evaluate the surface integral. s z2 ds, s is the part of the paraboloid x = y2 z2 given by 0 ≤ x ≤ 1
Answers
The solution of the surface integral is ∫∫∫ z² r dz dθ dr
To begin, we first need to parametrize the surface S. A common way to do this is to use cylindrical coordinates (r, θ, z), where r and θ are polar coordinates in the x-y plane and z is the height of the surface above the x-y plane. Using this parametrization, we have:
x = r² cos²θ + z² y = r² sin²θ + z² z = z
To find the limits of integration for r, θ, and z, we use the bounds given in the problem. Since 0 ≤ x ≤ 4, we have 0 ≤ r² cos²θ + z² ≤ 4. Simplifying this inequality gives us:
-z ≤ r cosθ ≤ √(4 - z²)
Since r is always positive, we can divide both sides by r to get:
-cosθ ≤ cosθ ≤ √(4/r² - z²/r²)
The left-hand side gives us θ = π, and the right-hand side gives us θ = 0. For z, we have 0 ≤ z ≤ √(4 - r² cos²θ). Finally, for r, we have 0 ≤ r ≤ 2.
With our parametrization and limits of integration determined, we can now write the surface integral as a triple integral in cylindrical coordinates:
∬ S z² dS = ∫∫∫ z² r dz dθ dr
where the limits of integration are:
0 ≤ r ≤ 2 π ≤ θ ≤ 0 0 ≤ z ≤ √(4 - r² cos²θ)
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Related Questions
Determine whether the differential equation is linear.y′+x√y=x2
Answers
The differential equation is not a linear.
The given differential equation is: y′ + x√y = x^2
To determine if this differential equation is linear, we need to check if it can be written in the standard linear form:
y′ + p(x)y = q(x)
Comparing this standard form with the given equation, we can see that the term x√y prevents the equation from being linear. In a linear equation, the dependent variable y and its derivatives (in this case, y′) must appear with a power of 1, and not be inside any non-linear functions like a square root. Since x√y is a non-linear term, the given differential equation is not linear.
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Your purchase at the store tias come ous to $428.85 before any discounts and before any taxes. As a valued customer you recolve a discount. If the total price after a discount and taxes of 13% was $452.98, then what was the rate of discount you received? Convert to a percent and round to the nearest tenth. Inclide the unit symbol. agt=(1+rt)(1−rjd)p
Answers
The rate of discount is approximately 6.4%.
Given that, the purchase at the store "Tias" come to $428.85 before any discounts and before any taxes.
The total price after a discount and taxes of 13% was $452.98.
The formula to find out the rate of discount is `tag=(1+r*t)(1-r*j)*p`, where `tag` is the total price after a discount and taxes, `p` is the initial price, `r` is the rate of discount, `t` is the tax rate, and `j` is the rate of tax.
So we can say that `452.98=(1-r*0.13)(1+r*0)*428.85`
On solving, we get, `r≈6.4%`
Hence, the rate of discount is approximately 6.4%.
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19(x) = -x – 3, solve for a when g(x) = 6.
solve for x
Answers
Answer:
x=\(-\frac{9}{19}\)
Step-by-step explanation:
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided in the accompanying table. Which of these values for the level of significance is the smallest for which each explanatory variable is significant individually?
Regression Statistics
Multiple R 0.8479
R Square 0.7189
Adjusted R Square 0.7069
Standard Error 17.5571
Observations 50
ANOVA
df SS MS F Significance F
Regression 37043.3236 18521.6618 0.0000
Residual 14487.7627 308.2503 Total 49 51531.0863 Coefficients Standard Error t Stat P-value
Intercept −5.5146 7.2273 −0.7630 0.4493
Income 0.4262 0.0392 10.8668 0.0000
Size 5.5437 1.6949 3.2708 0.0020
Also
SSR(X1|X2)=36400.6326
and
SSR(X2|X1)=3297.7917
A.
0.050
B.
0.001
C.
0.010
D.
0.025
Answers
The smallest value of the level of significance for which each explanatory variable is significant individually is 0.001, which is option B.
