assume that all the given functions have continuous second-order partial derivatives. if z = f(x, y), where x = r2 s2 and y = 9rs, find ∂2z/(∂r ∂s). (compare with this example.)

To use the Integral Test to determine whether the series is convergent or divergent, we need to evaluate the integral ∫(xe^(-9x) dx) from 1 to ∞.

Let's evaluate the integral first:

∫(xe^(-9x) dx) from 1 to ∞

We use integration by parts for this, where:

u = x, dv = e^(-9x) dx
du = dx, v = -1/9 e^(-9x)

According to the integration by parts formula, ∫u dv = uv - ∫v du.

So, ∫(xe^(-9x) dx) = -1/9 x e^(-9x) - ∫(-1/9 e^(-9x) dx)

Now, we can integrate -1/9 e^(-9x) dx:

∫(-1/9 e^(-9x) dx) = (-1/9) * (-1/9) * e^(-9x) = 1/81 e^(-9x)

Thus, our integral becomes:

-1/9 x e^(-9x) - 1/81 e^(-9x)

Now we must evaluate the integral from 1 to ∞:

lim (x→∞) [ -1/9 x e^(-9x) - 1/81 e^(-9x) ] - [ -1/9 (1) e^(-9) - 1/81 e^(-9) ]

Since the exponential term e^(-9x) approaches 0 as x approaches ∞, the limit becomes:

0 - [ -1/9 e^(-9) - 1/81 e^(-9) ] = 1/9 e^(-9) + 1/81 e^(-9)

Since the integral is finite, the series is convergent.

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Answer:

Cam has b-7 dollars

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

840 are  4-letter passwords can be formed using the letters by permutation .

What are some examples of permutation?

We are to count all possible 4-letter passwords that can be generated from the letters a, b, c, d, e, f, g .

There are 7 letters in total.

      n = 7 r = 4

 P(n , r ) = 7!/( n - r )!

  P( 7 ,4 ) = 7!/( 7 - 4)!

              = 7!/3!

             = 7 * 6 * 5 * 4 * 3 * 2 * 1/3!

              = 7 * 6 * 5 * 4

               = 840

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Answer:

(-9,2)

Step-by-step explanation:

The rule for reflecting over the x axis is

(x,y)→(x,−y)

(-9, -2) becomes ( -9, - -2) = (-9,2)

Answer:

(-9,2)

Step-by-step explanation:

It will be -9,2 because when you reflect across x axis you change the y axis not the x axis because if you imagine it it works like that

From the question

The probability a student at school A is in grade 10 is

From the table

Number of students in grade 10 at school A = 25

Total number of students in School A = 120

Therefore

The probability a student at school A is in grade 10 is

Hence, The probability a student at school A is in grade 10 is 5/24

The probability a student at school B is in grade 10 is

From the table

Number of students in grade 10 at school B = 20

Total number of students in School A = 80

Therefore

The probability a student at school B is in grade 10 is

Hence, The probability a student at school B is in grade 10 is 1/4

Since, the probability a student at school B is in grade 10 is greater than the probability a tudent at school A is in grade 10 then

It is less like

Answer:

92F

Step-by-step explanation:

the record high January temperature in Austin, Texas, is 90F. the record low January temperature is -2F. Find the difference between the high and low temperatures.

= 90 - (-2)

= 90 + 2

= 92F

Answer: F. n = s/180 + 2

Step-by-step explanation:

         To find the equation that solves for n, we will isolate the n variable.

Given:

     S = (n - 2) x 180

Divide both sides of the equation by 180:

     \(\frac{S}{180}\) = n - 2

Add 2 to both sides of the equation:

     \(\frac{S}{180}\) + 2 = n

Reflexive property:

    n = \(\frac{S}{180}\) + 2

                   F. n = s/180 + 2

The exact values of the trigonometric functions are (a) cos(19π/6) = √3/2,

(b) cos(-7π/6) = -√3/2, (c) cos(-11π/6) = -√3/2

To find the exact values of the trigonometric functions at the given angles, we can use the unit circle and the periodicity and symmetry properties of the functions.

(a) cos(19π/6):

First, we note that 19π/6 is equivalent to 18π/6 + π/6, which is equivalent to 3π + π/6. Since cosine has period 2π, we can reduce 3π to π and write:

cos(19π/6) = cos(3π + π/6) = cos(π/6) = √3/2

(b) cos(-7π/6):

We can use the symmetry property of cosine to write:

cos(-7π/6) = cos(π - 7π/6) = -cos(π/6) = -√3/2

(c) cos(-11π/6):

We can again use the symmetry property of cosine to write:

cos(-11π/6) = cos(π - 11π/6) = -cos(π/6) = -√3/2

Therefore, the exact values of the trigonometric functions are:

(a) cos(19π/6) = √3/2

(b) cos(-7π/6) = -√3/2

(c) cos(-11π/6) = -√3/2

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Using the simplex method, the optimal solution for the given linear program is z = 14, with x1 = 0 and x2 = 5. There are no alternative optimal solutions.

