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

What is the first thing you do before solving an adding fraction problem
Pls help

Answers

Answer:

The first thing you do is make the denominators equal on both sides.

Step-by-step explanation:

As a example if you have the equation:

[tex]\frac{1}{2}[/tex] + [tex]\frac{2}{5}[/tex] =

you would multiply the denominator by the smallest multiple. I would do 2 * 5= 10

this would make the equation

[tex]\frac{x}{10} + \frac{x}{10} = ...[/tex]

next you have to do the same with the numerator.

so sence you multiplied the [tex]\frac{1}{2}[/tex] by five you will get [tex]\frac{5}{10}[/tex]

same with the other fraction except you multiplied it by two.[tex]\frac{2}{5}[/tex] x 2 = [tex]\frac{4}{10}[/tex]

next you add and simplify if needed

Answer:

3 simple steps

Step-by-step explanation:

1.     Make sure the bottom numbers ( the denominators ) are the same

       IF DIFFERENT find the LCD

2.    Add the top numbers (the numerators )

3.    simplify the fraction if needed

ex:  1/4 +1/4 = 2/4  (bottoms were the same) simplify  1/2

       1/3 + 1/6    LCD of 3 and 6 so make the bottom numbers 6

                         so multiply  1/3 x  2 = 2/6

        now you have 2/6 + 1/6 = 3/6    simplify 1/2

someone helppp please!!

Answers

Answer:

because ΔMLN ≅ ΔYZX

=> MN = YX = 4

Step-by-step explanation:

Answer:

I think its four

Step-by-step explanation:


What is an equation for the line that passes through the points (-2, 3) and (2, 1)

Answers

First find slope
(1-3)/(2+2) = -2/4 = -1/2
Y = -1/2x + b, plug in point
3 = -1/2(-2) + b
3 = 1 + b, b= 2
Final equation: y = -1/2x + 3

Make w the subject of the formula y - aw = 2w - 1

Answers

Answer:

[tex]w=\frac{y+1}{a-2} (a\neq 2)[/tex]

Step-by-step explanation:

[tex]y - aw=2w-1\\y-aw-2w=-1\\-aw-2w=-1-y\\-w(a-2)=-(y+1)\\w(a-2)=y+1\\w=\frac{y+1}{a-2} (a\neq 2)[/tex]

Hope this helps!

Find the perimeter for the irregular polygons below

Answers

Answer:

1. 23

2. 17

Step-by-step explanation:

perimeter is the sum of length of all sides of a figure so if you add up the lengths of the sides you get 23 and 17 respectively.

can someone answer these?

Answers

Answer:

1. SSS

2.SSA

3.ASA

Step-by-step explanation:

For number one there is three congruent sides with the on in the middle

For number two there is two sides and one angle congruent

And number three has an embedded side between the two angles

can u pls help me with this question ​

Answers

Answer:

The correct answer is D, 6/8.

Step-by-step explanation:

For ratios or fractions an equivalent fraction has the same value but just more pieces. Think of it like a pizza. But to make sure they are equivalent you have to multiply or divide them by a fraction equal to 1. In other words the numerator and the denominator have to be the same number. So, when we multiply 3/4 by 2/2 you get 6/8 because 3 x 2 = 6 (numerators) and 4 x 2 = 8 (denominators).

If you have any additional questions please don't hesitate to ask me or your teacher to be sure you master the subject. Stay safe and please mark brainliest! :)

FOR 20 POINTS!!!!! Luis has $12 and wants to buy 6.6 pounds of apples. Apples cost $1.80 per pound. Luis rounded each value and estimated that he does not have enough money to cover the cost of the apples before sales tax is applied. Which best explains how his estimate relates to the actual product? Because each value rounds up, his estimate is higher than the actual product. He might have enough money to buy the apples. Because each value rounds up, his estimate is higher than the actual product. He does not have enough money to buy the apples. Because each value rounds up, his estimate is lower than the actual product. He does not have enough money to buy the apples. Because each value rounds up, his estimate is lower than the actual product. He might have enough money to buy the apples.

Answers

Answer: Hope this helps.

Because each value rounds up, his estimate is higher than the actual product. He might have enough money to buy the apples. So A.

Step-by-step explanation:

We don't actually know what it was that Luis was estimating. Assuming he was estimating the cost of the apples he wants to buy, rounding up both the price and quantity will give an estimate of $2/lb × 7 lb = $14, which is more than he has to spend.

Luis could refine his estimate by realizing the actual price is 10% less than the vaue he used, and the actual quantity is not quite 6% less than the value he used. The amount Luis has is about 14% less than the cost he estimated, so considering estimation errors, he probabaly has enough money.

The best choice among the answers is the one shown above.

the price of a video game was reduced by $60 to 45. By what percentage was the price of the video game reduced?

