use the chain rule to find ∂z/∂s and ∂z/∂t. z = er cos(), r = st, = s6 t6 ∂z ∂s = ∂z ∂t =

Answers

Answer 1

we differentiate the function z = e^[tex](stcos(θ))^{2}[/tex] with respect to s and t. The results are ∂z/∂s = e[tex](stcos(θ))^{2}[/tex]t and ∂z/∂t = [tex]-se^{(stcos(θ) }[/tex])×sin(θ).

Given the function z = [tex]e^{(rcos(θ)) }[/tex], where r = st and θ = [tex]s^{6}[/tex] × [tex]t^{6}[/tex], we want to find the partial derivatives ∂z/∂s and ∂z/∂t.

Applying the chain rule, we differentiate z with respect to s and t separately:

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

= [tex]e^{(rcos(θ)) }[/tex] × t + 0

= [tex]e^{(rcos(θ)) }[/tex] × t

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

= [tex]e^{(rcos(θ)) }[/tex] × scos(θ)t + [tex]e^{(rcos(θ)) }[/tex] × [tex]6s^6 t^5[/tex]

= [tex]e^{(rcos(θ)) }[/tex] × scos(θ)t + [tex]6s^6t^5[/tex] × [tex]e^{(rcos(θ)) }[/tex]

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Related Questions

The table represents some points on the graph of the exponential function that models the radioactive decay of a sample of xenon-135.

Which statement about the graph of this function is true?

(See the picture below)

A) There is an asymptote at y = 70.

B) The y-intercept is located at (0, 70).

C) There is an asymptote at x = 0.

D) The x-intercept is located at (70, 0).

Answers

Answer: b the y-intercept is located at (0,70)

The exponential curve passes through the point (0, 70). Then the correct option is B.

What is an exponent?

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

The table addresses a few focuses on the diagram of the outstanding capability that models the radioactive rot of an example of xenon-135.

At x = 4.6, the value of 'y' will be 49.5.

[tex]\rm 49.5 = ab^{4.6} \ \ \ \ \ \ \ ...1\\[/tex]

At x = 9.2, the value of 'y' will be 35.

[tex]\rm 35= ab^{9.2} \ \ \ \ \ \ \ ...2[/tex]

From equations 1 and 2, then we have

[tex]\rm \dfrac{b^{9.2}}{b^{4.6}} = \dfrac{35}{49.5}\\\\b^{4.6} = 0.707\\\\b = 0.927\\[/tex]

Then the value of 'a' will be

[tex]\rm 49.5 = a (0.927)^{4.6}\\\\a = 70[/tex]

Then the equation is given as,

y = 70 · (0.927)ˣ

The graph is given below.

The exponential curve passes through the point (0, 70). Then the correct option is B.

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What additional information would you need to prove

Answers

Answer:

A

Step-by-step explanation:

We use the Hypotenuse Leg Theorem

When we know the hypotenuse and a leg of a triangle.

We know The Hypotenuse (TO) so we need to know A leg of the triangle which the only leg is TM and OR.

A teepee is designed to have a diameter of 10 ft and a volume of 366ft³ what is the height? A.15ft , b.14 ft, c 5ft, or 1 ft

Answers

Answer:

B.  14 ft approx

Step-by-step explanation:

Given data

A teepee  has a conical shape

Diameter= 10ft

radius= 5 ft

Volume = 366ft³

Height = ????

The expression for the volume is

V= 1/3πr^2 h

substitute

366= 1/3*3.142*5^2*h

366= 1/3*78.55*h

366= 26.18h

h= 366/26.18

h=13.98 ft

h= 14 ft approx

Hence the Height is 14 ft approx

Answer:

14 ft

Step-by-step explanation:

a p e x!

Ayuda!
Necesito el inciso k) por 10 puntos

Answers

Answer:

x=47is your answer

3x-11=130(alternate angle)

3x=130+11

x=141/3=47

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Answers

Answer:

Done :)

Step-by-step explanation:

Best of luck!

Oh okie so cute ☺️ cute lol

someone on this god forsaken planet help me

Answers

Answer: Lol

B (-8,-5)

D (-10,-4)

C (-8,3)

Step-by-step explanation:

Angles are not necessarily drown to scale.

Answers

Tbh I don’t know about this

Answer:

ask ur teacher its pointless

Step-by-step explanation:

no one knows

(1x)/(2)=12

PLEASE SHOW THE WORK!!!

Answers

Answer:24

Step-by-step explanation:

simplify 1 * x to x

x/2=12

multiply both sides by 2

x=12 * 2

simplify 12 * 2 to24

x=24

1. Use the inequality 12≥6(12x+2).
a. Apply the Distributive Property to the right side.

b. Solve the inequality.

Answers

The answer would be 72x + 12 but I’m not sure but that’s what I got
12_>6(12x+2)
12_>72x+12
-12 -12
0_> 72x
/72 /72
Zero divided by anything is zero.
0_>x

What is the correct vocabulary term for a number variable product or quotient in an expression ​

Answers

Number variable is the main number for a product or quotient equation

There are 24 pints of juice in 2 containers, how many pints of juice in 1 container?

Question 1 options:

6


12


2


48

Answers

If they are the same size, it should be 12.
For example, if I had two cups of water and they can both hold 12 oz’s, and I have 24 oz’s. 12 ozs will hold the total 24.

2. The weather forecast calls for 12 cm of snow. How many inches
can you expect?

4. You have a 1.5 gal jug. How many litres will it hold?

5. Joe is travelling in the United States. A road sign indicates he is
228 mi from his destination. How many kilometres is Joe from
his destination?

Answers

Answer:

2. 1 inch

4. 5.68 liters(if we estimate)

5. 366.96 kilometers

Step-by-step explanation:

2. centimeters to inches

4. gallons to liters

5. miles to kilometers

Three pounds of flour are divided into 6 containers so that each container holds the same number of pounds of flour

Answers

Answer:

0.5 pounds per container.

Step-by-step explanation:

just divide 3 pound by 6 containers so it would be 3/6 which is equal to 1/2 which is the same as 0.5

There each container holds a number of pounds of flour which would be  0.5 pounds.

What is the division operation?

In mathematics, divides left-hand operands into right-hand operands in the division operation.

If three pounds of flour are divided into 6 containers so that each container holds the same number of pounds of flour, we can find out how many pounds of flour each container holds by dividing the total amount of flour by the number of containers.

We can use the following equation to find out how many pounds of flour each container holds:

pounds of flour per container = total pounds of flour / number of containers

So, using this equation:

pounds of flour per container = 3 / 6

Apply the division operation, and we get

pounds of flour per container = 0.5

Each container holds 0.5 pounds of flour.

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Use a unit multiplier to convert 0.37 liters to milliliters.

Answers

Answer:

370

Step-by-step explanation:

Multiply the number of liters (L) by 1,000 to find the number of milliliters (mL). There are 1,000 times as many milliliters as there are liters. For instance, say you have 3 liters. Simply multiply 3 liters by 1,000 to get 3,000 milliliters.

Paisley invests money in an account paying a simple interest of 8.9% per year. If she invests $80 and no money will be added or removed from the investment, how much will she have in one year, in dollars and cents?​

Answers

it will be removed

Step-by-step explanation:

Ella is 66 inches tall. Andy is 6 1/2 feet tall. Who is taller? By how much? (12 inches = 1 foot)

Answers

Answer:

Andy is taller by one foot or 12 inches

Step-by-step explanation:

Ella = 66 inches = 5'6"

Andy = 6 1/2 feet = 6'6"

Andy is taller by one foot or 12 inches

Andy is taller by one foot or 12 inches

Given:

Ella is 66 inches and Andy is 6 1/2 feet.

12 inches = 1 feet.

Convert inches in to feet.

12 inches = 1 feet.

1 inches = 1/12 = 0.083

66 inches = (0.083 * 66) = 5.5 feet.

Andy = 6 1/2 feet = 6.5 feet.

6.5 > 5.5 (6.5 is greater than 5.5).

Andy is taller by one feet or 12 inches

Therefore, Andy is taller by one feet.