To solve the linear program using the simplex method, we start by converting the problem into standard form with all constraints in the form of inequalities and non-negative variables. The initial tableau for the problem is as follows:

 |   x1  |   x2  |   s1   |   s2   |   b   |

--------------------------------------------

z |  -3   |   6   |   0    |   0    |   0   |

--------------------------------------------

s1|   5   |   7   |   1    |   0    |   35  |

--------------------------------------------

s2|  -1   |   2   |   0    |   1    |   2   |

--------------------------------------------

Next, we perform the simplex iterations to improve the objective function value. After performing the necessary row operations, we arrive at the final tableau:

 |   x1  |   x2  |   s1   |   s2   |   b   |

--------------------------------------------

z |   0   |   1   |  3/2   |  -1/2  |   14  |

--------------------------------------------

s1|   0   |   0   |   4    |   3    |   5   |

--------------------------------------------

s2|   1   |   0   |  -1/2  |   5/2  |   3   |

--------------------------------------------

From the final tableau, we can see that the optimal solution is z = 14, with x1 = 0 and x2 = 5. The decision variable x1 is at its lower bound, indicating that it is non-basic. Therefore, there are no alternative optimal solutions in this case.

In summary, the optimal solution for the given linear program is z = 14, with x1 = 0 and x2 = 5. There are no alternative optimal solutions.

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Answer:

The fourth graph to the right.

Step-by-step explanation:

Answer:

75+5n

Step-by-step explanation:

Answer:

A) X= 6

B) X = 33

Step-by-step explanation:

You can use the power rule for derivatives for each problem (though you could also use the product rule for the fourth curve).

y = x ² + 6x - 1   ==>   dy/dx = 2x + 6

y = x ² - 5x + 1   ==>   dy/dx = 2x - 5

y = 2 - 4x - x ²   ==>   dy/dx = -4 - 2x

y = (1 + x) (7 - x) = 7 + 6x - x ²   ==>   dy/dx = 6 - 2x

--

or, using the product rule,

dy/dx = (1 + x) (-1) + 1 (7 - x) = -1 - x + 7 - x = 6 - 2x

--

Now, stationary points occur where the derivative is zero. We have

2x + 6 = 0   ==>   x = -3

2x - 5 = 0   ==>   x = 5/2

-4 - 2x = 0   ==>   x = -2

6 - 2x = 0   ==>   x = 3

Answer:

14

Step-by-step explanation:

substitute -2 into x in the equation

f(x) = -x^2 - 9x

f(-2) = -(-2)^2 - 9(-2)

f(-2) = 14 after calculation

Answer:

x=11

Step-by-step explanation:

The angles are opposite interior angles and opposite interior angles are equal when the lines are parallel.

4x = 2x+22

Subtract 2x from each side

4x -2x = 2x+22-2x

2x = 22

Divide by 2

2x/2  =22/2

x = 11

To simplify a radical expression, you can use a few different techniques. One common technique is to factor the expression under the radical sign (the radicand) as much as possible.

Another technique you can use is to use the properties of radicals. For example, you can use the product property of radicals to combine like terms under the radical sign

You can also use the quotient property of radicals to divide out a factor under the radical sign. Finally, some radicals are unsimplifiable by these methods. You can approximate a value of radical or try to get it in a form of fraction with radical.

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Answer:

x =4

Step-by-step explanation:

so pretty much you're give the values for theta and phi, so all you have to do is insert the values in their corresponding position and simplify it. After the simplification process, the answer should be no less or more than 4.

Answer:

the answer is 4

Step-by-step explanation:

by simplification;

=》

\( \frac{a + b}{a - b} \)

** putting the value of a and b :-

=》

\( \frac{5 + 3}{5 - 3} \)

=》

\( \frac{8}{2} \)

=》

\(4\)

Answer: Pretty sure 8 feet and 3 inches

Step-by-step explanation: I think this because 40 inches is 3 feet and 4 inches 5'4 - 2 feet is 3'4 so their is a 2 feet difference so the shadow is 75 inches long which is equal to 6'3 so you do 6'3+2feet you get you answer 8 feet 3 inches

Answer:

b = \(\frac{a}{c}\)

Step-by-step explanation:

\(\frac{a}{b}\) = c ( multiply both sides by b )

a = bc ( isolate b by dividing both sides by c )

\(\frac{a}{c}\) = b

Since η² ≈ 0.33 and not 0.50, the statement "If an analysis of variance produces SS between = 20 and SS within = 40, then η² = 0.50" is false.

ANOVA, or Analysis of Variance, is a statistical method used to compare the means of two or more groups to determine if there are any statistically significant differences between them. It is commonly used in experimental and observational studies to analyze the variance between group means and within-group variability.

ANOVA tests the null hypothesis that the means of the groups are equal, against the alternative hypothesis that at least one of the group means is different. It calculates the F-statistic, which compares the between-group variability to the within-group variability. If the F-statistic is large enough and exceeds a critical value, it indicates that there is evidence to reject the null hypothesis and conclude that there are significant differences between the group means.

