Use the Chain Rule to find z/s and z/t.z = er cos(), r = st, =s6 + t6z/s = z/t =

z/s = [tex]e^(st cos(s^6 + t^6)) * (t cos(s^6 + t^6) - 6s^5 st sin(s^6 + t^6))[/tex]z/t = [tex]e^(st cos(s^6 + t^6)) * (s cos(s^6 + t^6) - 6t^5 st sin(s^6 + t^6))[/tex]To use the Chain Rule, we need to express z as a function of s and t. We have:z = [tex]e^{(r cos())}[/tex], where r = st and = [tex](s^6 + t^6)[/tex].First, let's find the partial derivative of z with respect to s:z/s = (z/r) * (r/s) + (z/) * (/s)To find (z/r), we can use the derivative of e^(r cos()) with respect to r, which is simply cos() * [tex]e^{(r cos())}[/tex]:z/r = cos() * [tex]e^{(r cos())}[/tex]To find (r/s), we can use the fact that r = st, so:r/s = tTo find (z/), we can use the derivative of e^(r cos()) with respect to , which is -r sin() * e^(r cos()):z/ = -r sin() * e^(r cos())To find (/s), we can use the fact that = s^6 + t^6, so:/s = 6s^5Putting it all together, we have:z/s = cos() * e^(r cos()) * t + (-r sin() * e^(r cos())) * 6s^5Simplifying this expression, we get:z/s = e^(st cos(s^6 + t^6)) * (t cos(s^6 + t^6) - 6s^5 st sin(s^6 + t^6))Similarly, we can find the partial derivative of z with respect to t:z/t = (z/r) * (r/t) + (z/) * (/t)To find (r/t), we can again use the fact that r = st, so:r/t = sTo find (/t), we have:/t = 6t^5Putting it all together, we have:z/t = cos() * e^(r cos()) * s + (-r sin() * e^(r cos())) * 6t^5Simplifying this expression, we get:z/t = e^(st cos(s^6 + t^6)) * (s cos(s^6 + t^6) - 6t^5 st sin(s^6 + t^6))In summary, using the Chain Rule, we have found that:z/s = e^(st cos(s^6 + t^6)) * (t cos(s^6 + t^6) - 6s^5 st sin(s^6 + t^6))z/t = e^(st cos(s^6 + t^6)) * (s cos(s^6 + t^6) - 6t^5 st sin(s^6 + t^6))These expressions represent the rate of change of zTo know more about partial derivative refer here:https://brainly.com/question/31397807#SPJ11

Mathematics High School

Use the Chain Rule to find ∂z/∂s and ∂z/∂t.
z = er cos(θ), r = st, θ =
s6 + t6
∂z/∂s = ∂z/∂t =

Answers

Answer 1

∂z/∂s = $e^(st cos(s^6 + t^6)) * (t cos(s^6 + t^6) - 6s^5 st sin(s^6 + t^6))$

∂z/∂t = $e^(st cos(s^6 + t^6)) * (s cos(s^6 + t^6) - 6t^5 st sin(s^6 + t^6))$

To use the Chain Rule, we need to express z as a function of s and t. We have:

z = $e^{(r cos(θ))}$, where r = st and θ = $(s^6 + t^6)$.

First, let's find the partial derivative of z with respect to s:

∂z/∂s = (∂z/∂r) * (∂r/∂s) + (∂z/∂θ) * (∂θ/∂s)

To find (∂z/∂r), we can use the derivative of e^(r cos(θ)) with respect to r, which is simply cos(θ) * $e^{(r cos(θ))}$:

∂z/∂r = cos(θ) * $e^{(r cos(θ))}$

To find (∂r/∂s), we can use the fact that r = st, so:

∂r/∂s = t

To find (∂z/∂θ), we can use the derivative of e^(r cos(θ)) with respect to θ, which is -r sin(θ) * e^(r cos(θ)):

∂z/∂θ = -r sin(θ) * e^(r cos(θ))

To find (∂θ/∂s), we can use the fact that θ = s^6 + t^6, so:

∂θ/∂s = 6s^5

Putting it all together, we have:

