Mathematics High School

Find dy/dx by implicit differentiation. y cos x = 5x2 + 3y2

Answers

Answer 1
Final answer:

To find dy/dx by implicit differentiation, differentiate both sides of the equation with respect to x. Apply the product rule and isolate dy/dx by moving terms.

Explanation:

To find dy/dx by implicit differentiation, we'll differentiate both sides of the equation with respect to x. Let's start by differentiating y cos x = 5x2 + 3y2:

Using the product rule, we have: dy/dx * cos x + y * (-sin x) = 10x + 6y * dy/dx

Next, isolate dy/dx by moving terms:

dy/dx * cos x - 6y * dy/dx = 10x - y * (-sin x)
dy/dx * (cos x - 6y) = 10x + y * sin x
dy/dx = (10x + y * sin x) / (cos x - 6y)

Related Questions

The set of ordered pairs represent a function. Write a rule that represent the function. (0,0), (1,6),(2,24), (3,54),(4,96)

Answers

All y coordinates are divisable by 6. What you then get is the square of x, so the function is:

f(x) = 6x²

The required function would be f(x) = 6x² which represents the set of ordered pairs.

What is a function?

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

We have been given that function as sets of ordered pairs :

(0,0), (1,6), (2,24), (3,54), (4,96)

First, we must identify a pattern. It appears that all yₓ values are multiples of 6.

We can divide yₓ by 6x since it is a multiple of 6 and a multiple of x:

y₁/ 6×1 = 1

y₂/ 6 ×2 = 2

y₃/ 6 ×3= 3

y₄/6×4 = 4

We can clearly see a pattern here ;

y/ 6×x = x

y = x × x × 6

y = 6x² = f(x)

Therefore, the required function would be f(x) = 6x² which represents the set of ordered pairs.

Learn more about the functions here:

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Use the four-step procedure to solve the following problem. How much water must be added to a gallon of 10% saline solution to create a 2% solution?

Answers

We have 1 gallon of 10% saline.
How much water (x liters of 0% saline) must be added to make a 2% saline solution?
.10 * 1 + 0x = .02 * (1 +x)
.1 = .02 + .02x
.08 = .02x
x = 4 gallons of water must be added


Answer:

4 gallons of water should be added in 10% saline solution.

Step-by-step explanation:

Let x gallon of water is added in one gallon of 10% saline solution.

Therefore total volume of 10% saline solution will become (1 + x) gallons

Since concentration of water is 0% so equation will be

0.10(1) + 0(x) = .02(1 + x)

0.10 = 0.02(1 + x)

1 + x = [tex]\frac{0.10}{0.02}[/tex]

x + 1 = 5

x = 5 - 1

x = 4 gallons

Therefore, 4 gallons of water should be added to 10% saline solution to create 2% solution.

matt ryan throws a ball 26 yards how many inches did he throw

Answers

936 inches. One yard alone is 36 inches so 26 yards is a very large number!

Two friends are renting an apartment. They pay the landlord the first month’s rent. The landlord also requires them to pay an additional half a month’s rent for a security deposit. The total amount they pay the landlord before moving in is $1725. What is the monthly rent?

Answers

So you could do $1725/3 (divided by) which would give you 575 then mulitply that by two and that will give you the months rent of, $1,150. I hope this helps!
1150
Total amount is 1 1/2 a months rent
Divide by 3 to get 1/2 a months rent
1725 / 3 = 575
1725 - 575 = 1150

If l and m are parallel, which pairs of angles are supplementary?

Answers

Pairs:

1 and 2

3 and 7

6 and 7

1 and 6

So therefore the answers would be:

1 and 2

3 and 7

6 and 7

Hope This Helps :)

Please mark as brainiest

Answer:

1 and 2

3 and 7

6 and 7

Step-by-step explanation:

Solve the equation a+b-c=180 for c

Answers

We need to make sure c is on one side:

a + b - c = 180

So let’s subtract a and b from both sides:

-c = -a -b + 180

Now, multiply both sides by -1:

c = a + b - 180

Hope this helps!

