Use this equation to find dy/dx. 4y cos(x) = x2 + y2

Answers

Answer 1

Let's differentiate implicitly,
don't worry about solving for y explicitly before differentiating.

(4y)cosx = x^2 + y^2

Apply product rule on the left,
and power rule on the right-hand terms,

(4y)'cosx + 4y(cosx)' = (x^2)' + (y^2)'
4y'cosx + 4y(-sinx) = 2x + 2yy'
4y'cosx - 4ysinx = 2x + 2yy'

Let's get both y' terms on the left side,
and everything else on the right,

4y'cosx -2yy' = 2x + 4ysinx

Factor y' out of each term,

y'(4cosx - 2y) = 2x + 4ysinx

Solve for y' (which is dy/dx) by dividing by the stuff,

y' = (2x + 4ysinx) / (4cosx - 2y)

You can divide a 2 out of everything to simplify it down a little bit.

y' = (x + 2ysinx) / (2cosx - y)

Related Questions

find all sets of three consecutive even integers whose sum is greater than 102 and less than 116

Answers

so three consecutive integers 2k,2(k+1),2(k+2)
there sum will be
2k+2(k+1)+2(k+2)
2k+2k+2+2k+4
6k+6
so setting the inequality
102<6k+6<116
subtracting 6 from all sides
96<6k<110
16<k<18.3333
since k is an integer
the only integers between 16 and 18.3
are 17 and 18
so
when k=17
2(17),2(17+1),2(17+2)
34,36,38
when k=18
2(18),2(18+1),2(18+2)
36,38,40
so to check are soultion we substitute
34+36+38=108 which is between 102 and 116
36+38+40=114 which is between 102 and 116
so our soultion is correct
the final answer will be
{{36,38,40},{38,40,42}}

What is the value of the expression 54.36 divided by 0.1

Answers

54.36 / 0.1 = 543.6 <==

A point P is 100m away from a vertical flag pole, which is 13m high. What is the angle of elevation to the top of the flagpole from P?

Answers

check the picture below.

make sure your calculator is in Degree mode, if you need the angle in degrees.

Serena has 6 photo albums with 15 photos in each. Her friend Maya has 8 albums with 13 photos in each. If Serena adds another 12 photos to her albums how many photos will Serena and Maya have in all?

Answers

serena has 6 photo albums with 15 photos in each
so serena has (6 * 15) = 90 photos.
maya has 8 albums with 13 photos in each.
so maya has (8 * 13) = 104 photos
if serena add another 12 photos to her album....(90 + 12) = 102 photos

so in total, serena and maya have 102 + 104 = 206 photos <=

serene=6x15=90
maya=8x13=104
serene=90+12=102
so add maya and serene;
102+104=206 answer

If (6 to the power of 2)x = 1, what is the value of x? Explain your answer.

If (6 to the power of 0)x = 1, what are the possible values of x? Explain your answer.

PLEASE HELP AND EXPLAIN I CANT FAIL THIS QUESTION HELPPP!!!

Answers

do you Mean
(6²)x = 1
if yes then x =1/(6²) = 6-² or 1/36

also (6^0)x= 1
recall 6^0 = 1
so you have 1x=1
x=1

solve the equation 0.35(x+4)=0.25(x-6)

Answers

Answer:

x=-29

Step-by-step explanation:

First multiply 0.35 by x+4 and 0.25 by x-6 after you do that you will get

0.35x+1.4=0.25x-1.5

now add 1.5 from -1.5 and 1.4 now your equation on will look like this

0.35x+2.9=0.25x

Now subtract 0.35x from both sides of the equation and your equation will look like this

2.9=0.1x

at this point you divide to get your answer, divide 2.9 and 0.1x by -0.1 and you will end up with 2.9 over -0.1 once you divide you will get -29=x

The value of x is -29.

What is Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

0.35(x+4)=0.25(x-6)

Now, solving for x

0.35 x + 1.4 = 0.25x - 1.5

0.10x = -2.9

x= -29

Hence, the value of x is -29.

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What symbols relate to the numbers 25 ? 35

Answers

The symbols that would relate the two would be 25 < 35

5/2(6x-7)+ 4/3(2+9x)

Answers

162x - 89 That is ur answer
6

5/2(6x-7)+ 4/3(2+9x)
=15x - 35/2 + 8/3 + 12x
= 27x - 105/6 + 16/6
= 27x - 89/6

The cartesian coordinates of a point in the xy-plane are (x, y) = (-3.84, -2.87) m. find the polar coordinates of this point.