In multiple regression analysis, the significance of each explanatory variable is determined by its p-value. The p-value for each variable tells us whether that variable is statistically significant or not. A p-value less than the level of significance (alpha) indicates that the variable is statistically significant. In this problem, the p-value for Income is 0.0000, which is less than any of the given options for alpha, indicating that Income is significant. Similarly, the p-value for Size is 0.0020, which is less than 0.010 but greater than 0.001, indicating that Size is also significant. Therefore, the smallest value of alpha for which both variables are individually significant is 0.001, which is option B.
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5 STARS 20 foot ladder is leaning against the side of a building the bottom of the ladder is 4 feet from the wall the bottom of the ladder is 4 feet from the wall how many feet above the ground does the ladder touch the wall
Answers
Answer:
400
The ladder is the hypotenuse of a right triangle. The 2 feet from the wall on the ground is one side, the distance up the wall is another side.
In a right triangle, the square of the hypotenuse is the sum of the squares of the other two sides. This is called the Pythagorean Theorem. In equation form:
c^2 = a^2 + b^2
Substitute the known values:
20^2 = 2^2 + b^2
Square the numbers:
400 = 4 + b^2
Subtract 4 from both sides:
b^2 = 400 - 4 = 396
Take the square root:
b = sqrt(396) = 19.9 (rounded) feet
Check:
20^2 ?= 2^2 + 19.9^2
400 ?= 4 + 396.01
400 ?= 400.01 (off just a bit due to rounding)
For each set of angles, decide if there is a triangle whose angles have these measures in degrees:
1. 60, 60, 60
2. 90, 90, 45
3. 30, 40, 50
4. 90, 45, 45
5. 120, 30, 30
Select ALL correct set of angles.
A.Set 1
B.Set 2
C.Set 3
D.Set 4
E.Set 5
Answers
Step-by-step explanation:
hope it helps correct me if wrong pa brainliest please
Answer:
set none
Step-by-step explanation:
A student from the community college is selected at random. Find the probability that the student is at last 31. Round approximations to three decimals places
Answers
Answer:
0.077
Step-by-step explanation:
From the table :
Number of students aged 31 - 35 = 60
Number of students over 35 = 26
Total number of students = total possible outcomes = 1123
Required outcome = (students aged 31 - 35) + over 35 = 60 + 26 = 86
Probability = required outcome / Total possible outcomes
Probability (at least 31) = 86 / 1123 = 0.0765
= 0.077 (3 decimal places)
Please help me i dont understand this
A triangle has two sides of length 4 and 7 . What value could the
length of the third side be ? Check all that apply
A. 3
B. 9
C. 11
D. 5
E. 7
F. 17
Answers
Answer:
A, B, D, E
Step-by-step explanation:
The third side of any triangle must be shorter than the other two combined. Thus, answer B and F are incorrect. All the other answers are correct.
Hope this helps.
Which is the better definition of an image?
Answers
The better definition of image for 8.G.A.1a, 8.G.A.1c, and 8.G.A.2 is:
The new position of a point, a line, a line segment, or a figure after a transformation.
How to explain the transformationThis definition is consistent with the standards that state that students should be able to "understand congruence and similarity, and use them to solve problems."
When a point, line, line segment, or figure is transformed, its image is the new position of that object. For example, if a point is reflected across a line, its image will be the point on the opposite side of the line that is the same distance from the line as the original point.
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Calculate the effective interest on £2000 at 3% interest
quarterly after 4 years.
Answers
The effective interest on £2000 at a 3% interest rate compounded quarterly over a period of 4 years is approximately £245.15.
To calculate the effective interest, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment (including interest)
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
n = the number of compounding periods per year
t = the number of years
In this case, the principal amount (P) is £2000, the annual interest rate (r) is 3% (or 0.03 as a decimal), the compounding is done quarterly (n = 4), and the investment period (t) is 4 years.
Plugging the values into the formula:
A = £2000(1 + 0.03/4)^(4*4)
= £2000(1 + 0.0075)^16
= £2000(1.0075)^16
≈ £2000(1.126825)
Calculating the future value:
A ≈ £2253.65
To find the effective interest, we subtract the principal amount from the future value:
Effective Interest = £2253.65 - £2000
≈ £253.65
Therefore, the effective interest on £2000 at a 3% interest rate compounded quarterly after 4 years is approximately £253.65.
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(-2,-5) on a graph. I really need to know.
Answers
Answer:
Step-by-step explanation:
The blue dot is where (-2,-5) is on a graph. Hope this helps!