We can determine if η² = 0.50 is true or false by calculating the effect size η² using the provided SS between and SS within values.
η² = SS_between / (SS_between + SS_within)
η² = 20 / (20 + 40)
η² = 20 / 60
η² = 1/3 ≈ 0.33
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True, the eta-squared value is indeed 0.50, indicating that 50% of the total variance is accounted for by the between-group variation.

The formula to calculate eta squared (η2) is:
η2 = SSbetween / (SSbetween + SSwithin)
If SSbetween = 20 and SSwithin = 40, then:
η2 = 20 / (20 + 40) = 0.5
Therefore, η2 = 0.50, which means that 50% of the total variance in the dependent variable can be attributed to the independent variable (or factor) being analyze. The statement "If an analysis of variance produces SS between = 20 and SS within = 40, then η 2 = 0.50" is true. To determine η 2 (eta-squared), you'll need to calculate the proportion of total variance explained by the between-group variation. This can be done using the formula η 2 = SS between / (SS between + SS within). In this case, η 2 = 20 / (20 + 40) = 20 / 60 = 0.50. Therefore, the eta-squared value is indeed 0.50, indicating that 50% of the total variance is accounted for by the between-group variation.

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Answer: C: Expression B and D

Step-by-step explanation:

Say the item is $100. 20% of 100 is equal to 100 (20/100)

When you simplify, it equals 20. So 20% of 100 is 20. This $20 is the amount of discount you receive.

So you have to subtract $20 from the $100 to find the sale price. The sale price is $80.

Now plug in 100 for p in each equation. The equation that equals 80 is the answer.

Only equation B and D equals 80 when 100 is plugged in.

The statement 2 is subtracted from the product of 5 and a number is

5x - 2.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, A statement an unknown number 'x' 2 is subtracted from the product of 5 and a number.

∴ 5×x - 2.

= 5x - 2 is the numerical expression.

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In system equation method,

a) Amount of red portion = 240 ml.

b) There are 300 mL of blue potion used and 100 mL of red potion used.

c)  There is a ratio of 2 (blue potion):1 (red potion), there will be a 35% amount of magical syrup.

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

(a)  We can use a system equation here to solve this.

Let x=amount of red potion used

Let y=total amount of potion in solution

Then,

=>200 + x =  y

=> 0.15(200) + 0.75x = 0.25y

0.15(200) because 15% of the blue potion=.15 and there is 200mL.

0.75x because 75% of the red potion=.75 and there is x amount of it

0.25y because we want 25% of the total potion=.25 and there is y amount of it.

We can substitute for y in the second equation:

=>0.15(200) + 0.75x = 0.25(200 + x)

=> 30 + 0.75x = 50 + 0.25x

=> -20 = -0.5x

=> x = 40

Knowing that x=40, we know that y=240, meaning our answer is 240.

b.) We can again use a system for this problem

Let x=Amount of red potion

Let y=Amount of blue potion

=> x + y = 400

=> 0.3(400) = 0.15y + 0.75x

0.3(400)=30% of the 400 mL

0.15y=15% of the magic syrup

0.75x=75% of the magic syrup

We can substitute for x in this equation:

=>120 = 0.15y + 0.75(400 - y)

120 = 0.15y + 300 - 0.75y

-180 = -0.6y

y = 300, x = 100

There are 300 mL of blue potion used and 100 mL of red potion used.

c.) Let x=amount of red potion

Let y=amount of blue potion

=> 0.15x + 0.75y = 0.35(x + y)

0.35(x+y) because the total amount of the potion is x+y

=>0.15x + 0.75y = 0.35x + 0.35y

0.4y = 0.2x

2y = x

Whenever there is a ratio of 2 (blue potion):1 (red potion), there will be a 35% amount of magical syrup.

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The velocity function v(t) is -cos(πt)/π + (4 + 1/π) and the position function s(t) is -(sin(πt)/π²) + (4 + 1/π)t + 2.

To find the velocity and position of the object, we need to integrate the given acceleration function with respect to time.

Given: Acceleration function: a(t) = sin(πt)

Initial velocity: v(0) = 4

Initial position: s(0) = 2

To find the velocity function v(t), we integrate the acceleration function with respect to time:

v(t) = ∫ a(t) dt

Integrating sin(πt) with respect to t gives us:

v(t) = -cos(πt)/π + C

Using the initial velocity condition v(0) = 4, we can solve for the constant C:

v(0) = -cos(π(0))/π + C

4 = -cos(0)/π + C

4 = -1/π + C

C = 4 + 1/π

So, the velocity function v(t) becomes:

v(t) = -cos(πt)/π + (4 + 1/π)

To find the position function s(t), we integrate the velocity function with respect to time:

s(t) = ∫ v(t) dt

Integrating -(cos(πt)/π + (4 + 1/π)) with respect to t gives us:

s(t) = -(sin(πt)/π²) + (4 + 1/π)t + D

Using the initial position condition s(0) = 2, we can solve for the constant D:

s(0) = -(sin(π(0))/π²) + (4 + 1/π)(0) + D

2 = 0 + 0 + D

D = 2

So, the position function s(t) becomes:

s(t) = -(sin(πt)/π²) + (4 + 1/π)t + 2

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Answer:

do you want me to solve or what is it.

Step-by-step explanation: