Pls help with my homework

Double integration in polar coordinates involves integrating a function over a two-dimensional region in the polar coordinate system. This is done by setting up a double integral in terms of r and θ, and integrating first with respect to r and then with respect to θ.

Double integration in polar coordinates involves integrating a function over a two-dimensional region in the polar coordinate system. The steps to double integrate a function in polar coordinates are as follows:

1. Determine the limits of integration for r and θ. These limits define the region over which the function will be integrated. Typically, the limits are determined by the boundaries of the region in the xy plane.

2. Write the function to be integrated in terms of r and θ. The function must be expressed in polar coordinates for integration in polar coordinates.

3. Set up the double integral by writing the function in polar coordinates, multiplying by the appropriate factors of r and integrating with respect to r first and then θ.

4. Integrate the function with respect to r, using the limits of integration for r determined in step 1.

5. Integrate the result from step 4 with respect to θ, using the limits of integration for θ determined in step 1.

The general form of a double integral in polar coordinates is:

∫∫f(r, θ)r dr dθ

where f(r, θ) is the function to be integrated, and r and θ are the polar coordinates.

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Answer

3.26$

Step-by-step explanation:

The null and alternative hypotheses for the fruit lover's hypothesis test can be stated as follows:

Null Hypothesis (H0): The actual mean number of segments is equal to or less than the historic value.

Alternative Hypothesis (Ha): The actual mean number of segments is greater than the historic value.

The null hypothesis (H0) assumes that there is no significant difference between the actual mean number of segments and the historic value. It suggests that any observed difference is due to random chance or sampling variability.

On the other hand, the alternative hypothesis (Ha) proposes that the actual mean number of segments is greater than the historic value. This hypothesis suggests that there is a meaningful and significant difference between the two means, indicating a potential increase in the number of segments.

By setting up these hypotheses, the fruit lover can conduct a hypothesis test to examine the evidence and determine whether there is enough statistical evidence to reject the null hypothesis in favor of the alternative hypothesis.

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Answer:

8(7-p)

Step-by-step explanation:

pull out greatest common factor

The measure of angle BC (m ∠BC) is 90°

From the question, we are to determine the measure of angle BC

From the given information, we have that

B P ⊥ P C

This means line BP is perpendicular to line PC

The angle between two perpendicular lines is 90°

Hence, the measure of angle BC (m ∠BC) is 90°.

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Graphically, the two lines will appear as two distinct lines running parallel to each other, never intersecting.

Mathematical statements known as algebraic rules connect two variables and are expressed as equations. One of the algebraic constants is area = length x width. As a result of a set of factors, you can also develop your own rule.

To solve the system of equations:

3x - 2y = 8

6x - 4y = 12

We can simplify the second equation by dividing both sides by 2:

3x - 2y = 8

3x - 2y = 6

Now we can see that the two equations represent two parallel lines with the same slope (-3/2) and different y-intercepts (4 and 3).

Since the two lines are parallel, they will never intersect and therefore there is no solution to the system of equations.

Graphically, the two lines will appear as two distinct lines running parallel to each other, never intersecting.

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We have the formulas for Bt and Dt using only the per capita rates (bt or dt) and population size (Nt) at time t:
Bt = bt * Nt, Dt = dt * Nt. These formulas allow  calculate absolute number of births (Bt) and deaths (Dt) using the given per capita rates and population size.

To find the formulas for Bt and Dt using the given per capita rates (bt or dt) and population size (Nt) at time t, we can rearrange the provided equations for per capita birth rate (bt) and per capita death rate (dt). Here are the steps:
The per capita birth rate (bt) is given by the equation bt = Bt/Nt. To find Bt, we need to isolate it by multiplying both sides of the equation by Nt. This gives us:
  Bt = bt * Nt
Similarly, the per capita death rate (dt) is given by the equation dt = Dt/Nt. To find Dt, we need to isolate it by multiplying both sides of the equation by Nt. This gives us:
  Dt = dt * Nt
Now, we have the formulas for Bt and Dt using only the per capita rates (bt or dt) and population size (Nt) at time t:
- Bt = bt * Nt
- Dt = dt * Nt
These formulas allow you to calculate the absolute number of births (Bt) and deaths (Dt) using the given per capita rates and population size at a specific time.

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The practical range of the function is between $100 and $625.