Answer:

Step-by-step explanation:

we are given the equation a+b-c=180

Now to solve it for c we need to isolate the c

first step can be addition of c to  both side

a+b-c+c=180+c

a+b=180+c

now in second step we subtract 180 from both sides to get

a+b-180=180+c-180

a+b-180 = c

c= a+b-180

four more than the product of one and a number x

Answers

(X times 1) + 4 will be your answer

hope this helps
Hi there! I don't know if you want the answer or the equation, but I'll put both. :)

The equation would be "4 more" than 1*x. This would be (1 * x) + 4.

The answer to this expression would be x + 4.

Which grouping shows duple meter?
a. one two three four five, one two three four five
b. one two three four five six, one two three four five six
c. one two three, one two three
d. one two, one two, one two, one two?

Answers

Duple meter is a musical meter considered by a main division of 2 beats to the bar, typically specified by 2 and multiples (simple) or 6 and multiples (compound) in the upper figure of the time signature. It is ONE TWO, ONE TWO, ONE TWO, ONE TWO which is letter d. 

Answer: D: ONE TWO, ONE TWO, ONE TWO, ONE TWO

Step-by-step explanation:

Use compatible numbers to solve the problem 326 divided by 44.
A 320 divided by 32 = 10
B 320 divided by 40 = 8
C 330 divided by 30 = 11
D 352 divided by 44 = 8

Answers

b. is the answer to this problem

Which axis in a chart displays the descriptive labels for the data points?

Answers

Value axis in a chart displays the descriptive for the data point. ValueAxis is the class which displays value axis for the chart. The chart can have any number of value axes. For Serial chart one value axis is created automatically. For XY Chart two value axes are created automatically.

420,983 estimate it then estimate 39,932 then you have to add thoes then you have to add that and that and then you have to add 420,983 plus 39,932 and see if your answer is close to the estimate

Answers

Final answer:

By rounding numbers to the nearest large place value, we estimated the sum of 420,983 and 39,932 as 460,000. The exact sum is 460,915, demonstrating that our estimation was a close approximation to the actual value.

Explanation:

To estimate the sum of 420,983 and 39,932, we can round these numbers to the nearest ten thousand and thousand, respectively. Rounding 420,983 to the nearest ten thousand gives us 420,000, and rounding 39,932 to the nearest thousand gives us 40,000.

Now, we add the estimated numbers: 420,000 + 40,000 = 460,000.

To find the exact sum of 420,983 and 39,932, we add the two numbers together without estimating: 420,983 + 39,932 = 460,915.

Comparing our estimate of 460,000 with the exact answer of 460,915, we can see that our estimate is very close to the exact amount, showing that our estimation was a good approximation. To find the estimate for 420,983, we round it to the nearest 100,000, which is 400,000. For the estimate of 39,932, we round it to the nearest 10,000, which is 40,000. When we add these two estimates, we get 440,000. Next, we add the actual numbers 420,983 and 39,932, which gives us 460,915. Comparing this with our estimate, we can see that our answer is close to the estimate.

Final answer:

To estimate the sum of 420,983 and 39,932, round each number to the nearest thousand and add them together. Then compare the estimate with the actual sum.

Explanation:

To estimate the sum of 420,983 and 39,932, we can round each number to the nearest thousand. 420,983 rounded to the nearest thousand is 421,000, and 39,932 rounded to the nearest thousand is 40,000. Now, we can add these rounded numbers together: 421,000 + 40,000 = 461,000. This is our estimate for the sum.

Next, we add the actual numbers 420,983 and 39,932 together: 420,983 + 39,932 = 460,915. Finally, we compare our estimate (461,000) with the actual sum (460,915) to see if they are close. In this case, our estimate is slightly higher than the actual sum.

3x-2y=-39 and x+3y=31 solution using elimination

Answers

This is hard to write... I hope this makes sense to you...
3x-2y=-39
x+3y= 31
We want to use elimination therefor, we need to either get our x or our y to add together to get zero. 
To do this, we will multiply -3 to (x=3y=31) 
NEW EQUATION
3x-2y=-39 PLUS
-3x-9y= -93 Equals
Answer: -11y= -54 
y= 4.9
Plug in to solve for x (put new y in)
3x-2(4.9)=-39
x= -9.73 
Solving for x on 3x - 2y = -39:
First, we must add 2y to both sides.
3x - 2y + 2y = -39 + 2y
3x = 2y - 39
Next, we divide both sides by 3.
3x/3 = 2y - 39/3
Answer: 2/3y - 13

Solving for y on x+3y=31:
First, we must add -x to both of the sides.
x + 3y + -x = 31 + -x
3y = -x + 31
Next, we must divide both sides by 3. (Like last time.)
3y/3 = -x + 31/3
Answer: y = -1/3x + 31/3

I hope this helps! (And what you're looking for! :>)

Can anyone help me with this, and maybe explain it?

