find a. (dw/dx)y and b. (dw/dz)y at the point (x,y,z) = (-pi, -1, 2pi) if w=x^2 y^2 z^2 and ysinz zsinx=0

Answers

Answer 1

The values for \((dw/dx)y\) is\(-2*pi^2\)and\((dw/dz)y\) is 0.

What are the values of (dw/dx)y and (dw/dz)y?

We are given:

\(w = x^2 y^2 z^2\)

ysinz zsinx = 0

Part a: To find (dw/dx)y, we need to differentiate w with respect to x, treating y as a constant, and evaluate the result at (x,y,z) = (-pi, -1, 2pi).

Taking the partial derivative of w with respect to x, we get:

\(∂w/∂x = 2xy^2 z^2\)

So, \((dw/dx)y = 2xy^2 z^2.\)

Substituting (x,y,z) = (-pi, -1, 2pi), we get:

\((dw/dx)y = 2*(-pi)(-1)^2(2pi)^2 = 8pi^4\)

Therefore,\((dw/dx)y = 8pi^4.\)

Part b: To find (dw/dz)y, we need to differentiate w with respect to z, treating x and y as constants, and evaluate the result at (x,y,z) = (-pi, -1, 2pi).

Taking partial derivative of w with respect to z, we get:

\(∂w/∂z = 2x^2 y^2 z\)

Using the given equation ysinz zsinx=0, we can infer that either y=0 or sinz=0 or z=0 or sinx=0.

If y=0, then \((dw/dz)y=0.\)

If sinz=0, then z=kπ where k is an integer. But z=2π, so k=2. Thus, z=2π.

If z=0, then\((dw/dz)y=0.\)

If sinx=0, then x=jπ where j is an integer. But x=-π, so j=-1. Thus, x=-π.

Substituting (x,y,z) = (-pi, -1, 2pi), we get:

\((dw/dz)y = 2*(-pi)^2*(-1)^2*(2pi) = 4pi^3\)

Therefore, \((dw/dz)y = 4pi^3.\)

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Related Questions

2cm:5m into simplest form​

Answers

Answer:

1m=100cm

Step-by-step explanation:

do it correctly, sooo ya

which of the following sets of numbers could represent sides of a triangle?

Answers

Answer:

Hey mate...

Step-by-step explanation:

This is ur answer.....

The sum of the lengths of any two sides of a triangle must be greater than the third side. (a)(8,11,19)⇒8+11 not greater than 19 , (N.G.) (d)(13,4,8)⇒4+8<13 , (NG). Hence, option (b) is the only answer.

Hope it helps!

Brainliest pls!

Follow me! :)

the set of negative integers less than 0 but greater than -10?
help me please ​

Answers

S.S{-1 ,-2,-3,-4,-5,-6,-7,-8,-9}

Its only asking numbers less than zero but greater than-10 so 0 and -10 will not be included. Only numbers in bn

What is the primary purpose of data democratization?
a) make data accessible to all users
b) make data inaccessible to all users

Answers

The main goal of data democratization is to make data accessible to all users. Option (a) is correct.

Given the primary goal of data democratization.

Data democratization is the ability to make information in a digital format accessible to the average end user. The goal of data democratization is to allow non-professionals to collect and analyze data without the need for outside help. This requires us to support access with an easy way for people to understand data, so they can use it to accelerate decision-making and uncover opportunities for a business. The goal is for everyone to be able to use the data at any time to make decisions without barriers of access or understanding.

Therefore, the main goal of data democratization is to make data accessible to all users.

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PLEASE HELP!! Find the value of x.

PLEASE HELP!! Find the value of x.

Answers

Answer:

choice 1) x = 4

Step-by-step explanation:

∠2 = ∠6

4x+44 = 6x+36

reduce:

2x = 8

x = 4

QUICK PLEAAASEEEEE HELPPP!
Given the expression: 4x2 + 18x − 10

Part A: What is the greatest common factor? Explain how to find it. (3 points)

Part B: Factor the expression completely. Show all necessary steps. (5 points)

Part C: Check your factoring from Part B by multiplying. Show all necessary steps. (2 points)

Answers

Answer:

Part A: 8+10 = 18.

Part B: (x -5)(x+0.5)

Step-by-step explanation:

Part A: to find the greatest common factor of the expression, multiply 4 x -10 to get -40. Then, find the factors of -40 which add up to 18. These factors are 8+10. You may need to tweak around with the signs of the numbers.

Part B:you could just put the equation in a graphing calculator or use the quadratic formula. But, re-write the middle with -5 and 0.5, like this: 4x^2-5x+0.5x-10. Then do 4x(x-0.5) + (5x +10). After that, rewrite the equation again like this: (4x-0.5)(5X+10)

Answer:

Part A: the common factor is 2 because it is the most occurring.

