Answer:
[tex]y'=\frac{-9x^2-2y}{2(x+4y)}[/tex]
General Formulas and Concepts:
Algebra
Equality PropertiesCalculus
Chain Rule: [tex]\frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]Basic Power Rule: f’(x) = c·nxⁿ⁻¹Derivative of a constant equals 0Implicit DifferentiationStep-by-step explanation:
Step 1: Define equation
3x³ + 2xy + 4y² = 0
Step 2: Find 1st Derivative
Set up Derivative: [tex]\frac{dy}{dx} [3x^3 + 2xy + 4y^2 = 0][/tex]Take Implicit Differentiation: [tex]9x^2+(2y+2xy')+8yy'=0[/tex]Step 3: Find Derivative (Solve for y')
Define: [tex]9x^2+(2y+2xy')+8yy'=0[/tex]Move 9x² over: [tex]2y+2xy'+8yy'=-9x^2[/tex]Move 2y over: [tex]2xy'+8yy'=-9x^2-2y[/tex]Factor y': [tex]y'(2x+8y)=-9x^2-2y[/tex]Isolate y': [tex]y'=\frac{-9x^2-2y}{2x+8y}[/tex]Factor GCF: [tex]y'=\frac{-9x^2-2y}{2(x+4y)}[/tex]Answer:
[tex]\frac{dy}{dx}= -\frac{9x^2+2y}{2(x+4y)}[/tex]
Step-by-step explanation:
Find the derivative of [tex]3x^3 + 2xy + 4y^2 = 0[/tex].
In order to find the derivative of this function, [tex]\frac{dy}{dx}[/tex], we can start by noticing that there are two variables in this problem, x and y.
Since we want the derivative with respect to x, every time we encounter the variable “y” in this problem we can change it to [tex]\frac{dy}{dx}[/tex]. We will see this happen later on in the solving process by using implicit differentiation.
Let’s start by taking the derivative of the entire function:
[tex]\frac{d}{dx} (3x^3 + 2xy + 4y^2 = 0)[/tex]Using the Power Rule and the Product Rule, we can perform implicit differentiation on this equation. Let’s take the derivative of each separate piece in this function:
[tex]3x^3 \rightarrow 3(3x^3^-^1) \rightarrow 9x^2[/tex] Power Rule
[tex]2xy \rightarrow (2x \times \frac{dy}{dx} + y \times 2)[/tex] Product Rule
[tex]4y^2 \rightarrow 2(4y) \times \frac{dy}{dx} \rightarrow 8y \times \frac{dy}{dx}[/tex] Power Rule & Implicit Differentiation
Let’s combine these steps into one comprehensive operation:
[tex]9x^2 + (2x \times \frac{dy}{dx} + y \times 2) + 8y \times \frac{dy}{dx} = 0[/tex]Simplify.
[tex]9x^2 + 2x\frac{dy}{dx} + 2y + 8y \frac{dy}{dx} = 0[/tex]Keep all terms containing [tex]\frac{dy}{dx}[/tex] on the left side of the equation and move everything else to the right side of the equation. This way we can solve for [tex]\frac{dy}{dx}[/tex], which, in this case, is the derivative of the original function.
Subtract [tex]9x^2[/tex] and [tex]2y[/tex] from both sides of the equation.
[tex]2x\frac{dy}{dx} +8y \frac{dy}{dx} = -9x^2-2y[/tex]Factor out dy/dx from the left side of the equation.
[tex]\frac{dy}{dx}(2x+8y) = -9x^2-2y[/tex]Divide both sides of the equation by (2x + 8y).
[tex]\frac{dy}{dx}= \frac{-9x^2-2y}{2x+8y}[/tex]You can leave it in this form, or you can convert this to either:
[tex]\frac{dy}{dx}= \frac{-9x^2-2y}{2(x+4y)}[/tex][tex]\frac{dy}{dx}= -\frac{9x^2+2y}{2(x+4y)}[/tex]Describe the change in the graph of the transformation from f to g. f(x) =x^2 + 5 g(x)=(x-6^2 + 5)
Answer:
need more imformacion
Geometry help don’t take points if I get 70%+ I’ll give some away!!
is 1.30 bigger than 1.3?
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Question Help
1
Geraldo has a gold chain that is 34 inches long. He cuts it into 2-inch-long chains. How many gold
chains does Geraldo have now?
Geraldo has 17 gold chains as calculated by the basic arithmetic operation of division.
Division is an arithmetic operation in which a number is broken down into smaller pieces.