∂z/∂s = cos(θ) * e^(r cos(θ)) * t + (-r sin(θ) * e^(r cos(θ))) * 6s^5

Simplifying this expression, we get:

∂z/∂s = e^(st cos(s^6 + t^6)) * (t cos(s^6 + t^6) - 6s^5 st sin(s^6 + t^6))

Similarly, we can find the partial derivative of z with respect to t:

∂z/∂t = (∂z/∂r) * (∂r/∂t) + (∂z/∂θ) * (∂θ/∂t)

To find (∂r/∂t), we can again use the fact that r = st, so:

∂r/∂t = s

To find (∂θ/∂t), we have:

∂θ/∂t = 6t^5

Putting it all together, we have:

∂z/∂t = cos(θ) * e^(r cos(θ)) * s + (-r sin(θ) * e^(r cos(θ))) * 6t^5

Simplifying this expression, we get:

∂z/∂t = e^(st cos(s^6 + t^6)) * (s cos(s^6 + t^6) - 6t^5 st sin(s^6 + t^6))

In summary, using the Chain Rule, we have found that:

∂z/∂s = e^(st cos(s^6 + t^6)) * (t cos(s^6 + t^6) - 6s^5 st sin(s^6 + t^6))

∂z/∂t = e^(st cos(s^6 + t^6)) * (s cos(s^6 + t^6) - 6t^5 st sin(s^6 + t^6))

These expressions represent the rate of change of z

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Related Questions

Convert 21.73 m to customary units.

The smallest tick mark on 1" = 1' 0" architect’s scale is ………… inch/inches.

A fractional ruler was used for scale measurements of a line on the 1/4" = 1'-0" scale. The two ends of the line correspond to 6 2.7/4" and 9 6/8". What is the length of the line in inches. [roundoff the answer to one decimal places]

Multiply 3/5 x 17/13 and reduce answer to lowest form of fraction. (mixed fraction if applicable)

Answers

To convert 21.73 m to customary units, we need to use the conversion factors as follows:

meter = 39.37 inches1

inch = 2.54

cm1 foot

= 12 inches

We have:

21.7.

3 m

= 21.73 x 39.37 inches (since 1 mete

r = 39.37 inches)

= 856.301 inches

= 71 feet 4.3 inches (since 1 foot = 12 inches)

The smallest tick mark on

1" = 1' 0"

architect’s scale is 1/16 inch.

This means that there are 16 tick marks in an inch. A fractional ruler was used for scale measurements of a line on the 1/4" = 1'-0" scale. The two ends of the line correspond to 6 2.7/4" and 9 6/8". To get the length of the line in inches, we need to convert the two ends to inches, then subtract them to get the length as follows:

$6 2.7/4" \\= 6 x 12 + 2.7\\ = 74.7" (since 1 foot\\ = 12 inches)\\9 6/8" = 9 x 12 + 6 \\= 114" (since 1 foo\\t = 12 inches)$

Length of the line = 114 - 74.7 = 39.3 inches (rounded off to one decimal place)

Multiplying 3/5 by

$17/13\\ gives:\\3/5 x 17/13\\= (3 x 17)/(5 x 13)\\= 51/65$

This is already in its lowest form.

Therefore, the answer is:51/65 (an improper fraction)

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Use limits to determine if
x+3
f(x) = is continuous at x = 3.

Answers

The correct answer is (d) No, it is not continuous because lim x→3 f(x) ≠ lim x→3 f(x).

To determine if the function f(x) = (x+3)/(x²-9) is continuous at x=3, we need to check if the limit of the function exists as x approaches 3 from both the left and the right, and whether this limit is equal to the value of the function at x=3.

First, we can check the limit as x approaches 3 from the left:

lim x→3- f(x) = lim x→3- (x+3)/(x²-9) = (-3)/(0-) = ∞

Next, we can check the limit as x approaches 3 from the right:

lim x→3+ f(x) = lim x→3+ (x+3)/(x²-9) = (6)/(0+) = ∞

Since both one-sided limits are infinite, the limit as x approaches 3 does not exist.

Therefore, the function f(x) = (x+3)/(x²-9) is not continuous at x=3.