Answers

We know from the signs of x and y that this point is in QIII. Thus, the angle as measured from the positive x-axis is also in QIII.
First, use the Pyth. Thm. to determine the length of the ray from the origin to this point: (-3.84)^2 + (-2.87)^2 = L^2; L = sqrt (22.98), or approx. 4.79. The angle is 0.64 radian + pi radians, or 3.78 radians (which, as you can verify, is in QIII.

Thus, the point (-3.84, -2.87) becomes (4.79, 3.78 rad) in polar coordinates.
Let me know if you need help with the trigonometry involved here.

Suppose that you invest $5873 in an account that earns interest at an APR of 4.4%, compounded monthly. Determine the accumulated balance after 7 years.

Answers

Given:
P = $5873, the principal
r = 4.4% = 0.044, the interest rate
n = 12, twelve monthly compoundings in a year
t = 7 years

Note that
n*t = 12*7 = 84
r/n = 0.044/12 = 0.003667

The accumulated balance after 7 years is
A = 5873*(1 + 0.003667)⁸⁴ = $7,986.90

Answer: $7,986.90

If P is the midpoint of XY,XP=8x-2 and PY=12x-30 find the value X

Answers

check the picture below.

P being the midpoint, will cut XY in two equal halves.

Using the midpoint concept, it is found that x = 7.

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

The midpoint divides a segment into two segments of equal length.P is the midpoint of XY, thus XP = PY.

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

[tex]XP = 8x - 2[/tex]

[tex]PY = 12x - 30[/tex]

Since they are equal, we use it to find x.

[tex]XP = PY[/tex]

[tex]8x - 2 = 12x - 30[/tex]

[tex]4x = 28[/tex]

[tex]x = \frac{28}{4} = 7[/tex]

The value of x is 7.

A similar problem is given at https://brainly.com/question/10956693

negation of all owls fly?

Answers

Looking at this in terms of sets, let's call O the set of all owls, and F the set of all things that can fly. What this original statement is saying every animal that's a member of the set of all owls is also a member of the set of all things that can fly, or in other words, O⊂F (O is a subset of F). Negating this tells us that, while there's at least one element of O that also belongs to F, O is not contained entirely in F (O⊆F, in notation), so a good negation or our original statement might be:

Not all owls can fly.

...wow the other person was fantastic.. I’m not even gonna try competing...

Suppose you are a small business owner. How would a market demand schedule or a market demand curve be useful?

Answers

Because the market demand curve is the summation of all the individual demand curves in a given market. It shows the quantity demanded of the good by all individuals at varying price points. In other words, it shows the relationship between consumer demand and price.

Consider a point on the trans-australian highway, where two old wombats live. arrivals of cars at this point follow a poisson distribution; the average rate of arrivals is 1 car per 12 seconds.

Answers

Given that the arrivals of cars at the trans-australian highway follow a poisson distribution with the average rate of arrivals as 1 car per 12 seconds.

This is a Poisson distribution with a mean of 1 car every 12 seconds.

Part A:

The probability of a Poisson distribution is given by:

[tex]P(X=x)= \frac{e^{-\lambda}\lambda^x}{x!} [/tex]

Given tha one of the old wombats requires 12 seconds to cross the highway, and he starts out immediately after a car goes by.

The probability he will survive is the probability that no car passes through the point in the next 12 seconds.

[tex]P(x=0)= \frac{e^{-1}(1)^0}{0!} =e^{-1}=0.368[/tex]

Therefore, the probability that he will survive is 0.368

Part B:

Given that at the same point of the highway there is another old wombat, slower but tougher than in the previous exercise. He requires 24 seconds to cross the road, but it takes two cars to kill him. (A single car won’t even slow him down. The arrival rate of cars is still one car per 12 seconds.)

Since the arrival rate of cars is one car per 12 seconds, then, in 24 seconds the arrival rate is 2 cars. (i.e. λ = 2)

The probability that he survives is the probability that 2 cars did not pass through the point.

[tex]P(X\neq2)=1-P(X=2)=1- \frac{e^{-2}(2)^2}{2!} =1-0.135=0.865[/tex]

what sequence is next 3 9 27 81

Answers

You are multiply 3 each time, so your next number is

81 x 3 = 243

your answer is 243

hope this helps

courtlynn combines 7/8 cup sour cream with 1/2 cup cream cheese. she then divides the mixture between two bowls. how much mixture does courtlynn put in each bowl?