Answers

Answer:

25% reduced

Step-by-step explanation:

45/60= .75

1-.75=.25

(HELP 50 POINTS)
A beach lifeguard wants to create the largest triangular area he can with three lengths of rope to provide beach goers with maximum amount of space to play and swim in the water. Multiple buoys are attached to each rope in order to identify the designated swimming area. The first rope is 42 feet long, the second is 50 feet long, and then the third is 107 feet long. The lifeguard can only cut one of the ropes in order to create a triangle with the largest possible perimeter. How much rope, in feet, will be remaining after the lifeguard creates the designated swimming triangle? (Note: answer should be a whole number.)

Answers

Answer:

16

Step-by-step explanation:

I am doing Prepworks Basic triangles as well :D

4.5.36
A smoke jumper jumps from a plane that is 1500 ft above the ground. The function h= - 16t^2+ 1500 gives the jumper's height h in feet during the free fall att seconds
a. How long is the jumper free fall if the parachute opens at 1000 ft?
b. How long is the jumper in free fall if the parachute opens at 940 ft?
c. What is a reasonable domain and range for the function h?

Answers

We have a jumper that jumps from 1500ft above the ground, such that its height as a function of time is given by:

h(t) = -16*t^2 + 1500

The solutions are:

A) 5.59 seconds

B) 5.91 seconds

C) D = (0s, 9.68s)

    R = [0ft, 1500ft]

Notice that when t = 0, h = 1500, then at the initial time (t = 0) the height is 1500 (in ft), which means that the zero of the height is the ground.

a) How long is the jumper free fall if the parachute opens at 1000 ft?

Here we need to solve:

h = 1000 = -16*t^2 + 1500

Now we just need to solve this for t:

16*t^2 = 1500 - 1000 = 500

t^2 = 500/16 = 31.25

t = √31.25 = 5.59

So it takes 5.59 seconds to open the parachute.

B) similar to before, this time we need to solve:

h = 940 = -16*t^2 + 1500

16*t^2  =1500 - 940 = 560

t^2 = 560/16 = 35

t = √35 = 5.91

So it takes 5.91 seconds to open the parachute.

C) The domain is the set of inputs that we can use in the function.

The minimum of the domain is t = 0, when the jumper jumps.

To find the maximum of the domain we need to find the maximum time at which he could open the parachute, that is when h = 0ft, just in the ground.

Then we solve:

h = 0 = -16*t^2 + 1500

16*t^2 = 1500

t = √(1500/16) = 9.68

Then a reasonable domain is (0s, 9.68s)

And the range is the set of possible outputs, which will be all the possible heights of the jumper. We know that all of these are between 0ft and 1500ft, thus the range is [0ft, 1500ft]

If you want to learn more, you can read:

https://brainly.com/question/1632425

If triangle ABC is equilateral, and side AC is 7m long, how long is side BC?

Answers

Answer:

7m

Step-by-step explanation:

In an equilateral triangle all the sides and angles are the same

I believe the answer is 8m

This graph shows linear
y = f(x) and y = g(x).

Find the solution to the equation f(x) - g(x) = 0

Answers

Step-by-step explanation:

This graph shows linear

y = f(x) and y = g(x).

Find the solution to the equation f(x) - g(x) = 0

If the circumference of the circle is 24 inches what is the
approximate diameter

Answers

Answer:

7.64 in.

Step-by-step explanation:

The diameter of the circle whose circumference is 24 inches is 7.654 inches.

What is a circle?

A circle is a two-dimensional object made up of points that are spaced out from a given point (center) on the plane by a fixed or constant distance (radius).

Given:

The circumference of the circle, C = 24 inches,

Calculate the radius of the circle as shown below,

Circumference = [tex]2\pi r[/tex]

C = 2 × π r

r = 24 / 2π

r = 3.819

r = 3.82 inches

Calculate the diameter as shown below,

Diameter = 2 × r

Diameter = 2 × 3.82

Diameter = 7.639 inches

Thus, the diameter is 7.64 inches.

To know more about circle:

https://brainly.com/question/266951

#SPJ2

Answer this please thanks

Answers

Answer:

The answer is yes, since the graph is an equal line throughout.

Step-by-step explanation:

The linear equation when b= 5 and m = -2 is O y = 5x – 2. Oy= 5x + 2. y = -2x - 5. O y = -2x + 5​

Answers

Answer:

y = -2x + 5

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

m - slope b - y-intercept

Step-by-step explanation:

Step 1: Define given

y-intercept b = 5

Slope m = -2

Step 2: Write function

y = -2x + 5

(04.04 LC)
On a coordinate grid, point T is at (2,-4) and point Sis at (2,6). The distance (in units) between points T and Sis
numbers, such as 2.) (5 points)
(Input only whole

Answers

Answer:

The distance 'd' between T and S:

[tex]d=10[/tex]

Step-by-step explanation:

As the point 'T' is located at (2, -4)

