Find a formula for dy/dx if sin x + cos y + sec(xy) = 251

Answers

Answer 1

Answer:

[tex]\displaystyle \frac{dy}{dx} = \frac{-cos(x) - ysec(xy)tan(xy)}{-sin(y) + xsec(xy)tan(xy)}[/tex]

General Formulas and Concepts:

Pre-Algebra

Distributive Property

Algebra I

Factoring

Calculus

Derivatives

Derivative Notation

Derivative of a constant is 0

Trig Differentiation

Derivative Rule [Chain Rule]:                                                                                       [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Implicit Differentiation

Step-by-step explanation:

Step 1: Define

Identify

sin(x) + cos(y) + sec(xy) = 251

Step 2: Differentiate

[Implicit Differentiation] Trig Differentiation [Chain Rule]:                             [tex]\displaystyle cos(x) - sin(y)\frac{dy}{dx} + sec(xy)tan(xy) \cdot (y + x\frac{dy}{dx}) = 0[/tex]                       [Subtraction Property of Equality] Isolate  [tex]\displaystyle \frac{dy}{dx}[/tex]  terms:                                     [tex]\displaystyle -sin(y)\frac{dy}{dx} + sec(xy)tan(xy) \cdot (y + x\frac{dy}{dx}) = -cos(x)[/tex][Distributive Property] Distribute sec(xy)tan(xy):                                            [tex]\displaystyle -sin(y)\frac{dy}{dx} + ysec(xy)tan(xy) + xsec(xy)tan(xy)\frac{dy}{dx} = -cos(x)[/tex][Subtraction Property of Equality] Isolate  [tex]\displaystyle \frac{dy}{dx}[/tex]  terms:                                     [tex]\displaystyle -sin(y)\frac{dy}{dx} + xsec(xy)tan(xy)\frac{dy}{dx} = -cos(x) - ysec(xy)tan(xy)[/tex]Factor out  [tex]\displaystyle \frac{dy}{dx}[/tex]:                                                                                                   [tex]\displaystyle \frac{dy}{dx}[-sin(y) + xsec(xy)tan(xy)] = -cos(x) - ysec(xy)tan(xy)[/tex][Division Property of Equality] Isolate  [tex]\displaystyle \frac{dy}{dx}[/tex]:                                                      [tex]\displaystyle \frac{dy}{dx} = \frac{-cos(x) - ysec(xy)tan(xy)}{-sin(y) + xsec(xy)tan(xy)}[/tex]

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Implicit Differentiation

Book: College Calculus 10e


Related Questions

Luis, Pedro y Ernesto fueron a comer pizza. Entre Luis y Ernesto comieron el doble que Pedro. Pedro comió el doble que Ernesto. Entre los 3 se comieron una pizza ¿Qué porción se comió cada uno?

Answers

Answer:

Luis comió 1/2 pizza, Pedro comió 1/3 pizza y Ernesto comió 1/6 pizza.

Step-by-step explanation:

Dado que Luis, Pedro y Ernesto fueron a comer pizza, y entre Luis y Ernesto comieron el doble que Pedro, y Pedro comió el doble que Ernesto, y entre los 3 se comieron una pizza, para determinar qué porción se comió cada uno se debe realizar el siguiente cálculo:  

L + P + E = 1

L + E = 2P

P = 2E

L + E = 4E

L = 4E - E

L = 3E

3E + 2E + E = 1

6E = 1

E = 1/6

E = 0.166

P = 0.166 x 2

P = 0.333

L = 0.166 x 3  

L = 0.5  

L = 1/2

Por lo tanto, Luis comió 1/2 pizza, Pedro comió 1/3 pizza y Ernesto comió 1/6 pizza.

What is the volume of this prism?


28 cubic units
9 cubic units
17 cubic units

Answers

Answer: C) 17 cubic units

==================================

Work Shown:

L = 5 = length

W = 2 = width

H = 1.7 = height

V = volume

V = L*W*H

V = 5*2*1.7

V = 17 cubic units

It takes 3 hours for a boat to travel upstream against the current and 1.8 hours to travel the same distance downstream with the current. What is the speed of the boat in still water if the speed of the current is 3 mph?