This can be calculated using the formula y=10x, where x is the number of subscriptions sold each week and y is the amount of money earned. To calculate the amount of money earned for selling t subscriptions each week, we can use the formula y = 10t. This can be interpreted as saying the amount of money (y) is equal to 10 times the number of subscriptions sold (t). For example, if Clarence sells 15 subscriptions each week, then we can calculate the amount of money he earns by plugging in t = 15. y = 10(15) = 150. This means Clarence earns $150 each week by selling 15 subscriptions. For example, if Clarence sells 10 subscriptions each week, he would earn $100 (10 x 10 = 100). If he sells 25 subscriptions each week, he would earn $625 (25 x 25 = 625). The practical range of the function is therefore $100 to $625.

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Answer:

The angles are supplementary.

x 50° x = 180°

Step-by-step explanation:

Answer:

Hi, don't worry, I am not one of those persons who want to answer just because of points. Please look in the chat. Brainliest please...

Step-by-step explanation:

The slope of the tangent line to the level curve of the paraboloid f(x, y) = \(16 - x^2/4 - y^2/16\) at point P(0, 16) is 0. Additionally, the tangent line is orthogonal (perpendicular) to the gradient at that point.

To compute the slope of the tangent line at point P, we need to find the partial derivatives of f(x, y) with respect to x and y. The partial derivative with respect to x is -x/2, and the partial derivative with respect to y is -y/8. Evaluating these derivatives at point P, we have df/dx = 0 and df/dy = -2. Therefore, the slope of the tangent line at P is given by the ratio of these derivatives, which is 0/(-2) = 0.

To verify that the tangent line is orthogonal to the gradient at point P, we need to compute the gradient of f(x, y) and evaluate it at P. The gradient of f(x, y) is given by (∂f/∂x, ∂f/∂y), which in this case is (-x/2, -y/8). At point P, the gradient is (0, -2). The dot product of the gradient and the tangent line's slope is (0, -2) · (0, 0) = 0, indicating that the tangent line is orthogonal to the gradient.

In summary, the slope of the tangent line to the level curve at point P(0, 16) is 0, and the tangent line is orthogonal to the gradient of the paraboloid at that point.

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Answer:

16.8

Step-by-step explanation:

Answer:

None really look like a solution. I mean, that's what I think, honestly.

Answer:

The Value of 9a+6b is 27. and the value of 4x+3y is 30.

Explanation

1)

3a+2b=9

multiplying both by side by 3

or, 3×( 3a+2b)=3×9

Hence, 9a+6b=27

2)

8x+6y=60

Dividing both by side by 2

or, (8x+6y)/2 = 60/2

Hence, 4x+3y=30

Answer:

x = 2

Step-by-step explanation:

Any lower base angle is supplementary to any upper base angle, then

51x + 3 + 75 = 180

51x + 78 = 180 ( subtract 78 from both sides )

51x = 102 ( divide both sides by 51 )

x = 2

its the first one

a system can only be a function if there is only one value of y for each value of x. there cannot be two or more values of y for one single value of x in a function.

Answer:

The water level decreased by 1/18 inches each hour.

Step-by-step explanation:

A rate of change is a rate that describes how one quantity changes in relation to another quantity. Between 11 P.M. and 8:54 A.M.​, the water level in a swimming pool decreased by 11/20, for each hour it decreases by 33/554

A rate of change is a rate that describes how one quantity changes in relation to another quantity.

Given that,  Between 11 P.M. and 8:54 A.M.​, the water level in a swimming pool decreased by 11/20. Assuming that the water level decreased at a constant​ rate, we need to find the amount of water level drop each​ hour.

In an hour we will have sixty minutes.

We need to calculate the number of minutes between 11 pm and 8: 54 am.

The minutes between 11 P.M. and 8:54 A.M. is 594 minutes.

So in 554 min water level drop is 11/20.

So in 1 min=11/20×1/554

So in 60 min

We need to multiply with sixty

= 60(11/20×1/554)

We need to solve 60(11/20×1/554), we get

=3(11/554)

3 times of eleven  by five hundred fifty four.

=33/554

Hence 33/554  water level drop each​ hour when water level decreased at a constant​ rate.

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Answer:

20x^2+7x−6

Step-by-step explanation:

Answer:

The slope is 2. It represents the price of the cookies.

Step-by-step explanation:

The slope is 2 because its in frount of the x and 2 is the price of the cookies.

Answer:

Wrong values are plotted in the question statement graph.

Please find correct graph.

Step-by-step explanation:

Given that:

\(y =x+3\) and \(-1<x<5\)

i.e. we can put a value of x in the equation which is greater than -1 and lesser than 5.

OR

we can say, the points where x = -1 and x = 5 will not be included in the graph (they will be shown as hollow circle).