Answers

4/5 because 7/8+1/2=8/10 so half of 8/10 is 4/5 and half goes in to each bowl

its 14/8 because to divide you have to swich one fraction and then multiply

George exercises 15 minutes a day, every day of the year. How many minutes a year does George exercise? Write and solve an equation to find the answer.

Answers

15 minutes 365 days
----------------- * --------------- = 5475 minutes/year
day 1 year

For each sequence, find a formula for the general term, a_n. for example, answer n ^2 if given the sequence: \lbrace 1, 4, 9, 16, 25, 36, . . . \rbrace

Answers

This is clearly a sequence of the squares of the integers {1, 2, 3, .... }.

The general term is an = n^2.

A dance studio charges an application fee of $75 and $50 per month for membership. This is represented by the linear equation C = 50x + 75, where C represents the cost and x represents the number of months. They are running a "no application fee" special during the month of January. How should the linear equation be changed to represent the new price?

Answers

The first one is C = 50x + 75, where 75 is the application fee. When they take out the application fee, it will become:

C = 50x +75 (-75)

your answer will be C = 50x

hope this helps

Final answer:

To represent the new price during the 'no application fee' special, the dance studio's cost equation would change from C = 50x + 75 to C = 50x by removing the $75 application fee.

Explanation:

The dance studio's original cost equation is C = 50x + 75, where C represents the total cost and x represents the number of months of membership. The $75 in the equation represents the application fee. During the "no application fee" special in January, this fee is waived, so the new equation would only include the monthly membership cost, which is $50 per month. The new equation would be C = 50x, removing the application fee entirely from the cost calculation.

Tyler is playing a game in which he needs to guess an integer. Which of the following is a number that tyler can gues

Answers

well a interger is any negative number so -1 or -2 or -3 or -4......

A problem states: "There are 9 more children than parents in a room. There are 25 people in the room in all. How many children are there in the room?"

Let c represent the number of children.

Which expression represents the number of parents?

c−9
9−c
c⋅9
c + 9

Answers

C-9 because once you take away the children number, you will have the remaining adults

Answer: c-9

Step-by-step explanation: i did the quiz

Which mathematical expression is equivalent to the expression "nine less than six times the number t"?

Question 5 options:

A. 6 - 9t

B. 6t - 9

C. 9 - 6t

D. 9t - 6

Answers

The answer is C. 9-6t because it nine les than so you would be subtracting then it said six times the number t so you would have to multiply 6 times t.

The Expression is 6t - 9.

What is Equations?

An equation is a mathematical statement that connects two expressions of equal value by using the "equal to" symbol.

A mathematical statement with two algebraic expressions on either side of an "equal to (=)" sign is called an equation. It demonstrates the equality of the relationship between the expression written on the left and right sides.

Given Expression "nine less than six times the number t"

which means number 9 should less than product of 6 and t

six times the number t implies the product of t and 6 which is equal to

6t,

and subtract 9 from 6t we get

6t - 9

Hence the expression "nine less than six times the number t" is 6t - 9.

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which has the greater volume: a 4 meter cube or a rectangular solid that that is 8 meters long, 2 meters wide and 2 meters high

Answers

Answer:

The cube has the greater volume.

Step-by-step explanation:

The volume of a cube is given as:

[tex]V=x^3[/tex]

Where [tex]x[/tex] is the measure of 1 side (all sides of a cube are same)

The volume of a rectangular solid is given as:

[tex]V=l*w*h[/tex]

Where [tex]l[/tex] is the length, [tex]w[/tex] is the width, and [tex]h[/tex] is the height.

From the problem,

Volume of cube = [tex](4)^{3}=64[/tex] [since each side is given as 4]Volume of rectangular solid = [tex]8*2*2=32[/tex] [the length is given as 8, width is 2, and height is 2]

The cube has the greater volume.

Assume that the salaries of elementary school teachers in the united states are normally distributed with a mean of $32,000 and a standard deviation of $3000. if 100 teachers are randomly selected, find the probability that their mean salary is less than $32,500.