Answers

Answer:

Step-by-step explanation:

There are a couple of things to know before we set up the table for this problem. First, we need to remember that if the boat is traveling against the current, that the current is going to slow the boat down; likewise, going with the current will speed the boat up. Second, we need to realize that if the boat's distance against the current is the same as the distance with the current, then the distances in the equations will be set equal to one another.

Set up the table with U (against the current) and D (with the current) on the outside and fill in what we are given:

                      d           =           r            x            t

U    

D

This is the table. Now we will fill it in:

                     d           =           r              x            t

U                                         r - 3             x            3

D                                         r + 3             x           1.8

The formula for the distance equation is at the top of the table as d = rt. We already decided that the distances that the boat traveled upstream and downstream were the same so we will set those d values equal to each other, but we first need to get the d value for each row. If distance = rate times time, then for the first row:

d = (r - 3)3 and

d = 3r - 9. For the second row:

d = (r + 3)1.8 and

d = 1.8r + 5.4. Setting them equal to each other:

3r - 9 = 1.8r + 5.4 and

1.2r = 14.4 so

r = 12 mph

what is the correct answer?

Answers

Answer:

well we can see the sign's a trapezoid

area of trapezoid = 1/ 2 × sum of parallel sides × height

= 1/ 2 × (7+5) × 4

= 1/ 2 × 12 × 4

= 24 Sq feet

that's first option

Elena is feeding her neighbor's dogs. Each dog gets 2/3
cup of dog food, and she uses 3 1/3 cups of food. How many dogs does her neighbor have?
5 5/8 cups of water fill 4 1/2 identical water bottles. How many cups fill each bottle?

Answers

Answer:

5 dogs

1 1/4 cups per bottle

Step-by-step explanation:

10/3 ÷ 2/3 get solved by 10/3 x 3/2, which gives you 30/6 or 5

45/8 ÷ 9/2 is 45/8 x 2/9 which is 5/4 or 1 1/4

What is the length of the hypotenuse?

A. 10
B. 14
C. 48
D. 100

Answers

Option A= 10

Process

Using Pythagoras Theorem,

8²+6²= (hypotenuse)²

64+36= (hypotenuse)²

(hypotenuse)²= 100

hypotenuse= √100

hypotenuse= 10

So Option A= 10

Hope This Helps You ❤️

Answer:

The hypotenuse is A. 10.

Step-by-step explanation:

To find the length of hypotenuse we can use  the pythagoras theorem formula:

[tex]a^{2} +b^{2} =c^{2}[/tex]

[tex]=>6^{2} +8^{2} = c^{2}[/tex]

[tex]=> 36 + 64 = c^{2}[/tex]

[tex]=> 100 =c^{2}[/tex]

[tex]=> c = \sqrt{100}[/tex]

∴ [tex]c[/tex] [tex]= 10[/tex]

Graph the system of​ equations, and determine the solution.
x+5y=5
2x+10y=60

Answers

Step-by-step explanation:

the systems have no solution

the lines are parallel each other

graph as attached

PLEASE HELP ME WITH THIS

Answers

Answer:

AB = Secant

DB = Diameter

AB = Chord

OB = Radius

BC = Tangent

Step-by-step explanation:

The image provided below is a great reference!

Note: The answers are put in order.

Use the given scale factor in the side length of the scale drawing to determine the side links of the real object

Answers

Answer:

A. side a is 7 inches long, side b is 6 inches long,and side c is 3 inches long

Step-by-step explanation:

Here is the complete question. Please find attached a diagram showing the scaled and real drawing

Use the given scale factor and the side lengths of the scale drawing to determine the side lengths of the real object

A. side a is 7 inches long, side b is 6 inches long,and side c is 3 inches long

B. side a is 30 inches long, side b is 25 inches long, and side c is 20 inches long

C. side a is 40 inches long, side b is 35 inches long,and side c is 20 inches long

D. side a is 175 inches long,side b is 150 inches long, and side c is inches long

A scale drawing is a reduced form in terms of dimensions of an original image / building / object

the scale drawing is usually reduced at a constant dimension

scale of the drawing = original dimensions / dimensions of the scale drawing

The scaled drawing is an enlarged image of the original triangle.