A company that makes robotic vacuums claims their newest model of vacuum lasts, on average, two hours when starting on a full charge. To investigate this claim, a consumer group purchases a random sample of five vacuums of this model. They charge each unit fully and then measure the amount of time each unit runs. Here are the data (in hours): 2.2, 1.85, 2.15, 1.95, and 1.90. They would like to know if the data provide convincing evidence that the true mean run time differs from two hours. What are the appropriate hypotheses?
H0: μ = 2 versus Ha: μ < 2, where μ = the true mean run time for all vacuums of this model
H0: μ = 2 versus Ha: μ > 2, where μ = the true mean run time for all vacuums of this model
H0: μ = 2 versus Ha: μ ≠ 2, where μ = the true mean run time for all vacuums of this model
H0: μ ≠ 2 versus Ha: μ = 2, where μ = the true mean run time for all vacuums of this model
Answers
Answer:
The answer is C. H0: μ = 2 versus Ha: μ ≠ 2, where μ = the true mean run time for all vacuums of this model
Step-by-step explanation:
EDGE 2021
test the series for convergence or divergence. [infinity] 1 n 9n n = 1
Answers
The given series is convergence and converges to 1/8. The given series is: 1/9 + 1/81 + 1/729 + ….+ 1/(9^n)+……..Using the Geometric progression formula, we have: a = 1/9, r = 1/9.∴ sum of the series = a / (1 - r) = (1/9) / [1 - (1/9)] = (1/9) / (8/9) = 1/8. Hence, the series converges to 1/8.
In mathematics, a series is an infinite sequence of numbers added together. When dealing with infinite sequences, convergences, and divergence become essential concepts. In this problem, we will test the series for convergence or divergence.
To do this, we will use the Geometric progression formula :
The given series is:
1/9 + 1/81 + 1/729 + ….+ 1/(9^n)+……..
Using the Geometric progression formula, we have
a = 1/9
r = 1/9.
∴ the sum of the series
= a / (1 - r)
= (1/9) / [1 - (1/9)]
= (1/9) / (8/9)
= 1/8
Therefore, the series converges to 1/8. In conclusion, the given series converges to 1/8.
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The lines shown below are perpendicular. Find the slope-intercept form of the equation of line y2.
y2
(-3,7)
Y₁ = 3x-6
Answers
Answer:
\(y2 = -\dfrac{1}{3}x + 6\)
Step-by-step explanation:
Perpendicular lines have slopes that when multiplied will result in a value of -1
In other words, the slope of y2 = - 1/(slope of y1)
y1 = 3x - 6
Slope of y1 = 3
So slope of y2 = -1/3
Equation of y2 is of the form
\(y_2 = -\dfrac{1}{3}x_2 + b\)
The line passes through (-3, 7)
To find b plug in y2 = 7, x2 = -3 into the above equation and solve for b
\(7 = -\dfrac{1}{3}(-3) + b\)
=> 7 = 1 + b
b = 7-1 = 6
So the equation of line y2 is
\(y2 = -\dfrac{1}{3}x + 6\)
Hint: If you look at the graph, line y2 crosses at b = 6
We need not have used equations to solve for b but we have to be careful. We can at least the graph value to see if our b value is close to it
A gardener wants to divide a square piece of lawn in half diagonally. what is the length of the diagonal side of the square is 8 fr. leave your answer in simplest radical form.
16√8
2√8
8√2
4
Answers
The answer is option C, 8√2.
The length of the diagonal side of the square is 8 fr. Hence the gardener wants to divide a square piece of lawn in half diagonally, which means to find the length of a diagonal bisector of a square. Let's solve the problem: Length of the diagonal side of the square = 8 fr.
Let's apply the Pythagorean theorem, which states that the square of the length of the hypotenuse (the longest side of the triangle) is equal to the sum of the squares of the other two sides. Therefore, the formula to find the length of the diagonal (d) of the square with side a is given by d = a√2.
Now we can find the length of the diagonal of the square using the formula given above: d = a√2d = 8√2Thus, the length of the diagonal side of the square is 8 fr. Hence the length of the diagonal of the square is 8√2 fr. Therefore, the answer is option C, 8√2.
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What is the answer for this question 5 + (x^2 - xy) - 4
Answers
Answer: x^2−xy+1
Step-by-step explanation:
simplify:
5+x^2−xy−4
5+x^2+−xy+−4
Combine Like Terms:
5+x^2+−xy+−4
(x^2)+(−xy)+(5+−4)
x^2+−xy+1
A car travels 35 km in half an hour. What is the average speed of the car in km/hr?
Answers
Answer:
70 km in an hour
Step-by-step explanation:
35 x 2 is 70
Answer:
Step-by-step explanation:
70km/h
Source: https://www.gigacalculator.com/calculators/average-speed-calculator.php
Find the value of x that makes 25x^2 + 70x + c a perfect square trinomial
Answers
The value of x that makes 25x^2 + 70x + c a perfect square trinomial is c = 1225.
To make the quadratic expression 25x^2 + 70x + c a perfect square trinomial, we need to determine the value of c.
A perfect square trinomial can be written in the form (ax + b)^2, where a is the coefficient of the x^2 term and b is half the coefficient of the x term.
In this case, a = 25, so b = (1/2)(70) = 35.
Expanding (ax + b)^2, we have:
(25x + 35)^2 = 25x^2 + 2(25)(35)x + 35^2
= 25x^2 + 70x + 1225.
Comparing this with the given quadratic expression 25x^2 + 70x + c, we can see that c = 1225.
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Please answer ( GIVING BRAINLIEST)
Answers
Answer:
2.5º per hour
Step-by-step explanation:
2 hours is 5º
so divide 5 by 2
solve 2x^2+3x=-8
-3+/- 11i/4
-3+/- i square root of 55/4
-3+/- i square root of 23
3+/- i square root of 11
Answers
yes or no I am not very sure
Starting at 1:00 p.M., The temperature changes -4 degrees Fahrenheit per hour. Write and solve an equation to find how many hours (x) it will take to reach -1 °F.
Answers
Answer: it will take 5 hours to reach -1 °F.
Step-by-step explanation:
The temperature changes -4 degrees Fahrenheit per hour. This is a linear rate. The rate at which the temperature is decreasing is in arithmetic progression. The formula for determining the nth term of an arithmetic sequence is expressed as
Tn = a + (n - 1)d
Where
a represents the first term of the sequence(the starting point)
d represents the common difference.
n = x = the number of terms in the sequence(number of hours)
From the information given,
a = 0(at 1 pm, number of hours is 0)
d = - 4 degrees (it is decreasing)
Tn = -1 °F.
We want to determine the number of hours, x when Tn = -1 °F
Therefore,
- 1 = 0 + (x - 1)- 4
- 1 = - x + 4
x = 4 + 1
x = 5 hours
IF I SPEND $6,300 OUT OF $21,000 WHAT PERCENT DID I SPEND
Answers
Answer: 30%
Step-by-step explanation: Solution for 6300 is what percent of 21000: 6300:21000*100 = (6300*100):21000 = 630000:21000 = 30. Now we have: 6300 is what percent of 21000 = 30.
if we take 21000(origin amount) to be the 100%, what's 6300 off of it in percentage?
\(\begin{array}{ccll} Amount&\%\\ \cline{1-2} 21000 & 100\\ 6300& x \end{array} \implies \cfrac{21000}{6300}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{10}{3} ~~=~~ \cfrac{100}{x}\implies 10x=300\implies x=\cfrac{300}{10}\implies x=30\)
A research submarine dives at the rate of 6
feet every minute. What will the sub's
elevation be after 5 minutes of diving?
Which expression would describe this?
Answers
Y=5mins(let’s d number of elevation be y)
5x6=30
Y=30fts
a board measures 212 inches. how many feet is this? [ ? ] ft. give your rounded answer with one decimal place.
Answers
The board measures 212 inches which is equal to 17.7 feet.
Measurement:
Measurement is used to identify the quantity of the object.
Each object has its own measurements, like solid objects are measured using grams and the liquid one are measured using liters, etc.
For example,
We can buy the vegetables in grams because they are solid objects.
Instead, we have buy the milk in liters because they are liquid.
Given,
A board measures 212 inches.
Here we need to convert this into feet.
We know that,
1 inch = 0.0833333 feet.
So, 212 inches is equal to,
=> 212 x 0.0833333
=> 17.6667 feet.
Here we have to round the answer with one decimal place.