So, the point 'T' has the coordinates (2, -4)

And the point 'S' is located at (2, 6)

So, the point 'T' has the coordinates (2, 6)

The distance 'd' between T and S can be computed using the formula:

[tex]d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]

[tex]=\sqrt{\left(2-2\right)^2+\left(6-\left(-4\right)\right)^2}[/tex]

[tex]=\sqrt{\left(2-2\right)^2+\left(6+4\right)^2}[/tex]

[tex]=\sqrt{0+10^2}[/tex]

[tex]=\sqrt{10^2}[/tex]

[tex]d=10[/tex]

Therefore, the distance 'd' between T and S:

[tex]d=10[/tex]

Answer:

t and s

Step-by-step explanation:

4n-(7-6n)


Helppp plz

Answers

4n - (7-6n)
4n -7 +6n (multiply minus to 7-6n)
10n -7 is the answer

which two triangles are congruent? complete the congruence statement.​

Answers

The two at the top not the one at the botton

Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.)f(x) = 3 â 48x + 4x2, [5, 7]

Answers

Answer:

Step-by-step explanation:

The given equation is:

f(x) = 3 - 48x + 4x²      [5,7]

where; f(x) is continous and derivable in [5,7]

f'(x) = -48x + 8x

f(5) = 3 - 48(5) + 4(5)² = -137

f(7) = 3 - 48(7) + 4(7)² = -137

Thus, it satisfies the hypotheses of Rolle's Theorem

f'(x) = f'(c) = 0

-48 + 8c = 0

c =48/8

c = 6

f(x) = x2 – 2x +1
Find y-intercept and vertex

Answers

Answer:

Your answer is: The x-intercept is [tex](1 , 0)[/tex] and your y-intercept is[tex](0 , 1 )[/tex].

Your vertex is [tex](1 , 0)[/tex]

Step-by-step explanation:

In order to find the y-intercept you had to to find the x-intercept, substitute in  0  for  y  and solve for  x . To find the y-intercept, substitute in  0  for  x  and solve for  y.

In order to find the vertex you had rewrite the equation in vertex form and use this form to find the vertex [tex](h , k)[/tex].

Hope this helped : )

8 more than the quotient of a number and 2 is 14. find the number

Answers

Answer:

x = 12

Step-by-step explanation:

x/2 + 8 = 14Subtract 8 from both sides because it is the inverse operation of addition. x/2 = 6Multiply both sides by 12 because it is the inverse operation of division. x = 12

What is the factored form of the equation 4x^2-11+6=0

Answers

Answer:

(4x−3)(x−2)=0

Step-by-step explanation:

Step-by-step explanation:

4x²-11+6=0

4x²-5=0

x²=5

4

x=√5

4

hope it help u

F(x)=4x+5whsts the value of. F(-3). Is




Answers

Figure out the value

Answer:

F(-3) = -7

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Function Notation

Step-by-step explanation:

Step 1: Define

F(x) = 4x + 5

F(-3) is x = -3

Step 2: Evaluate

Substitute:                    F(-3) = 4(-3) + 5Multiply:                        F(-3) = -12 + 5Add:                              F(-3) = -7

Raul Del Valle's gross weekly salary is S615. His weekly federal withholding is S55. The Social Security tax is
6,2% of the first $97.500 he earns. The Medicare tax is 1.45% of gross pay. The state tax is 1.5% of gross pay.
Each week he pays $12.40 for medical insurance. How much is deducted from Raul's weekly wages for state tax
and Medicare tax?​

Answers

Answer:

Step-by-step explanationjiuijkk8

u:

What's a rule you could apply to any number that would predict which denominators will terminate

Answers

I believe it’s
Think/ pair/ share

9514 1404 393

Explanation:

The decimal equivalent of a fraction will terminate if its denominator can be factored using only the prime numbers 2 and/or 5.

1/4 = 1/(2·2) will terminate

1/15 = 1/(3·5) will not terminate

Two-thirds of the fruit in a basket are apples. One-fourth of the apples are green apples. What fraction of the fruit in the basket are green apples?

Answers

Answer:

1/6

Step-by-step explanation:

2/3*1/4

=2/12

=1/6

PLS GIVE BRAINLIEST

First, we need to find the least common denominator. This would be 12. So, our new fractions would be 8/12 and 3/12. We know that 8/12 of the basket are apples, and we need to take away the 3/12 of the green apples. This means there are 5/12 of the red apples.

Hope this helps :)

Please help me with this

Answers

Answer:

$62.50

Step-by-step explanation: 250 divided by 4 equals $62.10

Can sumone please help me w this question? It math. 10 points. What is the value of r in the equation 3r − 6 = 18?

Answers

In this problem r=4 !!!
the answer is r=8

3(8)-6=16

A restaurant bill is $75. You want to leave about a 20% tip. Which is a 20% tip?

Answers

75*.20= 15

The tip is $15
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