Use the Chain Rule to find the indicated partial derivatives. w = xy + yz + zx, x = r cos(θ), y = r sin(θ), z = rθ; âw âr , âw âθ when r = 4, θ = Ï2

Answers

Answer 1

Answer:

δw/δr = 4π

δw/δθ = -8π

Step-by-step explanation:

Given the following functions

w = xy + yz + zx, x = r cosθ y = r sinθ, z = rθ where r = 4 and θ = π/2

We are to find δw/δr and δw/δθ

δw/δr = δw/δx•δx/δr + δw/δy•δy/δr + δw/δz•δz/δr

δw/δx = y+z

δx/δr = cosθ

δw/δy = x+z

δy/δr = sinθ

δw/δz = y+x

δz/δr = θ

Substitute the given values into the formula

δw/δr = (y+z)cosθ+(x+z)sinθ+(y+x)θ

Substitute the value of x, y and z in terms of theta into the resulting function

δw/δr = (y+z)cosθ+(x+z)sinθ+(y+x)θ

δw/δr = (rsinθ+rθ)cosθ+(rcosθ+rθ)sinθ+(rsinθ+rcosθ)θ

Substitute r = 4 and θ = π/2

δw/δr = (4sinπ/2+4π/2)cosπ/2+(4cosπ/2+4π/2)sinπ/2+(4sinπ/2+4cosπ/2)π/2

Note that cos π/2 = 0 and sinπ/2 = 1

δw/δr = (4+2π)(0)+(0+2π)(1)+(4(1)+4(0))π/2

δw/δr = 0+2π+4π/2

δw/δr = 2π+2π

δw/δr = 4π

For δw/δθ

δw/δθ = δw/δx•δx/δθ + δw/δy•δy/δθ + δw/δz•δz/δθ

δw/δx = y+z

δx/δθ = -rsinθ

δw/δy = x+z

δy/δθ =rcosθ

δw/δz = y+x

δz/δθ = r

Substitute the given values into the formula

δw/δθ = (y+z)-rsinθ+(x+z)rcosθ+(y+x)r

Substitute the value of x, y and z in terms of theta into the resulting function

δw/δθ = (y+z)-rsinθ+(x+z)rcosθ+(y+x)r

δw/δθ = (rsinθ+rθ)-rsinθ+(rcosθ+rθ)rcosθ+(rsinθ+rcosθ)r

Substitute r = 4 and θ = π/2

δw/δθ = (4sinπ/2+4π/2)-4sinπ/2+(4cosπ/2+4π/2)4cosπ/2+(4sinπ/2+4cosπ/2)(4)

Note that cos π/2 = 0 and sinπ/2 = 1

δw/δθ = (4+2π)(-4)+(0+2π)(0)+(4(1)+4(0))(4)

δw/δθ = -16-8π+0+4(4)

δw/δθ = -16+16-8π

δw/δθ = -8π


Related Questions

Five of the 25 girls on Alden Middle School’s soccer team are seventh-grade students. Find the percentage of seventh graders on the team.

Answers

Answer:

20%

Step-by-step explanation:

5 divided by 25 multiplied by 100 will give you 20%.

I hope you understand

which of the following are properties of all rectangles? Select all that apply.​

Answers

Answer:

see explanation

Step-by-step explanation:

The rectangle has the following properties

• Opposite sides are parallel and congruent

• All angles are right angles

• The diagonals are congruent

• The diagonals bisect each other

Thus

They are quadrilaterals

Opposite sides are equal in length

All angles are 90°

Opposite sides are parallel

Rectangles are not parallelograms ( the angles of a parallelogram are not necessarily right and diagonals are not congruent )

1. Adding decimals is very similar to adding___________.
2.Line up the number vertically so that all the decimal points are_______.
3. Add extra______to the right of the number so that each number has the same number of digits to the right of the decimal point.
4. Place the______________of the result in line with the other decimal points.

Answers

Answers:

1. Adding decimals is very similar to adding whole numbers.

2. Line up the number vertically so that all the decimal points are aligned.

3. Add extra zeros to the right of he number so that each number has the same number of digits the right of the decimal point.

4. Place the decimal point of the result in line with the other decimal points.

I hope this helped you. If it is please click the thanks button. Thank You, Bye! ;-D

1. Adding decimals is very similar to adding whole numbers.

2. Line up the number vertically so that all the decimal points are aligned.

3. Add extra zeros to the right of the number so that each number has the same number of digits to the right of the decimal point.

4. Place the decimal point of the result in line with the other decimal points.

While adding two decimals.