So, that is,
=> 17.7 feet.
Therefore, the board measurement in feet is 17.7 feet.
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You and three of your friends have stock in a corporation and are interested in voting one of your friends in as a new director for the corporation. There are three director positions open, but your group only owns a minority of the shares of stock in the corporation. Do you think there is anything you and your friends can do to ensure that your candidate for the board of directors wins? no, unless you each agree in writing before the election to all vote the same way yes, if your candidate can get enough publicity no, a majority always wins yes, if the bylaws of the corporation allow you to pool your votes and vote them all for a single candidate
Answers
Yes, if the bylaws of the corporation allow you to pool your votes and vote them all for a single candidate, you and your friends can ensure that your candidate for the board of directors wins, even with a minority of shares.
The bylaws of a corporation outline the rules and procedures governing its operations, including the election of directors. In some cases, the bylaws may allow shareholders to pool their votes and vote them all for a single candidate. This means that if you and your friends collectively own enough shares to secure a majority of the votes, you can consolidate your voting power and ensure the victory of your candidate.
By pooling your votes, you can leverage your collective shares to outweigh the votes of other shareholders and increase the chances of your preferred candidate winning. This strategy enables you to overcome the disadvantage of holding a minority of shares and still have a significant impact on the election outcome.
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What is 5 to the second power
Answers
5^2
5x5=25
5^2=25
answer is 25
Answer: 25
Explanation: Ya welcome.
Choose the equation for the relationship shown in the graph.
A) y = x + 50
B) y = x – 50
C) y = 50 - x
D) x = 50 - y
Answers
Answer:
B) y = x - 50
Step-by-step explanation:
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Which is the balanced equation for S3 + O2 – SO2?
O O O O
S8 + 016 — 8S02
Se + O₂ → S₂ + O2
Se + O₂ → S₂0₂
Sg + 802 – 8802
Answers
S3 + 3O2 ——-> 3SO2
A recipe that makes 50 cookies calls for 1/5 cup of sugar and 5/6 cup offlour. The chef wants to proportionally increase the amount to get anew recipe using one cup of sugar. Using the new recipe, howmuch flour should the chef use? Give your answer as an improperfraction.
Answers
The given recipe that makes 50 cookies calls for 1/5 cup of sugar and 5/6 cup of flour. The chef wants to proportionally increase the amount to get a new recipe using one cup of sugar.
Let the new amount of flour be x.Then the new recipe using one cup of sugar should be in the ratio of (1/5)/1 = (x)/(5/6)Multiplying both sides by 5/6, we get:x = (5/6) * (1/5) * 1x = 1/6.
Therefore, the chef should use 1/6 cup of flour in the new recipe to make one cup of sugar.This is the final answer to the question.Let the new amount of flour be x.Then the new recipe using one cup of sugar should be in the ratio of (1/5)/1 = (x)/(5/6)Multiplying both sides by 5/6, we get:x = (5/6) * (1/5) * 1x = 1/6.
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in a small village of 300 residents, 190 own their home, and 110 rent. if a random sample of 20 residents is selected, then:
Answers
The probability of selecting 19 homeowners and 1 renter in a random sample of 20 residents in a small village with 190 homeowners and 110 renters.
To calculate the probability of randomly selecting a homeowner and a renter from a small village of 300 residents with 190 homeowners and 110 renters in a sample of 20 residents, follow these steps:
1. Calculate the probability of selecting a homeowner (P(homeowner)).
P(homeowner) = Number of homeowners / Total number of residents = 190 / 300
2. Calculate the probability of selecting a renter (P(renter)).
P(renter) = Number of renters / Total number of residents = 110 / 300
3. Calculate the number of ways to choose 19 homeowners and 1 renter from the sample (Combination).
C(190,19) × C(110,1) = (190! / (19! × (190-19)!)) × (110! / (1! × (110-1)!))
4. Calculate the number of ways to select a random sample of 20 residents (Combination).
C(300,20) = 300! / (20! × (300-20)!)
5. Calculate the probability of selecting 19 homeowners and 1 renter from the random sample of 20 residents.
Probability = (C(190,19) × C(110,1)) / C(300,20)
By calculating these values, you will find the probability of selecting 19 homeowners and 1 renter in a random sample of 20 residents in a small village with 190 homeowners and 110 renters.
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