Part B: 2(2x-1)(x+5)

Part C: 

(2x2x-2)(x+5)

(4x-2)(x+5)

4x+4x5x-2x-2x5

4x1+1+4x5x-2x-10

4x2+20x-2x-10

=4x2+18x-10

A dice is taken on which numbers from 6 to 11 are written on its six faces. The HCF of numbers written on any pair of opposite faces is always 1. Based on this information, answer the questions that follow. How many different possible combinations are possible for writing the numbers on six faces?

Answers

There are 120 different possible combinations for writing the numbers on the six faces of the dice, satisfying the given condition.

How to find how many different possible combinations are possible for writing the numbers on six faces

To find the different possible combinations for writing the numbers on the six faces of the dice, we can consider the prime factorization of each number from 6 to 11.

The numbers from 6 to 11 are:

6, 7, 8, 9, 10, 11

Prime factorization of these numbers:

6 = 2 * 3

7 = 7

8 = 2^3

9 = 3^2

10 = 2 * 5

11 = 11

Since the highest common factor (HCF) of numbers written on any pair of opposite faces is always 1, it means that no prime factor is common between the numbers on any pair of opposite faces.

To determine the different combinations, we can count the number of ways we can arrange the prime factors on the six faces of the dice without repeating any factor.

The prime factors are:

2, 3, 5, 7, 11

Considering that each face of the dice can have one prime factor, the number of different combinations is equal to the number of ways we can arrange these prime factors.

Using the concept of permutations, the number of different combinations can be calculated as:

5! (5 factorial) which is equal to 5 * 4 * 3 * 2 * 1 = 120

Therefore, there are 120 different possible combinations for writing the numbers on the six faces of the dice, satisfying the given condition.

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An architectural firm must decide on the size of a scale model to present to a client. The area of the base A​ (in ​) is related to the weight of the model W​ (in lbs) according to the equation . If the area of the base is currently and is increased by ​(while keeping the model to​ scale), determine the corresponding change in the weight of the model.

Answers

Answer:

The weight increases from 32 lbs to 64 lbs

Step-by-step explanation:

The question is not complete, the complete question is:

An architectural firm must decide on the size of a scale model to present to a client. The area of the base A (in ft^2) is related to the weight of the model W (in lbs) according to the equation W^2 = 4A^3. If the area of the base is currently 16 ft^2? and is increased by 16ft^2 (while keeping the model to scale), determine the corresponding change in the weight of the model

Solution:  

Given that the square of the area of the base (A) is directly proportional to the cube of the weight of the model (W). The relationship is given as:

W² = 4A³

This means a the weight increase, the area also increases. To the determine the corresponding change in the weight of the model, we have to determine the weight when the area is 16 ft² and increased by 16 ft².

At A = 16 ft²

W² = 4A³

W² = 4(16³)

W² = 1024

W = √1024 = 32

W = 32 lbs

When the area is increased by 16 ft² A = 16 ft² + 16 ft² = 32 ft²

W² = 4A³

W² = 4(32³)

W² = 4096

W = √4096 = 64

W = 64 lbs

The weight increases from 32 lbs to 64 lbs

Divide the first polynomial by the second. State the quotient and the remainder. x^3 - 5x^2 - 8x + 12
x - 6

Answers

The quotient of dividing

\(x^3 - 5x^2 - 8x + 12\)

by x - 6 is

\(x^2 - x - 2\)

with a remainder of 24.

To divide the polynomials, we can use long division. First, we divide x into

\(x^3\)

which gives us

\(x^2\)

We then multiply x - 6 by

\(x^2\)

to get

\(x^3 - 6x^2\)

We subtract this from the original polynomial to get:

\(x^3 - 5x^2 - 8x + 12 - (x^3 - 6x^2) \)

\(= x^2 - 8x + 12\)

We then repeat the process with x and

\(x^2 - x - 2\)

to get:

\(x^2 - 8x + 12\)

\( = (x^2 - x - 2)(x - 6) + 24\)

The quotient is

\(x^2 - x - 2\)

and the remainder is 24.

In polynomial long division, we divide the highest degree term of the dividend by the highest degree term of the divisor, and then multiply the divisor by the resulting quotient term to subtract it from the dividend. We repeat the process with the new dividend until we can no longer divide. The final result is the quotient plus any remaining terms, which form the remainder.

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What conditions would be enough to prove that P is the circumcenter of HJK ? Select all that apply.