Now, let us put the values one by one:

x = -1, y = -1 + 3 =2

x = 0, y = 0 + 3 = 3

x = 1, y = 1 + 3 = 4

x = 2, y = 2 + 3 = 5

x = 3, y = 3 + 3 = 6

x = 4, y = 4 + 3 = 7

x = 5, y = 5 + 3 = 8

Therefore, the table of values become:

\(\begin{center}\begin{tabular}{ c c } x & y\\ -1 & 2\\ 0 & 3 \\ 1 & 4 \\ 2 & 5 \\ 3 & 6 \\ 4 & 7 \\5 & 8\\\end{tabular}\end{center}\)

Points (-1, 2) and (5, 8) will not be included in the graph.

Please find attached corrected graph.

The diameter of the circle is approximately 60 inches.

To explain further, we can use the formula relating the central angle of a sector to the length of its intercepted arc. The formula states that the length of the intercepted arc (A) is equal to the radius (r) multiplied by the central angle (θ) in radians.

In this case, we are given the central angle (225 degrees) and the length of the intercepted arc (30π inches).

To find the diameter (d) of the circle, we need to find the radius (r) first. Since the length of the intercepted arc is equal to the radius multiplied by the central angle, we can set up the equation 30π = r * (225π/180). Simplifying this equation gives us r = 20 inches.

The diameter of the circle is twice the radius, so the diameter is equal to 2 * 20 inches, which is 40 inches. Therefore, the diameter of the circle is approximately 60 inches.

In summary, by using the formula for the relationship between central angle and intercepted arc length, we can determine the radius of the circle. Doubling the radius gives us the diameter, which is approximately 60 inches.

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Answer:

m = 0

y intercept = 1

Step-by-step explanation:

The given equation of the line is ,

\(\implies y = 1\)

We know that the Standard equation of Slope Intercept Form of the line is,

\(\implies y = mx + c\)

Where ,

On comparing to the Standard form of the line we get ,

\(\implies Slope = 0 \)

\(\implies y - intercept= 1\)

Slope of the line is 0, since y=mx+c, if m = 0, then y = c, where the constant (c)=1

y intercept of the line is y = 1.

Answered by GAUTHMATH

The probability of receiving grade in statistics or mathematics using the given probabilities is equal to 0.69.

As given in the question ,

Probability of grade in statistics  S 'P(S)' = 57%

                                                                  = 0.57

probability of grade in mathematics M 'P(M)' = 36%

                                                                          = 0.36

Probability of getting grade in both statistics and mathematics

' P(S∩M)' = 24%

                = 0.24

Probability of getting grade in statistics or mathematics 'P(S∪M)'

= P(S) + P(M) - P(S∩M)

Substitute the values of the probabilities of P(S), P(M) and P(S∩M) in the formula to get the probability of  P(S∪M) we have,

= 0.57 + 0.36 - 0.24

= 0.69

Therefore, the probability of the receiving  grade in statistics or mathematics is given by P(S∪M) = 0.69.

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Answer:

125-x

Step-by-step explanation:

i don't know what exactly you're aiming for, but if you want to write this as an equation, you would put it as 125-x. since we don't know what the number is, we would put a variable that we can sub in any number we want.

hope this made sense!

The phrase "decreased by" means subtraction. Also whenever you see "a number", you can think of x. So we have 125 - x is the answer. Just be careful in this section, the terms "from" and "less than" will require you to change the order that you see in the question. For us, the phrase was "decreased by" so we didn't need to change the order. The 125 was in front and the "number" was in the back. EXTRA: "125 from a number" would be x - 125 because you would have to switch the order.

We can observe

Its a geometric progression having first term 9(3)=27 and common ratio as 1/3

So

The firmula is

Option C

Answer:

\(a_n=27\left(\dfrac{1}{3}\right)^{n-1}\)

Step-by-step explanation:

From inspection of the graph, the given points are:

If we draw a line through the given points, the line is a curve rather than a straight line. If the line was a straight line, the graph would be modeled as an arithmetic sequence. Therefore, as the line is a curve, the given points are modeling a geometric sequence.

General form of a geometric sequence:

 \(a_n=ar^{n-1}\)

where:

Rewrite the given points as terms of the sequence:

To find the common ratio r, divide consecutive terms:

\(\implies r=\dfrac{a_3}{a_2}=\dfrac{3}{9}=\dfrac{1}{3}\)

Calculate the first term (a) by substituting the found value of r and the given values of one of the terms into the formula:

\(\implies a_2=9\)

\(\implies a\left(\dfrac{1}{3}\right)^{2-1}=9\)

\(\implies \dfrac{1}{3}a=9\)

\(\implies a=27\)

Substitute the found values of r and a into the general formula to create the sequence modeled by the graph:

\(a_n=27\left(\dfrac{1}{3}\right)^{n-1}\)

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Answer:

True false true

Step-by-step explanation:

Answer:

Individual ratings variation from average ratings for apple devices, is on average 3.762.