Answers

A linear equation has the form  y = mx + b where m and b are real numbers.  The value of b (you may know this as the y-intercept) is the value of y when x = 0. The value of m (the slope) is the RATE of increase; it tells how much y changes when x increases by 1.

In this problem, x represents the number of years since 2000, so x = 0 represents the year 2000.

Midwest: the value of y begins with 64.4 and increases by 0.3 each year.
y = 64.4 + 0.3x

West: the value of y begins with 63.2 and increases by 1.0 each year.
y = 63.2 + 1.0x

the sum of the ages of carl and daria is twice as much as the difference between their ages. how old is daira if carl is nine years old and is
A) older than she?
b) younger than she?
Show your work using algebra

Answers

c + d = 2(c - d)
c = 9

9 + d = 2(9 - d)
9 + d = 18 - 2d
d + 2d = 18 - 9
3d = 9
d = 9/3
d = 3 <=== daira is 3 when carl is 9 years old and older then she

if carl is 9 years old and is younger then she ...I dont really understand this question....carl is 9 and daira is 3......possibly...their is a difference of 6 years in their ages....so if carl is 9 and younger then she, the daira is 6 years older ?? making her 9 + 6 = 15....not sure about this one ....the whole question throws me off

A mail truck traveled 82 miles in 412 hours. The distance is the product of the rate and the time. To the nearest tenth, what was the average speed of the mail truck? Enter your answer in the box.

Answers

In this case, you are given the distance truck traveled(82 miles) and the time needed to do that( 412 hours). If you asked the speed/velocity of the truck, then the equation would be:

speed= distance / time
speed= 82 miles/ 412 hours
speed= 0.199= 0.2 mile/hour

Answer:

I took the test.  The answer was 18.2 m/ph

Step-by-step explanation:

50 POINTS! APEX ALGEBRA! PLEASE HELP!
What is the slope of the function, represented by the table of values below?
X: -2, 0, 3, 5, 8
Y: 13, 5, -7, -15, -27

A. -3
B. -4
C. -8
D. -5

Answers

pick any 2 points lets use:
(0,5) and (3,-7)

(y2-y1)/(x2-x1)
slope=(-7-5)/(3-0)=-12/3=-4

Answer is B. -4

The answer would be B.

how would you solve 3x-4=9x-21

Answers

3x - 9x = -21 + 4
-6x = -17
x = -17/-6
x = 17/6
3x - 4 = 9x - 21

Subtract 9x from both sides.

3x - 9x - 4 = -21

Add 4 to both sides.

3x - 9x = -21 + 4

Simplify.

-6x = -17

Divide both sides by -6.

x = 17/6 AND 2 5/6

~Hope I helped!~

I need help of question #36

Answers

check the picture below.

Describe the similarities and differences in the solution of 2x -7 =15 and 2x - 7 < 15

Answers

Both solutions will have values that exist at the "11" value. However, the major difference is due to one being an equation and the other an inequality. The first equation only has one solution. The inequality has infinitely many solutions, and they are all the values that are less than 11 (x<11).

Find the quotient of 5/31 divided by 15/23. Reduce your answer to the lowest fraction.