The correct answer is (d) No, it is not continuous because lim x→3 f(x) ≠ lim x→3 f(x).

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find volume of cylinder d= 42cm h= 7cm

Answers

Answer:

V≈9698.1

Step-by-step explanation:

Using the volume formula:

V=πr^2*h

Find the volume:

π*212*7

= 9698.09652

how to determine if a relation is a function calculator

Answers

Answer:

A relation is defined as the collection of inputs and outputs which are related to each other in some way. In case, if each input in relation has accurately one output, then the relation is called a function.

Based on the given relation, we found that it is not a function because it has repeating x-values. Remember, for a relation to be a function, each input (x-value) must correspond to exactly one output (y-value).

To determine if a relation is a function, you need to check if each input (x-value) corresponds to exactly one output (y-value). You can use the following steps:

1. Identify the given relation as a set of ordered pairs, where each ordered pair represents an input-output pair.

2. Check if there are any repeating x-values in the relation. If there are no repeating x-values, move to the next step. If there are repeating x-values, the relation is not a function.

3. For each unique x-value, check if there is only one corresponding y-value. If there is exactly one y-value for each x-value, then the relation is a function. If there is more than one y-value for any x-value, then the relation is not a function.

Let's consider an example relation: {(1, 2), (2, 3), (3, 4), (2, 5)}.

Step 1: Identify the relation as a set of ordered pairs: {(1, 2), (2, 3), (3, 4), (2, 5)}.

Step 2: Check for repeating x-values. In our example, we have a repeating x-value of 2. Therefore, the relation is not a function.

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(9.8)²-10² please help

Answers

Answer:

Step-by-step explanation:

-9

HELP PLEASE!!
The monthly rent for the first house is $1,190,
and the Bainters can expect it to increase 1.7%
every year. The Bainters want to calculate their monthly rent over time.

How much will the monthly rent be after 1
year?

Round your answer to the nearest whole dollar if necessary.

Remember to write down and keep your calculations.

Answers

We must raise the $1,190 starting rent by 1.7% in order to determine the monthly rent after a year.

We can begin by figuring out how much the rise will be:

Amount of increase: 1.7% of $1,190 multiplied by 0.017 times equals $20.23. (rounded to the nearest cent)

We must multiply the initial rent by this sum in order to determine the new monthly rate:

New rate is $1,190 plus $20.23 per month, or $1,210.23. (rounded to the nearest cent)

As a result, the rate will be $1,210 per month after a year.

What is the starting point?

When the input parameter value is 0, the output of a function is its starting value, or 0. The first number would be the amount of money you had to start with on day 0 if your function, for instance, was tracking the sum of money you earned over a specific period of time.

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The monthly rent after 1 year will be $1,210.

What is amount ?

"Amount" is a general term that refers to the quantity, value, or total of something. It can be used in different contexts to refer to different things.

To calculate the monthly rent after 1 year, we need to find the 1.7% increase and add it to the initial rent.

First, we need to calculate the amount of the increase:

Increase = 1.7% of $1,190

Increase = 0.017 × $1,190

Increase = $20.23 (rounded to two decimal places)

Next, we can find the new monthly rent by adding the increase to the initial rent:

New rent = $1,190 + $20.23

New rent = $1,210.23 (rounded to two decimal places)

Therefore, the monthly rent after 1 year will be $1,210.

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a manufacturer drills a hole through the center of a metal sphere of radius 5 inches. the hole has a radius of 3 inches. what is the volume of the resulting solid?

Answers

If the radius of the hole is 3 inches than the volume of the resulting solid is 410.29 in³ .

In the question ,

it is given that ,

the manufacturer drills a hole in the metal sphere that has radius of 5 inches ,

the radius of hole in sphere is 3 inches .

the volume of the metal sphere is = (4/3)×π×r³

= (4/3)×π×5³

= 523.33 in³

the volume of the hole of radius 3 inches is = (4/3)×π×3³

= 113.04 in³

So , the volume of the remaining solid is = 523.33 - 113.04

= 410.29 in³ .

Therefore , the Volume of the resulting solid is 410.29 in³ .