First, the decimals numbers are written under each other so that decimal points are lined up.The numbers are converted to like decimals by attaching the zeros. The number of zeros attached depends on the number with the maximum digits after the decimal point. The digits of each numbers are lined up so that each column contains digits in the same place. Addition is carried out the normal way by starting from the right to the left. The decimal point is then placed in the place as the numbers above it.

Learn more about decimal form here:

https://brainly.com/question/358789?referrer=searchResults

Learn more about decimal addition here:

https://brainly.com/question/13611222?referrer=searchResults

Find the unknown
*
7.8-2.15

Answers

The unknown or the answer is 5.65

Which is the net force acting on a 1.7-kg object that is accelerating at 5.0 m/s??

A. 8.5 N

B. 2.9 N

C. 0.34 N

D. 3.3 N

Answers

Answer:

A. 8.5 N

Step-by-step explanation: F = 8.5 N

The entrance for the amusement park is $40, visitors purchase additional $2
tickets for rides, games and food. How many tickets can you buy if you
brought $100 to spend at the park?

Answers

Answer:

2 tickets because round

Step-by-step explanation:

make an equation: 100=40x+2 and solve

2.45 tickets so only two

40+40 =80

100-80=20

but 100-2=98 so there is only 18$ left so not enough for another ticket

Answer:

30 Tickets

Step-by-step explanation:

In the question, it said that $40 is the entrance fee. Then, it said that visitors purchase additional tickets for rides, games, and food. This means that EACH ticket is 2 dollars.

Hence, $40 (entrance fee) + $2 (each ticket price) x (the number of tickets spent) = 100 (total amount of money).

So, the equation should be 40 + 2x = 100, which means x = 30.

100 - 40 = 60

60/2 = 30

30 tickets can be purchased

determine if the relation is a function
(-1, 5), (0,3), (2,3), (3, -1)

Answers

Answer:

This relation IS a function

Answer:

This is a function

Step-by-step explanation:

Down below none of them overlap

There is no two points in the lines.

Find the present value of an annuity due that pays $4000 at the beginning of each quarter for the next 7 years. Assume that money is worth 6.2%, compounded quarterly. If $90,000 is invested in an annuity that earns 5.4%, compounded quarterly, what payments will it provide at the end of each quarter for the next 7 1/2 years?

Answers

Answer:

Step-by-step explanation:

From the first question:

We are to find PV of the annuity.

Using the formula:

Present value of Annuity  = Annuity Amount × Present Value Annuity Factor i.e. PVAF (n , r)

Where , Annuity Amount = $4,000            

n = No. of periods = 7 years × 4 quarters per year = 28 periods but since the first payment is at beginning of the quarter, Then, n = 27 when considered for PVAF

r  = 6.2% / 4 quarters = 1.55%,

PVAF(n0,r) when first payment is at beginning of n i.e. n0 = 1 + { [1-(1+r)^ -n0 ]/r }

= 1 + { [1-(1+0.0155)^ {-27}]/0.0155 }

= 1 + [ (1 - 0.66015 ) ] / 0.0155]

= 1 + 21.926

= 22.926

PVAF(28,1.55%) = 22.926

Thus , Present Value of Annuity = $4,000 × 22.926  = $91704.00

2. Present value of Annuity due = Annuity Amount × Present Value Annuity Factor i.e. PVAF (n , r)

Present Value of Annuity  = $90,000

n = No. of periods = 7.5 years × 4 quarters per year = 30 periods

r  = 5.4% / 4 quarters = 1.35%,

PVAF(n,r) = [1-(1+r)^-n]/r

PVAF(n,r) = [1-(1+0.0135)^ -30]/0.0135

PVAF(30,1.35%) = (1 - 0.6688)/0.0135

PVAF(30,1.35%) = 0.3312/0.0135

PVAF(30,1.35%) = 24.53

Hence ;

$90,000 = Annuity Amount × 24.53

Annuity amount = $90,000/24.53 = $3,668.48

What is one hundred times greater than 40?

Answers

100 + 40 = 140
140 is 100 times greater than 40

if 3(2x-4)=-36 ,the value of x is

Answers

Answer:

x = -4

Step-by-step explanation:

Answer:-4

Step-by-step explanation:

PLEASE HELP WILL GIVE BRAINLIST

Answers

Answer:

greater than or equal to

Step-by-step explanation:

If f(x) = 2x^2 +1, complete the following:
a. f(-4)
b. f(-2)
c. f(0)
d. f(2)
e. f(4)

This is a timed test please i need help!!