There is a triangle HJK in which M, N and L are the points on the side HJ, side JK and side HK respectively. Segment HP is the angle bisectors of angle KHJ, segment JP is the angle bisectors of angle HJK, and segment KP is the angle bisectors of angle JKH. Segment HP, segment JP, and segment KP intersect each other at point P. Segment MP is perpendicular to side HJ, segment NP is perpendicular to side JK, and segment LP is perpendicular to side HK. The length of PM is 6x-14 and the length of LP is 3x+4.
A. L, M, and N are the midpoints of HK¯¯¯¯¯¯, HJ¯¯¯¯¯ and KJ¯¯¯¯¯ .
B. PL¯¯¯¯¯≅PM¯¯¯¯¯¯≅PN¯¯¯¯¯¯
C. PK¯¯¯¯¯¯≅HP¯¯¯¯¯¯≅PJ¯¯¯¯¯
D. △HJK is an acute triangle.

Answers

Answer:

B trust me

Step-by-step explanation:

a quick quiz consists of 5 5 multiple choice problems, each of which has 6 6 answers, only one of which is correct. if you make random guesses on all 5 5 problems, (a) what is the probability that all 5 5 of your answers are incorrect? answer: (b) what is the probability that all 5 5 of your answers are correct? answer

Answers

(a) The probability of getting all 5 answers incorrect is \((5/6)^{5}\) = 0.327.

(b) The probability of getting all 5 answers correct is \((1/6)^{5}\) = 0.00013.

Probability: Probability is a mathematical concept that measures the likelihood or chance of an event occurring. It is a value between 0 and 1, with 0 meaning that an event is impossible and 1 meaning that an event is certain to happen. Probabilities can also be expressed as percentages, with 0% meaning impossible and 100% meaning certain. Probability is used in many fields, including statistics, finance, and game theory, to make predictions and decisions based on uncertain information.

The quiz has 5 multiple choice questions with 6 options each, and only one of the options is correct.

(a) The probability of getting one answer incorrect is 5/6, so the probability of getting all 5 answers incorrect is \((5/6)^{5}\), which is equal to 0.327.

(b) The probability of getting one answer correct is 1/6, so the probability of getting all 5 answers correct is \((1/6)^{5}\), which is equal to 0.00013.

So, The probability of getting all 5 answers incorrect is 0.327 and the probability of getting all 5 answers correct is 0.00013.

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Twice the difference of a number and 4 is 3.​

Answers

Alright let’s use the variable X here for example.

2(X - 4) = 3
And that missing number is 5 1/2.
Which now equals 3.

MATH QUIZ!
COS A =
5 points
A
41
9
B
с
40

MATH QUIZ!COS A =5 pointsA419B40

Answers

Answer:

Your answer is A: 9/41

Step-by-step explanation:

A: 9/41

Simplify 7N - 2N + 3P + 2P.

Answers

Answer:

5N+5P

Step-by-step explanation:

7N-2N=5N

3P+2P=5P

7n-2n=5n
3p+3p=6p
5n+6p
Simplify 7N - 2N + 3P + 2P.

need help finding the area

need help finding the area

Answers

\(area \: \: of \: \: the \: \: given \: \: figure \: \: = \: \: 108 \: unit {}^{2} \)

How do you find what series converges to?

Answers

To find what series converges to, you can use the formula for the sum of an infinite geometric series.

which is:

S = a/(1 - r)

where S is the sum of the series, a is the first term of the series, and r is the common ratio between consecutive terms of the series.

This formula only works for geometric series, which are series where each term is a constant multiple of the previous term.

If the series is not geometric, you can try to find a pattern in the terms or use other convergence tests, such as the ratio test, the root test, or the comparison test. These tests can help you determine whether the series converges or diverges, but they may not give you a formula for the sum of the series.

If the series does converge, you may be able to find an approximation of the sum using numerical methods, such as partial sums or integration. However, finding an exact formula for the sum of a non-geometric series can be very difficult or even impossible in some cases.

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Can someone help me?? brainlest on the way if you do

Answers

Answer:

I will help if you tell me the question

Answer:

what do u need help with

Step-by-step explanation:

Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it.
lim (x â 3)/ (x² â 9)
xâ3

Answers

By using the L'Hospital's Rule, we have shown that the limit of x^(3/x) as x approaches infinity is equal to 1.

To find the limit of the function \(x^{3/x}\) as x approaches infinity, we can use L'Hopital's Rule, which states that if we have an indeterminate form of a fraction such as 0/0 or infinity/infinity, we can take the derivative of the numerator and the denominator separately until we no longer have an indeterminate form.