It is enlarged at a ratio of 5:1

original dimensions

a = 35/5 = 7

b = 30 / 5 = 6

c = 15/5 = 3

Jackie, Morgan, kyle and Chung ran the 100 meter dash. Jackie finished in 17.6 sec, Morgan finished in 17.06 sec, kyle finished in 17.66 sec, and chung finished in 17.066. Wich of them finished in the least amount of time

Answers

Answer:

Morgan (17.06 secs)

Step-by-step explanation:

Jackie, morgan, Kylie and chung ran the 100 meter dash race

Jackie finished the race in 17.6 secs

Morgan finished the race in 17.06 secs

Kylie finished the race in 17.66 secs

Chung finished the race in 17.066 secs

Hence Morgan finished the race in the least amount of time in 17.06 seconds

Multiplying and dividing rational expressions

Answers

Answer:

the answer in the picture

Step-by-step explanation:

Please I need help?!?!?!?!?!

Answers

Answer: y=7

Step-by-step explanation:

Using the formula: (y - y1) = 0 (x - x1)

Substitute x1 with -2, and y1 with 7 and set the slope as 0.

Y-7=0(x-(-2))

Y - 7 = 0 (x + 2)

Anything times 0 = 0, so cancel out the -2.

Y-7=0

Add the 7 to the 0.

Y = 7

Please provide an explanation.

Answers

Answer:

-9

Step-by-step explanation:

In a linear equation like this, the first number is the slope and the last number is the y-intercept

The numerator of a given fraction is 4 less than the denominator. if 3 is subtracted from the numerator and 5 is added to the denominator, the fraction becomes 1/4, what is the given fraction?​

Answers

Answer:

Step-by-step explanation:Given that the numerator of a given fraction is 4 less than its denominator.

Also given that 3 is subtracted from the numerator and 5 is added to the denominator, the fraction becomes one by fourth .

Let the fraction be  

Since the numerator of a given fraction is 4 less than its denominator we have,

Numerator=Denominator-4

⇒ a=b-4

Since 3 is subtracted from the numerator and 5 is added to the denominator, the fraction becomes one by fourth we have

4(a-3)=1(b+5)

4a-12=b+5

4a-b=17

4(b-4)-b=17   ( ∵ a=b-4)

4b-16-b=17

3b=17+16

3b=33

⇒ b=11

Now put b=11 in a=b-4 we get

a=11-4

⇒  the fraction is a/b=7/11

Which phrase represents the algebraic expression for r + 12?
A. The difference of a number and twelve.
B. The product of a number and twelve.
C. The quotient of a number and twelve.
D. The sum of a number and twelve.

Answers

Answer:

I guess d is the answer . cause the sum of a number (a number added to something) represented by a variable is added to twelve

What is the solution set of the equation (x - 2)(x - 8) = 0?
1)-2 and 8
2)-2 and -8
3) 2 and 8
4) 2 and -8

Answers

Answer:

Step-by-step explanation:

2 and 8

What is the area, in square units, of the shaded region? (nearest tenths place)

Answers

Answer:

169.6

Step-by-step explanation:

Subtract the polynomials.
( x^6 -2x^5 –x^3 — 7) – (3x^6 - 3x^5 -2x^ 2 – 5)

Answers

Answer: -2x^6+x^5-x^3-2+2x^2 Hope that helps!

