chose a sandwhich out of 55 students
8x - 4y = -4 solve for y.
The equation 8x - 4y = -4 have y as the subject to be equal to 2x + 1 expresses in terms of x.
How to evaluate for yTo solve for y in the equation 8x - 4y = -4, we must make y the subject and it should be positive as follows;
8x - 4y = -4
add 4y to both sides
8x - 4y + 4y= -4 + 4y
8x = - 4 + 4y
also to make y the subject;
- 4 + 4y = 8x
add 4 to both sides
- 4 + 4 + 4y = 8x + 4
4y = 8x + 4
factorize the right hand side
4y = 4(2x + 1)
divide through by the coefficient of y
4y/4 = [4(2x + 1)]/4
y = 2x + 1
Hence, the equation 8x - 4y = -4 has y = 2x + 1
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How many solutions does this equation have? –7q + 7 = 4 − 4q
- no solution
-one solution
-infinitely many solutions
Answer: One answer
Step-by-step explanation:
help me i don't get math 17 points
Answer:
805.92
Step-by-step explanation:
An ice cube weighs 20 grams. How much will it weigh after it melts?
Answer:well if a ice cub melts its probally gonna be 0
Step-by-step explanation:
im not so good sorry
PLEASE HELP ASAP - ILL GIVE BRAINIEST
Answer:
We know that:
A = lwFactorize the expression for the area and find the missing side
< 10 >Given:
A = x² + 10x + 21w = x + 3Find l:
l = A/w
l = (x² + 10x + 21)/(x + 3) =
(x + 3)(x + 7)/(x + 3 =
x + 7
------------------------------
< 11 >Given:
A = x² + 2x - 8l = x + 4Find w:
w = A/l
w = (x² + 2x - 8)/(x + 4) =
(x + 4)(x - 2)/(x + 4) =
x - 2
What is the domain of the following function represented by ordered pairs? {(4, 9), (–6, 1), (–2, 5), (3, 1)}
Answer:
4, -6, -2, 3
Step-by-step explanation:
Domain is all the x-values in an ordered pair or function
Range is all the y-values in an ordered pair or function
The x-values for this function is 4, -6, -2, 3
This is the domain
The range(y-values) would be 9, 1, 5
Remember to not input repeating values for domain and range. In the range of this function, there are two values of 1, but I only inputted 1, once.
-Chetan K
Help please :). I hate trigonometry
Answer: You shouldn't hate trig.
Step-by-step explanation:
SinΘ= opposite/hypotenuse
SinΘ=y/x
Sin(16) = 9/x
x = 9/Sin(16)
x= 32.7 cm
(4 pts) Solve the inequality graph the sotution and write the answer in interval notation. 2) X + 29/x+3<9
The given inequality is X + 29/x+3<9. We have to solve this inequality, graph the solution and write the answer in interval notation.Steps to solve the inequality:Step 1: Subtract 9 from both sides of the inequality.X + 29/x+3 - 9 < 0Step 2: Bring all the terms to the denominator.X(x+3) + 29 - 9(x+3) / x+3 < 0Simplifying it, (x^2 + 2x - 6x - 3) / (x+3) < 0x^2 - 4x - 3 / x+3 < 0Step 3: Find the critical values. They are the values of x which make the denominator zero. Here, the critical value is x = -3.Step 4: Find the sign of f(x) for values of x less than -3. We will choose x = -4.f(-4) = ((-4)^2 - 4(-4) - 3) / (-4+3) = 7 > 0Therefore, for x < -3, the sign of f(x) is positive (+).Step 5: Find the sign of f(x) for values of x between -3 and 1. We will choose x = 0.f(0) = (0^2 - 4(0) - 3) / (0+3) = -1Step 6: Find the sign of f(x) for values of x greater than 1. We will choose x = 2.f(2) = (2^2 - 4(2) - 3) / (2+3) = -3/5Therefore, for x > -3, the sign of f(x) is negative (-).Step 7: Plot the critical value on the number line. Use an open circle for less than or greater than inequalities and a closed circle for less than or equal to or greater than or equal to inequalities.Step 8: Write the solution in interval notation.(-∞,-3) U (1, 2+√7) U (2-√7, -3+√13) U (-3+√13,∞)The solution of the given inequality is (-∞,-3) U (1, 2+√7) U (2-√7, -3+√13) U (-3+√13,∞).
through: -1,4 and 0,0 point slope
Step-by-step explanation:
the slope = (4-0)/(-1-0) = 4/(-1) = -4
the equation : y = -4x
m = (Y2 - Y1)/(X2 - X1)
m = (0 - 4)/(0 - (-1))
m = -4/(0 + 1)
m = -4/1 = -4
You buy 10 pounds of bird seed at store A for $11.50.Your friend buys 15 pounds of bird seed at Store B for $19.50.How much less would u sped by buying 20 pounds of bird seed at the store with the better deal?