First, we can rewrite the function as e^(ln(\(x^{3/x}\))). Then, we can use the properties of logarithms to simplify it further as e^((3ln(x))/x). Now, we have an indeterminate form of infinity/infinity, and we can apply L'Hopital's Rule.

Taking the derivative of the numerator and denominator, we get:

lim x→∞ \(x^{3/x}\) = lim x→∞ e^((3ln(x))/x)

= e^(lim x→∞ (3ln(x))/x)

Using L'Hopital's Rule on the exponent, we get:

= e^(lim x→∞ (3/x²))

Since the denominator is approaching infinity faster than the numerator, the limit of 3/x² as x approaches infinity is zero, and we are left with:

= e^(0)

= 1

Therefore, the limit of \(x^{3/x}\) as x approaches infinity is 1.

Alternatively, we can use some algebraic manipulation and the squeeze theorem to find the limit without using L'Hopital's Rule. We can rewrite the function as \(x^{3/x}\) = (x^(1/x))³, and notice that as x approaches infinity, 1/x approaches zero, and so x^(1/x) approaches 1 (as the exponential function with base e^(1/x) approaches 1). Therefore, we have:

lim x→∞ \(x^{3/x}\)= lim x→∞ (x^(1/x))³

= 1³

= 1

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Complete Question:

Find the limit. Use L'Hospital's Rule if appropriate. If there is a more elementary method, consider using it.

lim x→∞ \(x^{3/x}\)

Debra has a rectangular garden. The length is six less than twice the width. The perimeter of her garden is 90 meters. What is the width and the length of the garden?

Answers

Answer:

width = 17 meters

length = 28 meters

Step-by-step explanation:

Since we are told that the length is equal to 6 less than twice the width, and we know that the perimeter of a rectangle is calculated by adding all the sides together, then we can create the following formula to calculate both the length (l) and width (w).

l = 2w-6

l + l + w + w = 90 ... substitute l with its formula

(2w-6) + (2w-6) + w + w = 90 ... combine like terms

6w - 12 = 90 ... add 12 on both sides

6w = 102 ... divide both sides by 6

w = 17 meters

Now that we know the width we can plug it into the length formula and solve for the length

l = 2w - 6

l = 2(17) - 6

l = 34 - 6

l = 28 meters

How do I find the area? I don’t know which one is the base or height.

How do I find the area? I dont know which one is the base or height.

Answers

Answer:

1

Step-by-step explanation:

the height is 2/3ft because it makes a right angle with the surface

base is 3 ft

area: 1/2 x 3 x 2/3 = 1 ft^2

consider joining our discørd server for additional geometry help; we also have an active amazon gc giveaway rn. code: RPEdT3erFm :)

Help me solve this please

Help me solve this please

Answers

5x-13y+2 hope this helps []~( ̄▽ ̄)~*

Simplify the following expression:

(66)4

Simplify the following expression:(66)4

Answers

Answer:

46656 to the power 4

Step-by-step explanation:

6 to the power 6 = 6 × 6 × 6 × 6 × 6 × 6 = 46656

(46656) to the power 4 = 46656 × 46656 × 46656 × 46656

This answer is undefined, so we will leave it at 46656 to the power 4.

John's library has 3 hardcover books for every 8 paperbacks. If he has 121 books in his library, how many of them are paperbacks. Will mark brainliest if correct. Pls show work.

Answers

Answer: 88

Step-by-step explanation:

1. Add 3 and 8 together

3 + 8 = 11

2. Divide 121 by 11

121/ 11 = 11

3. Multiply the amount of paperbacks in the stack of 11 books (8) by 11

11 x 8 = 88

88 Is your answer.

Charlene has a monthly salary of $3,410. With her present budget, Charlene has a net income that is 7% of her monthly salary. Charlene is going to reduce her net income by $125 each month and put this money towards paying down her debt. What will Charlene’s new net income be?

Answers

Answer:

A. $113.70

Step-by-step explanation:

The new net income of Charlene is $113.7 if Charlene has a monthly salary of $3,410. With her present budget, Charlene has a net income that is 7% of her monthly salary.

What is debt?

It is defined as the amount one party needs to pay to another party as the first party borrowed an amount that will be credited by the second party. Debt occurs when one party cannot be able to purchase something under normal circumstances.

Charlene net income = 7% of her monthly salary

Charlene net income = 3410(7/100) = $238.7

After paying the $125 from the net income:

= 238.7 - 125

= $113.7

Thus, the new net income of Charlene is $113.7 if Charlene has a monthly salary of $3,410. With her present budget, Charlene has a net income that is 7% of her monthly salary.