Step-by-step explanation:  

1. Remove Parentheses x^6-2x^5-x^3-7-3x^6+3x^5+2x^2+5

2. Collect like terms (x^6-3x^6)+(-2x^5+3x^5)-x^3+(-7+5)+2x^2

3. Simplify and your answer would be -2x^6+x^5-x^3-2+2x^2

in a box of pens, 30% of them are blue, 45% are red and the rest are black. if there are 360 red pens, find the total number of pens.

Answers

Answer:

800

Step-by-step explanation:

find the value of x
answers
118
62
82
28

Answers

Answer:

118°

Step-by-step explanation:

Don't think the answer is 62° this time both 118° and angle x are congruent.

What do I mean by that? Both angles measure the exact same thing.

The only difference is their line length (n) and (m).

In a geometric sequence, the ratio between consecutive terms is...

Answers

Answer: The same or equal

========================================================

Explanation:

Consider an example like 3, 6, 12, 24, 48, ...

The ratio between consecutive terms is

6/3 = 212/6 = 224/12 = 248/2 = 2

Each time we divide any given term over its previous one, we get the same ratio 2. We call this the common ratio. In terms of notation, the variable r is used for the common ratio, so r = 2 in this case.

As another example, the geometric sequence 5, 50, 500, 5000, ... has r = 10 as the common ratio because we multiply each term by 10 to get the next one. Moving forward has us multiply by r, moving backward and we divide by r. The value of r cannot be zero, but it can be negative.

An example with r being negative would be something like

1, -1, 1, -1, 1, -1, ....

we just bounce back and forth between those two values. In this case, r = -1.

A) By how many % did 40 increase to 70?

B) By how many % did 70 decrease to 40

Answers

Answer:

A. by 3 percent

B. by 3 percent

Answer:

A) 75% increase

B)42.8571% decrease

Step-by-step explanation:

The formula to do this is to subrtact the final value-starting value then divide by the starting value and finaly multiply by hundred

it should look like this

[tex]\frac{finalvalue-starting value}{starting value} *100[/tex]

PLZ HELPPPPPPPPPPPPPP​

Answers

Answer:

i believe it is a if not im sorry

Step-by-step explanation:

PLEASE SEE ATTACHED

THANK YOU!!!

Answers

Answer:

use waymath but type it the other way around

Step-by-step explanation:

Answer:

1) it's a circle, (4x + 12)² + (2y - 2)² = 64

2) it's a circle, (x + 4)² + (y - 3)² = 40

3) it's a parabola, (x + 3)² = -4(y - 1)

Step-by-step explanation:

Equation of a circle: (x - h)² + (y - k)² = r²

factorize the equation:

1) => 16x² + 96x + 144 + 4y² - 8y + 4 + 84 = 144 + 4

=> (4x + 12)² + (2y - 2)² = -84 + 144 + 4

=> (4x + 12)² + (2y - 2)² = 64 (equation of the circle)

Graph the circle using the radius and the center.(& compass for drawing circles)

=>(4x - (-12))² + (2y - 2)² = 8²

    (x  -   h   )² +  (y   - k)² = r²

Center: (h, k)  => (-12, 2)

Radius: √r²   => √64 = 8

2) => x² + 8x + 16 + y² - 6y + 9 - 15 = 16 + 9

=> (x + 4)² + (y - 3)² = 15 + 16 + 9

=> (x + 4)² + (y - 3)² = 40 (equation of the circle)

Graph the circle using the radius and the center.(& compass for drawing circles)

=> (x  - (-4)  )² +  (y - 3)² = 40

    (x  -   h   )² +  (y  - k)² = r²

Center: (h, k)  => (-4, 3)

Radius: √r²   => √40 ≈ 6.32

Equation of a parabola facing down: (x - h)² = 4a(y - k)

3) => x + 6x + 9 = -4y - 5 + 9

=> (x + 3)² = -4y + 4

=> (x + 3)² = -4(y - 1) (equation of the parabola)

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Down

=> (x - (-3))² = 4 × -1(y - 1)

    (x -  h  )² = 4 ×  a(y - k)

Vertex: (h, k)  =>  (−3,  1)

Focus:  (h, k + a)  => (-3, 1 + (-1)) => (−3,  0)

Axis of Symmetry:  x = h  => x  =  −3

Directrix:  y = k - a  => y = 1 - (-1) => y  =  2

x     |    y

−5    |   0

−4    |   3/4  

−3    |    1    

−2    |  3/4

−1     |    0

(graphs in the pictures below)

Please please help please

Answers

The answer is 25.6 per gallon

What’s the area of the shape?

