3x-6y+24 solve for y

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

lbvjy [14]

Step 1:
Start by putting $\frac{d}{dx}$ in front of each term

$\frac{d}{dx}[y cos x]= \frac{d}{dx}[5x^2]+ \frac{d}{dx}[ 3y^2]$
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Step 2:

Deal with the terms in 'x' and the constant terms
$\frac{d}{dx}[ycosx]= 10x+ \frac{d}{dx} [3y^2]$
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Step 3:

Use the chain rule for the terms in 'y'
$\frac{d}{dx}[ycosx]=10x+6y \frac{dy}{dx}$
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Step 4:

Use the product rule on the term in 'x' and 'y'
$(y) \frac{d}{dx} cos x+(cos x) \frac{d}{dx}y =10x+6y \frac{dy}{dx}
$
$y(-siny)+(cosx) \frac{dy}{dx} =10x+6y \frac{dy}{dx}$
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Step 5:

Rearrange to make $\frac{dy}{dx}$ the subject
$-y sin(y)+cos(x) \frac{dy}{dx} =10x+6y \frac{dy}{dx}$
$cos(x) \frac{dy}{dx}-6y \frac{dy}{dx}=10x+y sin(y)$
$[cos(x) - 6y] \frac{dy}{dx}=10x + y sin(y)$
$\frac{dy}{dx}= \frac{10x+ysin(y)}{cos(x)-6y}$ ⇒ Final Answer

5 0

3 years ago

A school band gives a year-end concert. It is held in a 400-seat auditorium. Each concert ticket sells for $10, and 85% of the t

bazaltina [42]

Answer: $3,400

Step-by-step explanation:

There are 400 seats in the auditorium which means that there are 400 tickets to be sold.

85% of these tickets are sold. The number of tickets sold is:

= 85% * 400

= 340 tickets were sold.

Each ticket sells for a total of $10.

The amount of money made from ticket sales is therefore:

= No. of tickets sold * price of ticket

= 340 * 10

= $3,400

6 0

2 years ago

The volume of the cone is 25.12 the height is 6 what is the area of the base

Gnoma [55]

Answer:

153.94

Step-by-step explanation:

AB=πr2=π·72≈153.93804

8 0

2 years ago

Read 2 more answers

Did i do this right?

Blizzard [7]

i belive you are correct

6 0

3 years ago

Read 2 more answers

A factory produces 90 packages of mixed nuts in 1 min. A quality control manager selected 10 of these 90 packages at random and

valentina_108 [34]

Answer:

34

explanation:

First of all, put the numbers in order

30, 31, 31, 32, 33, 35, 35, 35, 36, 36

Then, find the middle number.
In this case, there is an even amount of numbers so, we have to pick the 2 middle numbers which is 33 and 35.

Now all you have to do is add these two numbers together then divide by 2 which will give you 34.

or, in simpler questions like this one, you can just say 34 as you know it is between 33 and 35.

In other questions, it might have and odd amount of numbers, for example:

3, 3, 5, 8, 10

so all you would do here is pick the middle number which would be 5. (it has 2 numbers on each side of it)

7 0

2 years ago