One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division.The other operations are multiplication, addition, and subtraction.In its most basic form, the division of two natural numbers involves, among other things, counting how many times one number appears inside another. This count does not necessarily have to be an integer.The number that is divided is called the dividend, the number that is dividing is called divisor and the quotient is the number that is result of the division.Now Geraldo has a 34 inch long gold chain. Therefore if he cuts it into 2-inch long pieces then we will divide 34 by 2 and the quotient will give us the number of chains.
∴ 34 ÷ 2 = 17
Hence Geraldo will have 17 chains.
To learn more about division visit:
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Carly is doing a science experiment breeding mice. She starts out with 2 mice and they
are supposed to double every week. How many mice will she have after 4 weeks?
Answer:
16
Step-by-step explanation:
Week one: 2
Week two: 4
Week three: 8
Week four: 16
Every week just multiply the number you have by two and you will get the answer! Hope this helps!
Complete the square for the expression, then factor the trinomial.
x^2-4x
please explain how to do it as well! :)
Answer:
[tex]x {}^{2} - 4x \\ = x(x - 4)[/tex]
determine the measure of angle a. PLEASE HELP ASAP!
a.64 degrees
b.45 degrees
c.88 degrees
d.42 degrees
Answer:
D
Step-by-step explanation:
Remember that the sum of the interior angles of a triangle will always total 180.
Therefore:
[tex](9x+6)+(74)+(16x)=180\\[/tex]
Let’s solve for x:
Combine LIke Terms:
[tex](9x+16x)+(74+6)=180[/tex]
Add:
[tex]25x+80=180[/tex]
Subtract 80 from both sides:
[tex]25x=100[/tex]
Divide both sides by 25:
[tex]x=4[/tex]
Therefore, the value of x is 4.
Now, to find A, we can substitute it for A.
A is measured by:
[tex]\angle A=9x+6[/tex]
Substitute 4 for x and evaluate:
[tex]\angle A=9(4)+6=36+6=42\textdegree[/tex]
Hence, our answer is D.
A recipe has a ratio of 2 tablespoons of cinnamon to 6 tablespoons of sugar. How many tablespoons of cinnamon are needed for each tablespoon of sugar?
Answer:
1/3
Step-by-step explanation:
i got it right on the test because 2 divided by 6 is closest to 0.3 and 0.3 is the decimal version of 1/3
what is the solution for x in the equation?
Answer:
3
Step-by-step explanation:
combine like terms (so 1/2 and 3/2): 2 - x = x - 4
add x to both sides: 2 = 2x - 4
add 4 to both sides: 6 = 2x
divide both sides by 2: 3 = x
Identify the pattern for the following sequence. Find the next three terms in the sequence. 5, 2, -1, -4, ____, ____, ____,...
Answer: -7, -10, -13, -15
Step-by-step explanation: It’d changing by a constant difference of -3.
pls help:( this is due by the end of the day!! 16 points!
Answer:
P=90
q=122
Step-by-step explanation:
PLEASE HELP find the sins of z
Answer:
It's easy
Step-by-step explanation:
Check the attachment for your answer
Which equation matches the graph shown?
HELP PLSSSS
Answer:
Quadratic
Step-by-step explanation:
Write 9087,600540 in words in Indian system
Answer:
Nine Crore Eight Lakh Seventy Six Thousand Five
Step-by-step explanation:
Help with this question please
Answer:
180
Step-by-step explanation:
Answer:
I don't know
Step-by-step explanation:
I am confused as well someone please help
How many solutions does this system of equations have?
A. No Solutions
B. 2
C. 1
D. An infinite number of solutions
===================================================
Explanation:
Let's solve the first equation for y
4x - 2y = 6
4x-6 = 2y
2y = 4x-6
y = (4x-6)/2
y = (4x/2) - (6/2)
y = 2x - 3
After doing so, we see that 4x-2y = 6 is equivalent to y = 2x-3
Therefore, the original system of equations is effectively listing the same equation twice (one has a different form compared to the other).
Both equations in this system produce the same graph, which leads to infinitely many solutions. All solutions are on the line y = 2x-3.
You can say that all solutions are in the form (x, 2x-3) where x is any real number you want.
-------------------------------
Here's another approach using substitution
4x - 2y = 6 ... start with the first equation
4x - 2( y ) = 6
4x - 2( 2x-3 ) = 6 .... replace y with 2x-3; ie plug in y = 2x-3
4x - 2(2x) - 2(-3) = 6
4x - 4x + 6 = 6
0x + 6 = 6
0 + 6 = 6
6 = 6
We get a true statement. The last equation is always true regardless of what we plug in for x, so this is another way to see how we get to infinitely many solutions.
Side note: the system is considered dependent since one equation depends on the other. The system is also consistent since it has at least one solution.
Use two sets of coordinates to write an equation
to describe the relationship.