Answer:
$3
Step-by-step explanation:
You buy 10 pounds of bird seed at store A for $11.50 which means every pound is $1.15.
15 pounds of bird seeds store B for $19.50 is $1.30 per pound.
At store A = 20 * $1.15 = $23
At store B = 20 * $1.30 = $26
So, 26 - 23 = 3
Answer:
You would spend $3 less by buying 20 pounds of bird seeds at the store with the better deal.
Step-by-step explanation:
Given:
You can buy 10 pounds of birdseed at Store A for $11.50
10 pounds – $11.50
\(\mathrm{\dfrac{ \$11.50 }{ 10\:pounds }}=\mathrm{\dfrac{ \$1.50 }{ 1\:pound }}\)
1 pound – $1.15
To find the value for 20 pounds, we do:
20 pounds = 20 × 1.15 = $23
20 pounds = $23
Your friend buys 15 pounds of birdseed at Store B for $19.50
15 pounds – $19.50
\(\mathrm{\dfrac{ \$19.50 }{ 15\:pounds }}=\mathrm{\dfrac{ \$1.3 }{ 1\:pound }}\)
1 pound – $1.3
To find the value for 20 pounds, we do:
20 pounds = 20 × 1.3 = $26
20 pounds = $26
Now we compare each stores value for 20 pounds of bird seeds:
$23 < $26
The store with the better deal is: Store A
So, you would spend $3 less by buying 20 pounds of bird seeds at the store with the better deal.
pls answer this as fast as you can
Find asked slope
(See image for problem)
Answer:
D has the positive slope because it's the only line that goes upwards from left to right.
Step-by-step explanation:
which method is best for solving the system of equations,
3x+2y=4
-3x+y=2
The method which is best for solving the system of equations when you remove one variable by adding them is B Elimination
To answer the question, we need to know what system of equations are
What are system of equations?System of equations are pairs of equations that contain two unknowns
Ways of solving system of equationsWe have different ways of solving systems of equations which include
Guess and CheckEliminationGraphing and SubstitutionSince we have the system of equations
3x + 2y = 4
-3x + y = 2
The method which we can use to remove one variable by adding them is the elimination method.
Adding them, we have
3x + 2y = 4
+
-3x + y = 2
3y = 6
y = 6/3
y = 2
So, the method which we can use to remove one variable by adding them is B Elimination
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find the pattern of 1,2,6,18 and state if its arithmetic or geometric
Answer:
its a geometric sequence where each term is 3 times the previous term.
Step-by-step explanation:
{2,6,18,54,162,486,1458...}
3. Missing Digit Look for a pattern and find the missing digit x.
3 2 4 8
7 2 1 3
8 4 x 5
4 3 6 9
i need to get it done right now ... can someone please help with it
The missing digit (x) in the pattern is 3 in the second column and 4 in the fourth row. The completed pattern is as follows:
3 2 4 8
7 2 1 3
8 4 3 5
4 3 6 9
How to find the missing digitTo find the missing digit (x) in the given pattern, let's examine the columns and rows to identify any patterns.
Looking at the columns, we can see that the digits in the second column are increasing by 1 each time: 2, 4, x, 3. Therefore, the missing digit (x) must be 2 + 1 = 3.
Similarly, observing the rows, we notice that the digits in the fourth row are decreasing by 1 each time: 8, 5, x, 9. Thus, the missing digit (x) must be 5 - 1 = 4.
Therefore, the missing digit (x) in the pattern is 3 in the second column and 4 in the fourth row. The completed pattern is as follows:
3 2 4 8
7 2 1 3
8 4 3 5
4 3 6 9
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Evaluate (4/25) 1/2
A 4/5
B 4/25
C2/5
D2/25
2/25
Step-by-step explanation:
\(\begin{aligned}\tt\left(\frac{4}{25}\right)\cdot\frac{1}{2}&=\tt\frac{4}{50}\to(\div~2)\\&=\tt\frac{2}{25}\end{aligned}\)
Please help as fast as you can!!!!