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What is the exact value of cos(–60º)?
Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction
Negative one-half
One-half
StartFraction StartRoot 3 EndRoot Over 2 EndFraction

pls

Answers

-1/2

Step-by-step explanation:

i made a 100 so good luck bros

What is the exact value of cos(60)?Negative StartFraction StartRoot 3 EndRoot Over 2 EndFractionNegative

The value of cos(–60º) is -1/2. Therefore. option B is the correct answer.

We need to find the exact value of cos(–60º).

What are six different types of trigonometric functions?

There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

Now, cos (-60º)=-1/2=-0.5

The value of cos(–60º) is -1/2. Therefore. option B is the correct answer.

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expand the given function in an appropriate cosine or sine series. f(x) = x3, − < x

Answers

The given function f(x) = x^3 is an odd function, meaning it is symmetric about the origin and has rotational symmetry of 180 degrees. Since the function is odd.

1. To expand the function f(x) = x^3 in an appropriate cosine or sine series, we need to express it as a combination of trigonometric functions. However, the cosine terms in the series expansion will have coefficients of zero. Only the sine terms will contribute to the expansion.

2. Expanding f(x) = x^3 in a sine series, we can write it as:

f(x) = a₁sin(x) + a₃sin(3x) + a₅sin(5x) + ...

Here, a₁, a₃, a₅, ... are coefficients that determine the amplitude of each sine term. The coefficients can be determined using the formulas for Fourier series coefficients.

3. In summary, the expansion of the function f(x) = x^3 in an appropriate cosine or sine series consists of a series of sine terms with coefficients determined by the Fourier series coefficients. However, since the function is odd, only the sine terms contribute to the expansion.

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Show that, when SI units for µ0 and ε0 are entered, the units given by the right-hand side of the equation in the problem above are m/s.

Answers

The unit m/s represents the speed of light. Therefore, the units of the right-hand side of the equation prove that the speed of light is represented in the equation.

The equation mentioned in the question is as follows; The SI units of magnetic permeability and permittivity of free space are Henry/meter and farad/meter respectively. In order to prove that the units given by the right-hand side of the equation are m/s, we need to perform the following steps: Substitute the values of magnetic permeability and permittivity of free space in the equation. Let's substitute µ0 and ε0 values in the above equation, we get; In order to perform this step, we need to know the units of each component in the equation. A unit of force is Newton, and a unit of charge is Coulomb. A magnetic field has the unit Tesla. Let's find out the units of the right-hand side component of the above equation. We can now rearrange the equation to make it simpler.!)

The unit m/s represents the speed of light. Therefore, the units of the right-hand side of the equation prove that the speed of light is represented in the equation.

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please help me with this question

Answers

Answer:

The answer is A, the first one

Step-by-step explanation:

Hope this helps!

Please help me solve this ! Which figure can be formed from the net?

Answers

Answer:

Step-by-step explanation:

It is th eonly one with a asquare base and it maches the net.

Have an amazing day!

PLEASE RATE!

Option A is correct!

How??

First of all, it's base is square just like the net. The net in option D also has a square base.Now, Confusion is there that which one is correct?To understand that, look at the dimensions. The dimensions of Figure in Option A matches the net completely.. Hence, it is the correct option!!~

please help!! will mark brainliest

Answers

Answer:

Step-by-step explanation:

x is smaller than or equal to -5

x is an element of real numbers

HELP PLSS

This assignment is past the original due date of Sun 04/24/2022 11:59 pm. You were granted an extension Due Tue 05/17/2022 11:59 p Find the consumer's and producer's surplus if for a product D(x) = 25

Answers

To find the consumer's and producer's surplus, we need more information about the demand and supply functions or the market equilibrium.

You provided the demand function D(x) = 25, but we require additional details to proceed with the calculations. The consumer's surplus is the difference between the maximum price consumers are willing to pay and the price they actually pay. It represents the benefit or surplus gained by consumers in a market transaction.

The producer's surplus is the difference between the minimum price producers are willing to accept and the price they actually receive. It represents the benefit or surplus gained by producers in a market transaction.