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Actividades.
Iniciamos la clase leyendo atentamente la
siguiente situación
Joaquin compró un tanque para agua que tiene
forma de prisma rectangular, cuyas dimensiones
son √5m, √6m y √ 10m


¿Cual es el volumen del tanque de agua?
. Ancho- √5m
Largo - √6m
Altura - √10m

Answers

Answer:

ancho de ese culotote

Step-by-step explanation:

member of red velvet​

Answers

Answer:

joy

Step-by-step explanation:

Answer:

Irene

Wendy

Seulgi

Joy

Yeri

Step-by-step explanation:

if a polynomial function is in factored form, what would be a good first step in order to determine the degree of the function?

Answers

To determine the degree of a polynomial function given in factored form, a good first step is to count the highest power of the variable in the factored expression.

In factored form, a polynomial function is expressed as the product of linear factors or irreducible quadratic factors.

Each factor represents a root or zero of the function.

The degree of a polynomial is determined by the highest power of the variable in the expression.

To find the degree of the function, examine each factor in the factored form.

For linear factors, the degree is 1 since the highest power of the variable is 1.

For irreducible quadratic factors, the degree is 2 since the highest power of the variable is 2.

By observing the highest power in the factored expression, you can determine the degree of the polynomial function.

If the highest power is 1, the polynomial has a degree of 1 (linear function). If the highest power is 2, the polynomial has a degree of 2 (quadratic function). And so on.

It's important to note that the degree of a polynomial corresponds to the highest power of the variable in the expression and not the number of factors.

The number of factors indicates the number of roots or zeros of the polynomial, but it doesn't determine the degree.

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Shane and Abha earned a team badge that required their team to collect no less than 200020002000 cans for recycling. Abha collected 178178178 more cans than Shane did.

What is the solution set of the inequality?

Answers

The solution set of the inequality is represented as [911,∞)

How to find the solution set of the inequality?

let

x be the number of cans collected by Shane.

Therefore,

Since,  Abha collected 178 more cans than Shane did.

Therefore,

Abha  = 178 + x

Hence,

Also, Shane and Abha earned a team badge that required their team to collect no less than 2000 cans for recycling.

Therefore,

x + 178 + x ≥ 2000

2x + 178 ≥ 2000

2x ≥ 2000 - 178

2x ≥ 1822

x ≥ 1822 / 2

x ≥ 911

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30 POINTS DUE FRIDAY PLEASE HELP WELL WRITTEN ANSWERS ONLY!!!!!!!!!
6. Use the information presented in the section ”Is That Fair?’ to answer the following: The local news station wants to interview 8 students from a school. There are 25 students on the student council. Ten of the students are from the graduating class and 15 are from the other classes. The principal has a difficult time deciding which students from the council will get interviewed, so she tells the group of students that she will put all of the names in a bowl, mix the names, then the first 8 names who are selected from the bowl will get to be interviewed.


The next day, the principal returns with the names selected. It turns out that 5 of the students who get to be interviewed are in the graduating class and only 3 of the students selected are from other classes. The students who are not in the graduating class complain that this doesn’t seem fair. They suspect that the principal chose the group rather than selecting at random.

• Do you think the principal could have chosen this group of students at random like she promised? Explain your reasoning.

• Simulate the drawing many times to find some possible results.

o Cut a piece of paper into 25 equal-sized pieces. On 10 on the pieces of paper, write “graduating class.” On the other 15 pieces of paper, write “other classes.” Fold the papers in half and mix them up.

o Take turns with your partner to draw 8 pieces of paper and record the number of students chosen that are in the graduating class.

o Repeat this process 4 more times.

• Create a dot plot that shows the number of students chosen from the graduating class by all of the students in your class.






• Based on the dot plot, do you think it is reasonable that the principal selected the students for the interview at random and still chose 5 of the 8 students who are in the graduating class? Explain your reasoning.

30 POINTS DUE FRIDAY PLEASE HELP WELL WRITTEN ANSWERS ONLY!!!!!!!!!6. Use the information presented in

Answers

Answer:

Step-by-step explanation

The principal should not select the students randomly. He should select students based on there skills and experience but not all the students are experienced and skilled.

      The local news station wants to interview only 8 students when a total 25 students are present in those 10 students are from the graduating class and remaining 15 students are from other classes so The Principal name the students to participate in the interview conducted by the local news station

        The graduating class should be giving chance because other classes will have more chance but graduating classes will have few because they will be graduating  

what is the slope...​

what is the slope...

Answers

Answer:

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

Step-by-step explanation:

slope is rise over run
the line goes up 3 and over 1
so the slope is 3/1 which equals 3

ANSWER: 3
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