-2 1/3 - 1 3/4=
4=8/3
I hope this helps, I think thin is the right answer
There are 6 × 1012 raindrops in one thunder cloud. Which shows what a calculator would display for the number of raindrops in 5 thunder clouds?
A
1.2E12
B
1.2E13
C
3E12
D
3E13
Answer:
The answer is D
3E13
Step-by-step explanation:
6E12 x 5 = 30E12 or 3E13
Answer:
the answer is Dplease mark brainliest grasiasDetermine whether the sequence converges or diverges. If it converges, find the limit. If it diverges write NONE. (-1)"n 72 +5 a = liman 7200 L -/10 Points] DETAILS SCALCCC4 8.1.023. Determine whether the sequence converges or diverges. If it converges, find the limit. If it diverges write NONE. an = n2e-5 lim an 72-00 –/10 points) DETAILS SCALCCC4 8.1.029. Determine whether the sequence converges or diverges. If it converges, find the limit. If it diverges write NONE. (3n - 1)! (3n +1)! limon 7200
To determine whether the given sequence converges or diverges, we will examine each of the provided sequences and find their respective limits as n approaches infinity.
1. an = (-1)^n
The sequence alternates between -1 and 1 as n increases. Since it does not approach a specific value, the sequence diverges. Your answer for this sequence is NONE.
2. an = n^2 * e^(-n)
To find the limit as n approaches infinity, we can apply L'Hopital's Rule:
lim (n^2) / (e^n) as n approaches infinity.
Applying L'Hopital's Rule twice, we get:
lim (2n) / (e^n) and then lim (2) / (e^n).
As n approaches infinity, the denominator (e^n) increases without bound, so the limit becomes 0. The sequence converges to 0.
3. an = (3n - 1)! / (3n + 1)!
To find the limit as n approaches infinity, let's rewrite the sequence as:
an = 1 / [(3n)(3n + 1)]
As n approaches infinity, the denominator (3n)(3n + 1) increases without bound, and the sequence converges to 0.
In summary:
1. The sequence (-1)^n diverges (NONE).
2. The sequence n^2 * e^(-n) converges to 0.
3. The sequence (3n - 1)! / (3n + 1)! converges to 0.
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Will give brainleist
Answer:
c
Step-by-step explanation:
hope this helps
Answer:
B
Step-by-step explanation:
B has a proportional relationship between "a" and "b" as when you divide corresponding "b" values by their respective "a" values they will always give the same thing, that being 1.25 for this situation
\(25/20=1.25\)
\(30/24=1.25\)
\(40/32=1.25\)
this can also be done in reverse by dividing "a" values by their respective b" values to get the same value every time
Hope this helps
Morgan worked for three weeks during the summer earning money
on Mondays, Tuesdays, Wednesdays, Thursdays and Fridays. The
following matrix represents his earnings.
24 22 32
25 28 30
30 28 32
10 15 19
35 32 30
How much money did Morgan make in the first week?
The amount of money that Morgan was able to make in the first week would be $ 124
How to find the earnings with matrices ?Matrices are mathematical objects which have a rectangular array of numbers, symbols, or expressions laid out in rows and columns. Each element is identified by its row and column location inside the matrix.
The columns have five entries which means that this must be the amount earned per day of a week. The first week earnings would therefore be:
= 24 + 25 + 30 + 10 + 35
= $ 124
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construct a right-angled triangle ABC where angle A =90 degree , BC= 4.5cm and AC= 7cm. please ans fast........ Very urgent. Pls don't give wrong answers
Answer and Step-by-step explanation: The described right triangle is in the attachment.
As it is shown, AC is the hypotenuse and BC and AB are the sides, so use Pytagorean Theorem to find the unknown measure:
AC² = AB² + BC²
\(AB^{2} = AC^{2}-BC^{2}\)
\(AB =\sqrt{AC^{2}-BC^{2}}\)
\(AB =\sqrt{7^{2}-4.5^{2}}\)
\(AB =\sqrt{28.75}\)
AB = 5.4
Then, right triangle ABC measures:
AB = 5.4cm
BC = 4.5cm
AC = 7cm
i need some help 3z2−6z3z2−6z for z=5
Josh bought 6 CDs that were each the same price. Including sales tax, he paid a total of $106.20. Of that total, $5.40 was tax. What was the price of each CD before tax?
Answer:
16.809 was the price of each CD before tax