Answers

Can you make this question clearer to read

Answer: 0.9525

Step-by-step explanation:

Given : The salaries of elementary school teachers in the united states are normally distributed with a mean of [tex]\mu=\$32,000[/tex] and a standard deviation of [tex]\sigma=\$3000[/tex].

Sample size : n= 100

Let x be a random variable that denotes the salaries of elementary school teachers in the united states.

Formula : [tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

Then, the probability that their mean salary is less than $32,500 will be :-

[tex]P(x<32500)=P(\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}<\dfrac{32500-32000}{\dfrac{3000}{\sqrt{81}}})\\\\=P(z<\dfrac{500}{\dfrac{3000}{10}})\approx P(z<1.67)=0.9525\ \ [\text{Using z-value}][/tex]

Hence, the probability that their mean salary is less than $32,500 = 0.9525

Find the distance between 0,3 and -2-5 round nearest hundreth

Answers

The answer is 8.25
The formula for distance will be the √ (x2-x1)²+(y2-y1)². (as you can see)
Don't be intimidated!
Step one:
Take the two cordinates (0,3) and (-2,-5)
Step two: It doesn't matter which one you choose, but choose one to be your x1,y1 and another to be your x2,y2
In this situation I choose (0,3) to represent (x1,y1) and (-2,-5) to represent (x2,y2). DO NOT over think this, you got it!
Final Step:
Simply plug those numbers into the represented formula it should end up like
√(-2-0)²+(-5-3)²
Simply solve it yourself or use a calculator such as Desmos to find you answer

Hope this helps!

I want to draw your attention to the connection finding the distance between two points has with one of the oldest and most ubiquitous theorems in mathematics: the Pythagorean Theorem. If you'll recall, the Pythagorean Theorem states that, in any right triangle, the sum of the squares of its legs is equal to the square of its hypotenuse (the side opposite the triangle's right angle), or more formally:

a²+b²=c², where a and b are the length of the legs of the triangle, and c is the length of its hypotenuse.

What does that have to do with finding the distance between two points? For that, I want you to take a look at the two images I've attached to this post. If we just plot the two points on the x-y plane and draw a line between them, the connection to Pythagoras isn't too obvious, but when we connect the x and y components of the points, it should become immediately clear. The vertical and horizontal components of the points combine with the diagonal to form a right triangle, and the distance is the length of its hypotenuse!

We can't apply the theorem yet, though; we'll first need to find the lengths of the legs before we can determine the length of the hypotenuse. For that, we'll need to find the distance between each of the points' corresponding coordinates. To find those, we just need to subtract those coordinates from one another. We find the distance between the x coordinates to be 0 - (-2) = 2 and the distance between the y coordinates to be 3 - (-5) = 8.

(Note that we could've chosen to do the subtraction the other way around, too, obtaining negative differences. Usually, we'd deal with these by taking the absolute value of the result, but in this case, our answers will get squared away - literally - by the Pythagorean Theorem.)

Now that we have the legs of the triangle, we're ready to find the hypotenuse. We enter our values in:

2²+8² = d²
4 + 64 = d²
68 = d²
√68 = d

(we've chosen d here to represent "distance," though it plays the same role c did in the other statement of the theorem)

And from there, you can use the calculator of your choosing to get a good approximation.

One last note: here's a generalization of everything we did here, now that you have some background for why it is the way it is, and where exactly it comes from:

For any two points [tex](x_1,y_1), (x_2,y_2)[/tex]:

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

Marcos is organizing a fundraiser for his youth group. He spent $38.00 on paper products, $187.00 on food, and $40.00 on decorations. If his budget was $280.00, how much money does Marcos have left?
$15.00
$25.00
$115.00
$125.00

Answers

$15 hope this helped :))

Answer:

15$

These are simple algerbra problems.

What is the simplified form of the left side of the following equation?

2x-4+5x=8

Select the correct answer below.

A.2x+1
B.3x-4
C.5x-2
D.7x-4

Answers

Combine like terms.
The term 2x and the term 5x are like terms and can be combined into 7x.
The answer is 7x - 4

An airplane allows each passenger 36 kilograms of luggage. Carl has to lower the weight of his suitcase by 25% to stay within the limit. How much did the suitcase originally weight?

Answers

Let the original suitcase weight be x. This x will be reduced by multiplying it by (1.00-0.25), or 0.75. 0.75x = 36 kg. Solve for x.

Dividing both sides of this last equation by 0.75, we get x = 48.