Answers

Answer:

Hello! answer: 113.04

Step-by-step explanation:

It looks like you already selected the correct answer! What you do to find it is radius squared × 3.14 so

6 × 6 = 36 36 × 3.14 = 113.04 therefore that is the answer Hope that helps!

Find the slope-intercept equation of the line that passes through (2,-5) and has a slope of 1/3 ​

Answers

Answer:

y = 1/3x - 17/3

Step-by-step explanation:

Given:

Passes through (2, -5)

m = 1/3

Slope-intercept:

y - y1 = m(x - x1)

y - (-5) = 1/3(x - 2)

y + 5 = 1/3x - 2/3

y = 1/3x - 17/3

In ΔDEF, the measure of ∠F=90°, EF = 2.3 feet, and FD = 2.9 feet. Find the measure of ∠D to the nearest tenth of a degree.

Answers

Answer:

[tex]\theta=38.42 \textdegree[/tex]

Step-by-step explanation:

From the question we are told that:

Angle of F [tex]\angle F=90 \textdegree[/tex]

Length of [tex]EF = 2.3 feet,[/tex]

Length of [tex]FD= 2.9 feet,[/tex]

Generally the equation for Angle D [tex]\theta[/tex] is mathematically given by

Since [tex]\angle F=90[/tex].The triangle  is a right angle Triangle

Therefore

 [tex]tan \theta=\frac{EF}{FD}[/tex]

 [tex]tan \theta=\frac{2.3}{2.9}[/tex]

 [tex]\theta=tan^{-1} 0.793[/tex]

 [tex]\theta=38.42 \textdegree[/tex]

While walking outside on a field trip 75%, or 15, of the students in the class wore jackets. Find the number of

students in the entire class.

Answers

Answer:

20

Step-by-step explanation:

Do 15 divided by 0.75

This Question: 1 pt
1 of 20 (0 complete)
ZEFG and ZGFH are a linear pair, m ZEFG = 3n + 19, and mZGFH = 2n + 36. What are mZEFG and mZGFH?
mZEFG =
mZGFH =]
(Simplify your answers.)

Answers

[tex]\huge{ \mathfrak{  \underline{ Answer }\:  \:  ✓ }}[/tex]

Angles forming linear pair are :

[tex] \mathrm{\angle EFG \: \: and \: \: \angle GFH} [/tex]

And we know, they are supplymentary

[tex] \mathrm{\angle EFG \: + \: \angle GFH} = 180 \degree[/tex][tex]3n +1 9 \degree+ 2n + 36\degree = 180 \degree[/tex][tex]5n + 55\degree = 180\degree[/tex][tex]5n = 125\degree[/tex][tex]n = 25\degree[/tex]

So, the measures of the given angles are :

[tex] \mathrm{\angle EFG } = 3n + 19[/tex][tex] \mathrm{ \angle EFG = (3 \times 25\degree) + 19}[/tex][tex] \mathrm{ \angle EFG = 75 \degree+ 19\degree}[/tex][tex]\mathrm{ \angle EFG = 94\degree}[/tex]

And

[tex]\mathrm{ \angle GFH = 2n + 36}[/tex][tex]\mathrm{ \angle GFH = (2 \times 25\degree) + 36\degree}[/tex][tex]\mathrm{ \angle GFH = 50\degree + 36\degree}[/tex][tex]\mathrm{ \angle GFH = 86\degree }[/tex]

_____________________________

[tex]\mathrm{ ☠ \: TeeNForeveR \:☠ }[/tex]

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