Answers

Answer:

Sub the values in the brackets of each question into the equation

Step-by-step explanation:

eg. c. f(0) = 2(0)^2 + 1 = 1

Three friends each have some ribbon. Carol has 90 inches of ribbon, Tino has 7.5 feet of ribbon, and Baxter has 3.5 yards of ribbon. Express the total length of ribbon the three friends have in inches, feet, and yards.

Answers

Answer: 306 inches or 25.5 feet or 8.5 yards.

Step-by-step explanation:

Given: Carol has 90 inches of ribbon, Tino has 7.5 feet of ribbon, and Baxter has 3.5 yards of ribbon.

1 feet = 12 inches

length of ribbon Tino has = 12 x 7.5 = 90 inches

1 yard = 36 inches

length of ribbon Baxter has = 3.5 x 36 = 126 inches

Total ribbon they have = (length of ribbon Carol has) + (length of ribbon Tino has) + (length of ribbon Baxter has)

= (90+90+126) inches

= 306 inches

In feet , Total ribbon = [tex]\dfrac{306}{12}\text{ feet}[/tex]   [tex][\text{ 1 inch}=\dfrac{1}{12}\text{ feet}][/tex]

[tex]=\text{25.5 feet}[/tex]

In yards, Total ribbon =[tex]\dfrac{25.5}{3}\text{ yards}[/tex]    [tex][\text{1 feet}=\dfrac{1}{3}\text{ yard}][/tex]

[tex]=\text{ 8.5 yards}[/tex]

Hence, the total length of ribbon the three friends have is 306 inches or 25.5 feet or 8.5 yards.

Which rate is the lowest price?
$3.00/6 lb
$2.50/5 lb
$2.40/4 lb
$2.40/6 lb

Answers

2.40/6 I believe tell me if it is right
$3.00/6=2
$2.50/2=2
$2.40/4=.60
$2.40/6=.40 this is the lowest price

Can anyone help me with this question of m

Answers

Answer:

<DBC=31

Step-by-step explanation:

<ABC=<ABD+<DBC

125=94+<DBC

125-94=<DBC

31=<DBC

Tall Mountain is 8,678.37 feet higher than Mt. Might. What is the elevation of Tall Mountain?
The elevation of Tall Mountain is
feet.

Answers

Answer:

i wont give u a direct answer but i will tell u this.. Look up Mt. Mights height  and subtract 8,678.37 with a cauculator. The answer will tell you

Answer: 28,979.87

Step by step explanation: I GOT THE ANSWER CORRECT!!!!!! For any one wondering I am doing this question right no and what the other guy said about subtracting is wrong because i tried doing tat and it said it was wrong.

Please help me with this

Answers

Answer is C, 138°

It's the answer that makes the most sense.

At a toy store, Colton can buy a package of 6 mini footballs for $7.50, or a package of 8 mini footballs for $9.60. Which option has the lesser price?

Answers

Answer:

The 8-pack is better value

Step-by-step explanation:

$7.50/6 = $1.25 per ball

$9.60/8 = $1.20 per ball

The 8-pack is a better value if the toy store, Colton can buy a package of 6 mini footballs for $7.50, or a package of 8 mini footballs for $9.60.

What is a fraction?

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

At a toy store, Colton can buy a package of 6 mini footballs for $7.50, or a package of 8 mini footballs for $9.60.

For:

At a toy store, Colton can buy a package of 6 mini footballs for $7.50

Each ball price

$7.50/6 = $1.25 per ball

Each ball price

$9.60/8 = $1.20 per ball

The 8-pack is a better value

Thus, the 8-pack is a better value if the toy store, Colton can buy a package of 6 mini footballs for $7.50, or a package of 8 mini footballs for $9.60.

Learn more about the fraction here:

brainly.com/question/1301963

#SPJ2

For the following quadratic equation, find the discriminant.
5x^2– 10x – 255 = 0
please help meee

Answers

Answer:

5200

Step-by-step explanation:

STEP 1: The discriminant of a quadratic is the expression inside the radical of the quadratic formula.

[tex]b^2-4(ac)[/tex]

STEP 2: Substitute in the values of a, b, and c.

[tex](-10)^2-4(5)(-255)[/tex]

STEP 3: Evaluate the result to find the discriminant.

[tex]5200[/tex]

Roses need 14 times as much water as irises to bloom. if irises need 12 milliliters of water to bloom, how much water do roses needs ​

Answers

Answer:

168 milliliters

Step-by-step explanation:

Since roses need 14 times as much water as irises and we are given the water irises need, you multiply them together.

14•12=168

An auto mechanic earns $498.75 in 35 hours during the week. His pay is 2.50 more per hour on the weekends. If he works 6 hours on the weekend in addition to 35 hours during the week,hiw much does he earn

Answers

Answer:

Total pay= $599.25

Step-by-step explanation:

First, we need to calculate the unitary pay per hour:

Unitary pay= 498.75/35

Unitary pay= $14.25

Now, we can determine the total earn of 35 regular hours and 6 weekend hours:

Total pay= 498.75 + (14.25 + 2.5)*6

Total pay= 498.75 + 100.5

Total pay= $599.25

What is 2052 divided by 76

Answers

Answer:

27

Step-by-step explanation:

Answer:

Yes, by 27 times

Step-by-step explanation:

I hope it helps you

Linear equation: -1 (6x + (6x + 10) = 13
Step 1: -3x - 5 = 13
Step 2: -3x = 18
Step 3: x= -6

Which sequence describes the inverse operations used for steps 2 and 3 to solve the linear equation?
O the addition property of equality and then the division property of equality
O the addition property of equality and then the multiplication property of equality
O the subtraction property of equality and then the division property of equality
O the subtraction property of equality and then the multiplication property of equality

Answers

Answer:

the addition property of equality and then the division property of equality

1 point
6. Precipitation for the month of March was 4 inches less than average. In
April the precipitation was 14 inches less than average. How many inches
below average was the precipitation for both March and April?

Answers

Answer:

4 inches because March was 4 so april has to be 4 too

Step-by-step explanation:

I Need Helpp PLZZ i will mark as brainliest

Answers

Answer:

9x+18

Reasoning:

You multiply x by 9 and 2 by 9 and it expands out from 9(x+2) to 9x+18

I hope this helps and good luck!

Answer:

9x + 18

Step-by-step explanation:

9 times x = 9x

9 x 2 = 18

Point E is located at (-5,2). Point M is the reflection of point E across the y-axis. What is the distance between E and M?

Answers

Answer:

The distance is Ten

2 + 36 ÷ 12 - 6 = 8. where does the parenthesis go to make 8 the answer​

Answers

Answer:

The parenthesis go around the 12 and 6, just like this. (12 - 6)

Answer- 2 + 36 ÷ (12-6)

Help me pleaseeeeeee

Answers

The answer is the second one

Explanation above

Answer:

The correct answer is "y = 3/4x"

Step-by-step explanation:

Slope-intercept form is y2-y1/x2-x1. If you place the points into slope-intercept form you get 6-3/8-4.  After reducing the fractions you will get 3/4. So the equation is y = 3/4x.

12

A study was done to investigate the population of bald eagle breeding pairs over time. The correlating regression model is shown

below where x represents the number of years after 1986, and y represents the number of bald eagle breeding pairs. Interpret the y-

intercept

y=1.772-334

A. There were approacimately 334 eagle breeding pairs in 1986.

B. There were approximately 1.772 eagle breeding pairs in 1986.

c. There were approximately 1.772 additional eagle breeding pairs each year after 1986.

D. There were approximately 334 additional eagle breeding pairs each year after 1986

Answers

Complete question :

A study was done to investigate the population of bald eagle breeding pairs over time. The correlating regression model is shown

below, wiere x represents the number of years after 1986, and y represents the number of bald eagle breeding pairs. Interpret the y-

intercept

y = 1.772 +334x

Answer:

B. There were approximately 1.772 eagle breeding pairs in 1986

Step-by-step explanation:

Given the regression equation : y = 1.772 +334x

Recall the general form of a linear regression equation :

y = mx + c

y = predicted variable ; x = predictor Variable ; c = intercept ; m = slope

x = number of years after 1986 ; y = number of bald eagle pairs.

The intercept is a constant value at time t = 0

For x to be 0, on a graph, this this the value on the y axis where the regression line crosses the y - axis. That is in 1986; the number of y when in 1986 when x = 0 is 1.772

If AABC = ADEC,
ZB = 48° and ZE = x + 4

Answers

Answer:

[tex]x = 44^\circ[/tex]

Step-by-step explanation:

Triangle Congruence

Given triangle ABC is congruent to triangle DEC, then it's true that angle ABC is congruent to angle DEC.

The figure shows that:

[tex]m\angle B = 48^\circ[/tex]

[tex]m\angle E = x + 4^\circ[/tex]

Those angles are congruent, or have the same measure, thus:

[tex]x + 4^\circ = 48^\circ[/tex]

Subtracting 4°:

[tex]x = 48^\circ - 4^\circ[/tex]

[tex]\mathbf{x = 44^\circ}[/tex]

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