Carl's suitcase originally weighed 48 lb. 25% of that is 12. x less 12 is 36 lb, which is acceptable to the airline.

Marcus rented a movie for $4 and some video games for $6 each. He paid $22. How many games did he rent?Choose two answers: one for the equation that models this situation and one for the correct answer.

A.Equation: 6 + 4x = 22
B.Answer: 3 video games
C.Answer: 4 video games
D.Equation: 4 + 6x = 22

Answers

Your equation should be:

4 + 6x = 22

This is so because he only bought one movie, but he bought "some" video games. The variable x represents some in the problem.

Solve the equation.

4 + 6x = 22

Subtract 4 from both sides of the equation.

6x = 18

Divide both sides by 6.

x = 3

Marcus rented 3 video games.

Solution :

D. 4 + 6x = 22
B. 3 video games

Answer:

4 + 6x = 22 and 3 video games

Step-by-step explanation:

ape-x

If there is a positive correlation between salary and education, then based on the table shown, which of the following careers requires the most education? a. accountant b. paralegal c. photographer d. surveyor

Answers

it is A. accountant because out of the options you gave me that one gets paid the most

Answer:

Option a. accountant.

Step-by-step explanation:

We have been given the positive correlation graph between salary and education

Positive correlation means a linear relationship between two that means if education increases salary increases.

We need to tell which among the given options requires most education the one which will have highest salary.

That means the Accountant among the given option requires most education.

Because he has highest salary among given four options.

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Analyze the rhetorical technique in the sentence above. Write your answer in the box. Which type of triangle has one angle with a measurement greater than 90? A. Obtuse B. Acute C. Isosceles D. Right Explain why the Tennis Court Oath was a critical moment on the road to rebellion. The model of the mind that takes into account the human ability to mentally stimulate experiences is called the ______ model Please help me! And can you explain how you got that answer please? In the combustion chamber of an engine, the initial volume is 450 cm3 at a pressure of 1.0 atmosphere. If the piston displaces 402 cm3 of the total, what is the resulting pressure in the combustion chamber? (Assume negligible temperature change.) Hint: Calculate the new volume by subtracting the amount of space the piston takes up from the initial volume Which came first, the chicken or the egg?a.the egg, because the amniotic egg evolved well before the first bird.b.the egg, because the chicken is not a real species.c.the chicken, because during speciation the adult stage always precedes the juvenile stage.d.the chicken, because the amniotic egg did not evolve until after the first chicken appeared.e.the egg, because the chicken had to cross the road to sit on it? Review the chart, which shows the population sizes of three African animals in 1990 and in 2000. 1990 2000Lions . 100,000 . 47,000Cheetahs 50,000 7,500Zebras 15,000 2,500 Which explanation is best supported by the numbers in the chart?A)Lion and cheetah populations compete for the food source of zebras, and lions outcompete cheetahs.B)The dwindling zebra population has led to the decline of the predator lion and cheetah populations.C)Overhunting of lion and cheetah populations has led to a decline in the food source population.D)Lion and cheetah populations compete for the food source of zebras, and cheetahs outcompete lions. The minimal circumstances under which medical attention should be sought for a burn victim is when the surface area of a second degree burn is great than What is the name of the two-pronged selective prevention program that was based on developmental principles and targeted multiple risk factors in high-risk children? You know your professor is a "stickler" when it comes to spelling and grammar in your papers and you detest this, because you're enrolled in a business course, not an english course. however, you are going to proofread your papers so that you don't lose points on your assignments. which element of your attitude toward your professor does proofreading best describe? In kingdom xyz, the penalty for telling critical stories about the queen was having your tongue cut off. this is an example of using ____ to control people What is the length of each side of a cube whose volume is 8? Question 4 options: 1 2 3 4 Water iscrucial to all lifeessential to all lifenot that importantfound on most planets The individual whose name is associated with a natural experiment during an outbreak of cholera in london was A patient's cotranslational and post-translational processes have reversed roles. based on this knowledge, identify what type of sorting occurs with proteins destined for each organelle Multiplication property: if angle j equals 30 then 2m angle j equals Jose bought a bag of 6 oranges for $2.82. He also bought 5 pineapples. He gave the cashier $20 and received $1.43 change. How much did each pineapple cost? "____________ is a process whereby two or more parties reach a mutually agreeable arrangement." in electrolysis, electrons move between two metal strips called Steam Workshop Downloader