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Find the solution of the equation. 2(2x + 3) = -4 + 2(2x + 5)

Answers

Answer:

x = 2/3

Step-by-step explanation:

4x + 6 = 10x + 10

4x = 10x - 4

6x - 4

x = 2/3

Have a great day <3

2(2x + 3) = -4 + 2(2x + 5)
Divide both sides by 2
2x + 3 = -2 + (2x + 5)
Add 2 to both sides
2x + 3 + 2 = 2x + 5
2x + 5 = 2x + 5
Subtract 5 from both sides
2x = 2x
Divide both sides by 2
x = x

This means x can equal anything I believe.

help, look at picure

Answers

Answer:

x=3

Step-by-step explanation:

61/4=15 1/4

5(3)=15+(1/4)=15 1/4

which one of the following is NOT a polynomial option 1. x^2-2x+3 option 2. 11x-9. option 3. 3/y

Answers

Answer:

option 3

Step-by-step explanation:

what is the surface area of the cylinder with height 3km and radius 7km

Answers

Answer:

A=439.82 or A=439

Step-by-step explanation:

~~~~~~~~:)

4
1

(12−8×)=
3
2

(6×)

Answers

creo que es 32 por la cultura

What is the Value of X
What is the Length of JM?

Answers

Answer:

JM = 17

x = 12

Step-by-step explanation:

The given triangles are similar with ASA rule if so then x + 5 must be equal to 2x - 7

x + 5 = 2x - 7 and 5 + 7 = 2x - x

12 = x

The length of JM

2x - 7 can be written as 2×12 - 7 = 17

Twelve students share 3 pizzas equally. What fraction of a pizza does each student
get?

Answers

Answer: 4/12

Step-by-step explanation: 4 over 12


the equati...
Solve the equation 3(x + 4.5) = 36.
If you get stuck, use the diagram.
36
4.5
X = ?

Answers

Answer:

x = 7.5

Step-by-step explanation:

Answer:

75

Step-by-step explanation:

if you put 3 in the x it is now 3 but the x it is there with the 3 and do 3 with the 4.5 and then add them to each of them then you get your answer

NEE HELP!

Solve for x, round your answer to the nearest hundredth: 5lnx + 2 = 17

*need step-by-step solution

Answers

Answer:

e^3

Step-by-step explanation:

5ln(x)+2=17

5ln(x)=17-2

5ln(x)=15

ln(x)=15/5

ln(x)=3

e^ln(x)=e^3

x=e^3

Solve for x

X=4
3/2x+8=-1

Answers

x=-6
Solve for x by simplifying both sides of the equation, and then isolate the variable.

define el concepto de renacimiento y el de humanismo​

Answers

Answer:

Renacimiento es el nombre dado en el siglo XIX a un amplio movimiento cultural que se produjo en Europa Occidental durante los siglos XV y XVI. ... El Renacimiento fue fruto de la difusión de las ideas del humanismo, que determinaron una nueva concepción del hombre y del mundo.

Step-by-step explanation:

Please give thanks to all my answers and please mark as brilliant and please follow me

Plsssss help me, It says find the area

Answers

Answer:

It should be 136

Step-by-step explanation: I split it up into multiple pieces

Rectangle 1= 20*2=40

Rectangle 2= 14*4=56

Rectangle 3= 20*2=40

40+40+56=136

the area is 136
divide the figure into three rectangles and add all the areas to get the total area

Michael sells 136 newspapers each week. If there are 52 weeks in a year, how many newspapers does Michael sell in a year?

Answers

Answer:

7,072

Step-by-step explanation:

136 times 52 = 7,072

Answer:

7,072 newspaper in a year

Step-by-step explanation:

Multiply: 136*52=7,072

(I would put a picture of my work but I'm lazy right now lol)

Hope this helped!! :)

Stay safe and have a wonderful day/night!!!!!

Brainliest?!?!

Rodrigo practiced playing the guitar 15 1/3 hours over the past 3 weeks. He practiced for 5 1/4 hours during the first week and 5 2/3 hours during the second week.

Answers

Answer:

[tex]4 \frac{5}{12}[/tex]

Step-by-step explanation:

The computation of the number of hours practiced on the third week is given below:

= Total hours over the past 3 weeks - first week - second week

[tex]= 15 \frac{1}{3} - 5 \frac{1}{4} -5 \frac{2}{3}\\\\= \frac{46}{3} - \frac{21}{4} - \frac{17}{3}\\\\= \frac{184 - 63 - 68}{12} \\\\= \frac{53}{12}\\\\= 4 \frac{5}{12}[/tex]

Answer: is is correct

Step-by-step explanation:

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