Answers

Since (5/31)/(15/23)=(5/31)*(23/15) (by finding the reciprocal and multiplying), we get 115/465. Since they are both divisible by 5, we learn that 5 goes into 115 23 times and into 465 93 times (since 465/5=93), resulting in 23/93. Since 23 is a prime number (their only factors are 23 and 1), we end there

Find the smallest positive integer that satisfies the system of congruences \begin{align*} n &\equiv 2 \pmod{11}, \\ n &\equiv 3 \pmod{17}. \end{align*}

Answers

hello : 
the system of congruences is : 
n≡ 2 ( mod 11)
n ≡ 3 (mod 17) 
n = 11k+2......k ∈ N    ....(*)
n = 17L +3......L ∈ N
17L +3 = 11k+2
11k = 17L +1.....(1) 
by (1) : 11k ≡ 1  (mod 17)
33k ≡ 3(mod 17)...(2)
but : 33 ≡ -1 (mod 17) and  -3 ≡  14 (mod 17)
(2) : - k ≡3 (mod 17)
k≡ -3 (mod 17)  
k≡ 14 (mod 17) 
k = 17a+14
subsct in (*) :  n = 11(17a+14)+2
all positive integer that satisfies the system is : n = 187a +156...   a ∈ N 
all  smallest integer that satisfies the system is : n = 187+156 = 343 (when : a=1)

Find the domain and range of the relation and determine whether it is a function. y=x2-3

Answers

is that supposed to be x squared or 2x
A relation is a set of pairs, like {(2, 1), (5, 9), (3, 7)}

If the first coordinate is not repeated, like in this example, were we have only (2, 1) and not also (2, 8), for instance, then the relation is called a function.


A relation sometimes has too many pairs to be expressed by listing all of them. in such cases we use formulas which describe all the pairs.

We are given the relation is [tex]y=x^2-3[/tex]. This means that all pairs of this relation, are such that the second coordinate, is the first one squared, minus 3.

So each pair of this relation is : [tex](x, x^2-3)[/tex]


For any x, [tex]x^2-3[/tex] is only one value, 

for example, if x=10, y can only be [tex]x^2-3=10^2-3=97[/tex]


We cannot possibly have both (10, 97) and (10, 16), for example, because the formula does not allow that.

this means 10 does not repeat as a first pair in this relation, and nor does any other value.


this makes the relation a function


The Domain is the set of all possible values x can be. Clearly, x can be any value, because no x makes [tex]x^2-3[/tex] undefined


Answer: The relation is a function, with Domain all real numbers


How do I solve this?? I'm lost

Answers

Your insight that the function values differ by 5 every time is very important. So your f(x) will contain 5x as a term. You have to find a constant to add or subtract to make sure f(1)=-2.

f(x) = 5x-7 does the job.

The width of a rectangle is one half it's length. The perimeter is 54 cm. What are the width and the length of the rectangle?

Answers

If the width is w and the length is l, we have l/2=w and 2w+2l=54 (given the formula for the perimeter of a rectangle). Plugging l/2=w into the second equation, we have 2(l/2)+2l=54=l+2l=3l. Dividing both sides by 3, we get l=18. Since w=l/2, w=18/2=9

In how many ways could the 11 members of a soccer team line up if the captain and assistant captain must remain apart

Answers

2*11=22

They could have 22 different combinations.

What constant would be added to the expression x2−7xx2−7x in order to make it a perfect square?

Answers

ok

assuming ya mean [tex]x^2-7x[/tex]
since the quadratic coefient is 1, take 1/2 of the liner coeficient and square it
the linear coefient is -7
half of that is -7/2
squared we get 49/4
add that to get
[tex]x^2-7x+\frac{49}{4}[/tex]
it factors to
[tex](x-\frac{7}{2})(x-\frac{7}{2})[/tex] or [tex](x-\frac{7}{2})^2[/tex]

you must add [tex]\frac{49}{4}[/tex] to make it a perfect square

Which function below is the inverse of f(x) = x2 − 9? ±square root of the quantity x plus 9 x squared over 9 ±three times the square root of x 1 over quantity x squared minus 9?

Answers

its the first answer

Answer:

Step-by-step explanation:

The first answer.

Kara bought a DVD for $22 and a cd for less then the cost of the DVD. Let c represent the cost of the cd. Write an inequality to show the cost of the cd

Answers

c<d  

The cd costs less than the dvd, therefore, the cd is less than (or <) then the dvd

which system of equations represents the matrix shown below? See picture

Answers

Answer to this question is B
B is the correct solution. A shows a negative 7 and c and d show a z when there is none on the 1st equatiom

What type of function has an inverse that is also a function?

Answers

inverse proportional function
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