To calculate these surpluses, we typically need information about the supply function, equilibrium price, and equilibrium quantity. These values help determine the areas of the consumer's and producer's surpluses on the supply-demand graph.

Please provide the necessary information about the supply function, equilibrium price, or any other relevant details so that I can assist you in calculating the consumer's and producer's surplus accurately.

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Hey you can you help me pls

Answers

Answer:

diameter=14 radius=7

Step-by-step explanation:

diameter is given and radius is just half

What is the surface area of a right rectangular prism with the dimensions 4 m by 3 m by 10 m

Answers

The surface area is 164

PLS HELP!!!
I HAVE THE ANSWER!
I ONLY NEED TO SHOW THE WORK

Find the value of x by using the exterior angle theorem.

Answer: B

Answers

A=180-105
A=75

In the triangle
75+ 9x +12x =180
X=5

Cora is using successive approximations to estimate a positive solution to
f
(
x
)
=

g
(
x
)
, where
f
(
x
)
=
x
2
+
13
and
g
(
x
)
=
3
x
+
14
. The table shows her results for different input values of
x
.

Answers

By successive approximations we find that $x \approx 3.3$ for $f(x) = g(x)$.

How to find a solution of two functions by direct inspection

According to the table, the value of $x$ must be between 3 and 3.5. $x$ is the solution of $f(x) = g(x)$ if and only if $f(x) - g(x) = 0$. Let suppose that $x = 3.3$, then:

$3.3^{2}+13 = 3\cdot (3.3) + 14$

$-0.01$

As we need only two decimals, approximation seems to be reasonable.

By successive approximations we find that $x \approx 3.3$ for $f(x) = g(x)$. $\blacksquare$

Remark

Statement is incomplete and incorrectly formatted, correct form is presented below:

Cora is using successive approximations to estimate a positive solution to $f(x) = g(x)$, where $f(x) = x^{2}+13$ and $g(x) = 3\cdot x + 14$. The table shows her results for different input values of $x$:

x f(x) g(x)

0 13 14

1 14 17

2 17 20

3 22 23

4 29 26

3.5 25.25 24.5

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Which figure will have 26,666 tiles?

Answers

https://www.westerville.k12.oh.us/userfiles/4218/Classes/7005/4.1.6%20hw%20ans.pdf?id=540983

the grade a student received on an examination was transformed to a z value, which was negative. therefore, we know that he scored a) higher than 16 percent of the class.b) higher than 45 percent of the class.c) above the first quartile.d) below the mean.e) lower than 16 percent of the class.

Answers

The student's exam grade was converted to a negative z-score, indicating that they scored below the mean

Therefore, option d is correct.

When a grade is transformed into a z-score, it represents how many standard deviations the grade is away from the mean. The mean is always set at a z-score of 0, and positive z-scores indicate that a grade is above the mean, while negative z-scores indicate that a grade is below the mean.

In this question, the student's exam grade was transformed into a negative z-score, which means that the grade is below the mean. This is because the negative sign in the z-score indicates that the grade is a certain number of standard deviations below the mean. The further the z-score is below 0, the further the grade is below the mean.

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easy:
what is the surface area of the rectangular prism?
L times W times H= 3 cm times 2 cm times 4 cm

Answers

Answer:

l x w do the the math

Step-by-step explanation:

there

Answer:

u said free poinstt on that persons answer so Hi

Step-by-step explanation:

Use Excel to solve this: You want to buy a car for $50,000 and you can put $10,000 as a down payment and borrow the remaining $40,000. The bank will make a bank loan at a 9% per year over 3 years and monthly payments. What is the monthly payment?

Answers

In this case, the monthly payment for the car loan would be approximately $1,299.13.

To calculate the monthly payment for a bank loan using Excel, you can use the PMT function.

Here's how to do it:

1. Open Excel and create a new spreadsheet.

2. In cell A1, enter the loan amount: -40000 (negative because it's an outgoing payment).

3. In cell A2, enter the annual interest rate: 9%.

4. In cell A3, enter the loan duration in years: 3.

5. In cell A4, enter the formula to calculate the monthly payment: =PMT(A2/12, A3*12, A1).

6. The result in cell A4 will be the monthly payment.

So, in this case, the monthly payment for the car loan would be approximately $1,299.13.

