If e^xy-y^2=e-4,
then at x=1/2 and y=2,
dy/dx=?

Answers

Answer 1

Answer:

If  [tex]e^{x\cdot y}-y^{2} = e-4[/tex], then at  [tex]x = \frac{1}{2}[/tex] and [tex]y = 2[/tex], [tex]\frac{dy}{dx} \approx 2.059[/tex].

Step-by-step explanation:

Let [tex]e^{x\cdot y}-y^{2} = e-4[/tex]. At first we determine the first derivative of the function by implicit differentiation:

[tex]e^{x\cdot y}\cdot \left(y+x\cdot \frac{dy}{dx} \right)-2\cdot y \cdot \frac{dy}{dx} = 0[/tex]

[tex]y\cdot e^{x\cdot y}+x\cdot e^{x\cdot y}\cdot \frac{dy}{dx} -2\cdot y\cdot \frac{dy}{dx} = 0[/tex]

[tex]y\cdot e^{x\cdot y}= (2\cdot y -x\cdot e^{x\cdot y})\cdot \frac{dy}{dx}[/tex]

[tex]\frac{dy}{dx} = \frac{y\cdot e^{x\cdot y}}{2\cdot y - x\cdot e^{x\cdot y}}[/tex]

If we know that [tex]x = \frac{1}{2}[/tex] and [tex]y = 2[/tex], then the computed value of the function is:

[tex]\frac{dy}{dx} = \frac{(2)\cdot e^{\left(\frac{1}{2} \right)\cdot (2)}}{2\cdot (2)-\left(\frac{1}{2} \right)\cdot e^{\left(\frac{1}{2} \right)\cdot (2)}}[/tex]

[tex]\frac{dy}{dx} \approx 2.059[/tex]

If  [tex]e^{x\cdot y}-y^{2} = e-4[/tex], then at  [tex]x = \frac{1}{2}[/tex] and [tex]y = 2[/tex], [tex]\frac{dy}{dx} \approx 2.059[/tex].


Related Questions

Liza’s age is two more than thrice the age of her younger sister.if her sister is 5 years old, how old is Liza?

Answers

Answer:

17 years old.

Step-by-step explanation:

sisters age:5

5×3+2=17.

Answer:

Liza is 17 years old.

Step-by-step explanation:

Ley 'x' be the age of Liza's younger sister

As Liza’s age is two more than thrice the age of her younger sister

so the equation of Liza's age will be:

Liza's age = 3x+2

As x = 5 years is Liza's younger sister age

so

Liza's age = 3(5)+2

                 = 15+2

                  = 17 years

Therefore, Liza is 17 years old.

If sin t = -8/17 and t is a quadrant III angle, find cot t

Answers

Answer:cot t = 1.875

[tex]sin t=\frac{-8}{17}[/tex] but sin²t + cos²t = 1 ⇔ cos²t = 1 - sin²t

⇔cos t = [tex]\sqrt{1-sin^{2}t }=\sqrt{1-(\frac{-8}{17})^{2} }=|\frac{15}{17}|[/tex]

but  t is a quadrant III angle => cos t = [tex]\frac{-15}{17}[/tex]

=> cot t = [tex]\frac{-15}{17}:\frac{-8}{17}=\frac{15}{8}=1.875[/tex]

Step-by-step explanation:

Will mark brainliest

Answers

2.21 is the answer :-/

Hey luvs I NEED HELP ON THIS

Answers

Answer:

F. Outta. Here

Step-by-step explanation:

Answer:

a. 260m

b. 50m

Step-by-step explanation:

First, triangle POQ and triangle PNR are similar triangles, b/c they have one same angle(OQP), and OQ//NR.

Therefore, OP/OQ = NP/NR.

NP = OP + ON = 175 + 175 = 350

(a) 175/130 = 350 /NR, NR = 260

(b) 175/ (X+10) = 350/ (3X+5) , x = 15, NR = 50

4 A baby's t-shirt requires 5 yards of fabric. How many t-shirts can be made from 48 yards?​

Answers

Answer:

9 t-shirts

Step-by-step explanation:

divide 5 by 48 you will get 9.3 but that is not what it is asking it how many t-shirts can they total

witch is grater 18/24 or 55%

Answers

Answer:

i would say 18/24

Step-by-step explanation:

5 students share 2 candy bars what fraction of a candy bar does each student get?

Answers

Answer:

2/5

Step-by-step explanation:

Take the number of candy bars and divide by the number of students

2/5

Each will get 2/5 of a candy bar

Answer:

2/5

Step-by-step explanation:

What is the slope of a line with the equation y = 5x + ⅖ ?

Answers

Answer:

The slope would be 5

Step-by-step explanation:

The reason why it would be five is because the slope formula is y=mx+b with m being your slope and b being your y-intercept.

Answer:

slope: 5

Step-by-step explanation:

[tex]y=mx+b[/tex] is the equation used to find the slope of an equation. The slope is ALWAYS the "m" value. So.... in this equation y=5+2/5... the "m" value is 5.... making the slope of the equation 5.

what is the vertical change from point A to point B ?

What is the horizontal change to point A to point B?

Answers

Answer:

Vertical change= 1

Horizontal change= 2

Rate of change=  1/2

Step-by-step explanation:

The vertical change is how many units you go up on the triangle and the horizontal change is how many units you go left or right on the triangle. The rate of change is the vertical change over the horizontal change. So that is why 1/2 is the rate of change. Have a great day!

Answer:

4

Step-by-step explanation:

Every week, Hector’s 20 hours earns $210.00. He earns a constant amount of money per hour.

Part B
Write an equation that can be used to determine Hector's earnings, in dollars, m, for h hours of work.

Answers

Answer: 20 weeks in 1 week

in 2 weeks 40

Step-by-step explanation:

This proves that the equation is true

An outdoor adventure company charges $9 per hour for a mountain
bike plus a $5 fee for a helmet.

Answers

Answer:500

Step-by-step explanation:500 +7++U+U++UU+

Bart can paint 3/5 of a wall in 1/2 hour. How long does it take him to paint 5 walls?

Answers

Answer:

2 hours

Step-by-step explanation:

There are 11 books on a shelf , 7 of these books are new . The rest of them are used .
What is the ratio of new books to used book ?

Answers

Answer:

7:4

Step-by-step explanation:

11-7=4

7:4

The ratio of old books to the new books is new : old = 7 : 4.

What are ratio and proportion?

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, There are 11 books on a shelf, and 7 of these books are new.

So, The number of old books are (11 - 7) = 4.

So, In the self there is 7 new books and 4 old books.

Therefore the ratio of new books to old books,

new books : old books = 7 : 4.

learn more about proportion here :

https://brainly.com/question/7096655'

#SPJ2

Select the correct answer.
7
3
77
X
A) 363
C) 7
B) 33
D) 77

Answers

Answer:

B) 33

Step-by-step explanation:

Since , both these triangle are similar
Therefore the sides are in the same ratio
This implies , 3/7=x/77
=> x= 3*77/ 7
x= 33
Hope it helps :))

16. Write the following in standard form
36505000
pls need ans. fast ​

Answers

Answer:

3.6505*10^7

Step-by-step explanation:

PLS GIVE BRAINLIEST

Answer:

36,505,000

Step-by-step explanation:

36505000 is 36505000 in standard form.

Which can be used to expand the expression below?
5 3x
associative property
O commutative property
O distributive property
O subtracting

Answers

i think commutative i might be wrong

Answer:

the answer is disributive!

Step-by-step explanation:

Mike had to call a plumber. The plumber charged $55 for the service call plus, plus $22 for parts, and an hourly rate. He worked on the job for 3 hours. If Mike was charged $152, how much did the plumber charge per hour?
pls include the equation.

Answers

Answer: the answer is $456 and that is correct

Step-by-step explanation:

152×3= $456

Eighteen subtracted from half of a number (In an algebraic expression)

Answers

Answer:

1/2x-18

Step-by-step explanation:

18 subtracted from half of a number

We assume that the "number" is x

so 1/2x is the half of a number

We now need to have 18 subtracted from that so 1/2x-18

Find the distance between E(5,3) and F(-4,3).

Answers

Answer:

Ok I also fo not know but shall shall come to silicon valley of US So you can remember all thinks about this and tricks

Jay is 3 years less than 4 times Nelly’s age ( n ). Which expression represents Jay’s age?

Answers

Answer:

9

Step-by-step explanation: 3x4= 12  -3=9

Answer:

what's nelly's age

Step-by-step explanation:

4x divided by 3?

HELP ASAP DUE IN 5!!!!
The points in each table lie on a line. Find the slope of the line.

O 1/5
O 1
O 5
O None of the above

Answers

1/5 using the slope formula

Hal owns a printing company. Last Christmas, he charged $8 for a set of 25 greeting cards and $14 for a set of 50. a. Find two ordered pairs that represent the situation. (8,25) (14,50)

Answers

Answer:

(8, 25) and (14, 50)

Step-by-step explanation:

Total cost of a set of cards = price per unit x number of cards

                                             = p x n

Thus, the total cost of printing each set of cards depends on the price per unit and number of cards. So that it can be represented in ordered pair as: (p, n).

For the first set of greeting cards,

the cost of printing a card = $8.0

number of cards printed = 25

This can be represented in ordered pair as (8, 25)

                                                 

For the second set of greeting cards,

the cost of printing a card = $14.0

number of cards printed = 50

This can be represented in ordered pair as (14, 50)

Thus, the two ordered pairs that can represent the situations are (8, 25) and (14, 50).

Hurryyyy
Which system of linear inequalities is graphed?

Answers

Answer:

y ≥ 3x-1

x+3y ≤ 6

Step-by-step explanation:

what is the value of this expression below when z=3
10z^2-2z-2

Answers

Answer:

82

Step-by-step explanation:

10z^2-2z-2

10x3^2-2x3-2

90-6-2

90-8

82

Answer:

82

Step-by-step explanation:

Evaluate 10z² - 2z - 2 where z = 3:

[tex] \longrightarrow [/tex] 10z² - 2z - 2 = 10 × 3² - 2 × 3 - 2

3² = 9:

[tex] \longrightarrow [/tex] 10 × 9 - 2 × 3 - 2

10 × 9 = 90:

[tex] \longrightarrow [/tex] 90 - 2 × 3 - 2

-2 × 3 = -6:

[tex] \longrightarrow [/tex] 90 - 6 - 2

90 - 6 - 2 = 90 - (6 + 2):

[tex] \longrightarrow [/tex] 90 - (6 + 2)

6 + 2 = 8:

[tex] \longrightarrow [/tex] 90 - 8

[tex] \longrightarrow [/tex] 82

A city park has a large circular garden with a path around it. The diameter of the garden is 60 feet. Jason works for the City Park Department. He needs to spread plant food all over the garden. What is the area of the park he will cover with plant food?

Answers

Answer:

He will cover 2,827.433 feet² area of the park with plant food.

Step-by-step explanation:

The diameter of the garden is 60 feet and the radius will be 60 feet/2 = 30 feet.

diameter= 60 feet

radius = diameter/ 2= 60/2= 30 feet

The area of the circle can be found by the formula πr²

Area= πr²=π(30)²

 Area = 900π= 2,827.433 feet²

He will cover 2,827.433 feet² area of the park with plant food.

WILL MARK BRAINLYIST IF YOU ANSWER CORRECTLY!!!!!! As water evaporates from a potted plant, its weight changes at a rate of -1 5/8ounces per day. Part A Estimate the change in the potted plant’s weight after one week. Explain your thinking. Part B Write and solve an equation using exact values to show the change in the plant’s weight after one week. Part C Explain how your estimate shows your answer is reasonable.

Answers

For part A it would be 11 3/8 ( I did the math fam ) for part b it would be y = 1 5/8x, you just substitute the x for 7 and you’d get the answer from part a, For part C you would just say that you multiplied the 1 5/8 rate by 7 to get the total amount of weight lost within that week

Now I’ll take that brainliest fam, lmk if it was right

simplify (3a²b²)²+(ab)²​

Answers

Answer:

[tex]a^{2} b^{2}[/tex] (9[tex]a^{2} b^{2}[/tex] + 1)

Step-by-step explanation:

simplify (3a²b²)²+(ab)²​; for the first term, square the 3 and multiply the exponents by 2, also multiply the exponents by 2 in the second term

[tex]9a^{4} b^{4} + a^{2} b^{2}[/tex] ; factor out [tex]a^{2} b^{2}[/tex]

[tex]a^{2} b^{2}[/tex] (9[tex]a^{2} b^{2}[/tex] + 1)

(3a^2b^2) + (ab)^2 = (3a^2b^2) + (a^2b^2)
= 4a^2b^2

22. Roberto is an advertising sales representative for a magazine. He earns a commission on
his total sales each month. Last month, Roberto sold $75,000 in advertising. His commission
was $12,750. What percent does Roberto earn as commission?

Answers

Answer:

17%

Step-by-step explanation:

12,750/75,000=0.17

Which means it's 17%

Brainliest please-

choose the graph that represents the linear equation y = 2x + 1

Answers

Answer:

The third option is the answer.

Step-by-step explanation:

In the formula y = mx + b, using the equation given,

m = 2, which means that the line goes up 2 units and right 1 unit.b = 1, which means that the y-intercept, or where the line touches the y-axis, is 1.

Answer:

the 3rd option

Step-by-step explanation:

In the formula y = tx + b, using the equation given,

t = 2, which means that the line goes up 2 units and right 1 unit.

b = 1, which means that the y-intercept, or where the line touches the y-axis, is 1.

y = (x + 6)(x – 7)
Distribution

Answers

Answer:

Y = [tex]x^{2}[/tex] - x - 42

Step-by-step explanation:

You can use the foil method

first, outside, inside, last

multiply the x’s together, the x times -7, the 6 times x, and then 6 times -7

Y = [tex]x^{2}[/tex] - x - 42

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