Step-by-step explanation:

Standard Deviation is a measure of dispersion, around the average value (mean).

Formula : Σ  I (x - u)^2 I   , where u = mean, n = no. of units

                        n

Standard Deviation of the ratings for Apple devices is 3.762, implies that :-

Individual ratings variation from average ratings for apple devices, is on average 3.762.

P(B∣A) is approximately 0.310, rounded to three decimal places.

To find the probability P(B∣A), we can use Bayes' theorem:

P(B∣A)= P(A) / P(A∣B)⋅P(B)

Given information:

P(B)=0.2

P(A∣B)=0.9

P(B')=0.8 (probability of not B)

P(A∣B′)=0.5 (probability of A given not B)

First, we need to calculate

P(A), the probability of event A. We can use the law of total probability to express P(A) in terms of the probabilities related to B and not B:

P(A)=P(A∣B)⋅P(B)+P(A∣B′)⋅P(B′)

Substituting the given values:

P(A)=0.9⋅0.2+0.5⋅0.8=0.18+0.4=0.58

Now, we can substitute the known values into Bayes' theorem:

P(B∣A)= P(A)/ P(A∣B)⋅P(B)

= 0. 9.0.2 / 0.58

Calculating this expression:

P(B∣A)≈ 0.5 80.18 ≈0.310

Therefore, P(B∣A) is approximately 0.310, rounded to three decimal places.

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The derivative dy/dx of the equation ysin(x^2) = xsin(y^2) is given by (sin(y^2) - ycos(x^2)2x) / (sin(x^2) - 2yxcos(y^2)).

In the given equation, y and x are both variables, and y is implicitly defined as a function of x. To find dy/dx, we differentiate each term using the chain rule and product rule as necessary.

Differentiating the left-hand side of the equation, we apply the product rule to ysin(x^2). The derivative of ysin(x^2) with respect to x is dy/dxsin(x^2) + ycos(x^2)*2x.

Differentiating the right-hand side of the equation, we apply the product rule to xsin(y^2). The derivative of xsin(y^2) with respect to x is sin(y^2) + x*cos(y^2)2ydy/dx.

Now we have two expression for the derivative of the left and right sides of the equation. To isolate dy/dx, we can rearrange the terms and solve for it.

Taking the derivative of ysin(x^2) = xsin(y^2) with respect to x using implicit differentiation yields:
dy/dxsin(x^2) + ycos(x^2)2x = sin(y^2) + xcos(y^2)2ydy/dx.

By rearranging the terms, we can solve for dy/dx:
dy/dx * (sin(x^2) - 2yxcos(y^2)) = sin(y^2) - y*cos(x^2)*2x.

Finally, we can obtain the value of dy/dx by dividing both sides by (sin(x^2) - 2yxcos(y^2)):
dy/dx = (sin(y^2) - ycos(x^2)2x) / (sin(x^2) - 2yxcos(y^2)).

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The radius of convergence is 0, and the interval of convergence is the single point x = 0.

To obtain the radius of convergence and interval of convergence of the series we can use the ratio test.

\(\[ \sum_{n=1}^{\infty} \frac{2 \cdot 4 \cdot 6 \cdots (2n)}{3 \cdot 5 \cdot 7 \cdots (2n+1)}x^{2n+1} \]\)

The ratio test states that if \(\( L = \lim_{n \to \infty} \left| \frac{a_{n+1}}{a_n} \right| \)\), then the series converges if \(\( L < 1 \)\) and diverges if \(\( L > 1 \). If \( L = 1 \)\), the test is inconclusive.

Let's calculate the limit:

\(\[ L = \lim_{n \to \infty} \left| \frac{\frac{2 \cdot 4 \cdot 6 \cdots (2(n+1))}{3 \cdot 5 \cdot 7 \cdots (2(n+1)+1)}x^{2(n+1)+1}}{\frac{2 \cdot 4 \cdot 6 \cdots (2n)}{3 \cdot 5 \cdot 7 \cdots (2n+1)}x^{2n+1}} \right| \]\)

Simplifying the expression:

\(\[ L = \lim_{n \to \infty} \left| \frac{(2n+2)(2n+1)x^{2n+3}}{(2n+1)(2n)x^{2n+1}} \right| \]\)

\(\[ L = \lim_{n \to \infty} \left| \frac{(2n+2)x^2}{x^2} \right| \]\)

\(\[ L = \lim_{n \to \infty} 2(n+1) = \infty \]\\\)

Since the limit is infinity, the series diverges for all values of  x , except when x = 0 and hence the radius of convergence is 0, and the interval of convergence is the single point x = 0.

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