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x2 + 5x + 6
x2 + 8x + 12
y2-7y + 12
y? - 11y + 28
x2 - 3x - 40

Answers

here I hope this helps you. Always have 2 bracket when factoring trinomials and know you prime factors

What is 6*10^-5-4*10^-6

Answers

Answer:

0.000056

Step-by-step explanation:

$ \\ 6 \times {10}^{ - 5 } - 4 \times {10}^{ - 6} $

$ \\ \longrightarrow6 \times \frac{1}{ {10}^{5} } - 4 \times \frac{1}{ {10}^{6} } $

$ \\ \longmapsto6 \times \frac{1}{ 100000 } - 4 \times \frac{1}{1000000}$

$ \\ \longmapsto0.00006 - 0.000004$

$ \\ \longmapsto0.000056$

What is the value of the x-coordinate that is 6 units to the right of (3.25,-4)?
O -2.75
Ο 2
Ο Ο Ο Ο
9.25
Ο 10
w

Answers

9.25 hope I have a nice day and stuff I have to write 20 words so

Solve the math problem

I will mark brainliest

Answers

Let a number be x

$\\ \sf\longmapsto \dfrac{x}{x}$

$\\ \sf\longmapsto 1$

And we know that.

$\\ \sf\longmapsto n/1=n,n\in N,Z,R,Q$

So all questions have the answer as per the question .Just rewrite them

last question, please help me.

Answers

Answer:

[(20×20)×26]/3 = 3467cm³

Step-by-step explanation:

The volum of a Pyramid is equal to:

Ab × h / 3

Ab = Area of the base = 20 × 20 = 400 cm²

h = height = 26 cm

so, yoi have: (400 × 26) / 3

PLEASE HELP, WILL GIVE BRAINLIEST
no links pls, i really need help

Answers

Answer:

4 units to the right

Step-by-step explanation:

the bigger units subtracted by the smaller units and the direction it is going

Answer:

I'm pretty sure the answer is D because a net force can't be just balanced to one side if there are two different forces, I hope this helps.

Step-by-step explanation:

Point M is the midpoint of line segment CD,
shown below.
What are the coordinates of point M?
C (6,10)
M
D (20, 18)

Answers

Answer:

M(13, 14)

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

Each coordinate of the midpoint is the average of endpoints:

x = (6 + 20)/2 = 26/2 = 13y = (10 + 18)/2 = 28/2 = 14

Therefore M is (13, 14).

Steve sells vacuum cleaners door to door. He earns a base salary of $500 plus $100 for every vacuum cleaner he sells. Steve also works selling encyclopedias door to door. He makes $300 plus $200 for every set of encyclopedias he sells.

How many items would Steve need to sell for the two salaries to be the same?

Answers

Answer:

Step-by-step explanation:

Let x = number of items Steve sells

Let y = salary earned

Create two equations:

Vacuum sales: y = 500 + 100x

Encyclopedia sales: y = 300 + 200x

Equal the equations and solve for x to find the number of items Steve needs to sell for the two salaries to be the same:

500 + 100x = 300 + 200x

Subtract 300 from both sides: 200 + 100x = 200x

Subtract 100x from both sides: 200 = 100x

Divide both sides by 100: 2 = x

Therefore, Steve would have to sell 2 items for the two salaries to be the same.

Answer: 04 items (02 each)

Step-by-step explanation:
Steve's base salary is $500 and $300 respectively for selling vacuum cleaner and encyclopedia. Along with that his bonus is $100 and $200 respectively. If he sells 02 items each, his earnings would be as follows:
For 02 vacuum cleaner: 500+100+100
= $700
For 02 encyclopedia: 300+200+200
= $700

Other Questions

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Use the Chain Rule to find ∂z/∂s and ∂z/∂t. z = er cos(θ), r = st, θ = s6 + t6 ∂z/∂s = ∂z/∂t =

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Use the Chain Rule to find ∂z/∂s and ∂z/∂t.
z = er cos(θ), r = st, θ =
s6 + t6
∂z/∂s = ∂z/∂t =