Answer/Step-by-step explanation:
An equation that describes the relationship can be written as [tex] y = mx [/tex].
Using the two sets of coordinates, (2, 140) and (4, 280), calculate the slope (m) as shown below:
[tex] \frac{y_2 - y_1}{x_2 - x_1} = \frac{280 - 140}{4 - 2} = \frac{140}{2} = 70 [/tex]
Substitute m = 70 into [tex] y = mx [/tex]
The equation would be:
[tex] y = 70x [/tex]
This equation can be interpreted as follows:
The heart's resting rate is 70 beats each minute.
SOMEONE PLEASE HELP ME PLEASEEEEEE PLEASEEE!!!
Evaluate the expression
d2 – 3e
if d = 9 and e =5
Answer:
18-15
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
Plug in: d = 9, e = 5
(9)2 - 3(5)
9 x 2 = 18
-3 x 5 = -15
18 - 15 = 3
What is accounting? What is the role of accounting in values?
Answer:
Found this on google, "Accounting creates values by maintaining transparency of accounts. Since man lives in the society, he has got a social life. For leading a social life he has to perform financial and material transactions daily. For carrying out these transactions successfully the existence of a sound environment is necessary."
Answer: Accounting is the process of recording financial transactions pertaining to a business.
Step-by-step explanation: The purpose of accounting is to accumulate and report on financial information about the performance, financial position, and cash flows of a business. This information is then used to reach decisions about how to manage the business, or invest in it, or lend money to it.
Which value of x makes the equation 0.5(x + 15) = 2 + 0.75(x - 4) true?
Answer:
Step-by-step explanation:
[tex]\frac{1}{2}(x+15) = 2 + \frac{3}{4}(x-4)[/tex]
To make this easier, to get ride of the fractions, we can multiply both sides by 4
[tex]2(x+15) = 8 + 3(x-4)[/tex]
now use the distributive property
[tex]2x + 30 = 8 + 3x - 12\\[/tex]
now we want to isolate x to one side and isolate all the constants to the other
[tex]2x - 3x = 8 - 12 - 30\\[/tex]
now simplify
[tex]-x = -34\\x = 34[/tex]
to test, we can plug in back to the original
[tex]\frac{1}{2}(34+15) = \frac{49}{2}\\\frac{8}{4} + \frac{3}{4}(34-4) = \frac{8}{4} + \frac{90}{4} = \frac{98}{4} = \frac{49}{2}[/tex]
it works
Sean has $250 in his bank account. He deposits $35 from his birthday and then
buys clothes for school for $75. How much is in his account now?
Answer:
210 dollars left
Step-by-step explanation:
Answer:
he has 210 dollars left
Step-by-step explanation:
250+35=285
285-75=210
Jonas has been saving for a video game . last year it costs $28 this year it costs $36 find the percent of change in the cost .
Answer:
Last year the cost was $28.
This year the cost is $36.
$36 - $28 = $8
Percent of increase = amount of increase ÷ original amount
$8/$28 = $0.286
$0.286 · 100 = 28.6%
There has been a 28.6% of change in the cost.
I don't have a question i just need brainly points:)
Sooooooooo
Vote as brainlyest!!
Answer:
Ok
Step-by-step explanation:
Answer:
That's not how you get brainliest haha
Step-by-step explanation:
You get brainliest when you answer a question. If the creator of the question thinks that your answer was great and it helped them, then they can mark it brainliest!
Hope this helps :)
An electrician charges a rate of $65 per hour plus a fee of $75 for a job done during the weekend. She earned $465 for a weekend job.
Part A. Enter an equation to find the number of hours, h, the electrician worked on this job.
Part B. How many hours did the electrician work?
Answer:
(465 - 75) ÷ 65
She worked for 6 hours
Step-by-step explanation:
Answer:
Step-by-step explanation:
jj
According to the U.S. Bureau of the Census in its Current Population Reports (Series P60) the average
poverty threshold was $8241 for a three-person household in 1993. For a group of 81 three-person households
the standard deviation was $972. Find a 99% confidence interval for the average poverty threshold for a three-
person household.
Answer:
lkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk
Step-by-step explanation:
A punch recipe calls for 3/4 cups of Sprite for 1 and 1/4 cups of juice. How much Sprite is needed for 5 cups of juice?
the answer is 3
could I get brainlisted?
Use the information in the graph to answer the following.
What is the verbal description of this transformation?
5)
What is the symbolic representation?
Answer:
Ff
Step-by-step explanation:
What is the quotient for 81/-9, -123 divided by -4, -94/-9, and 65 divided by (-5)
Step-by-step explanation:
geoff get on the security and I can you know what I mean to say that I am
Vicki earns $30 for washing 6 cars. If Vicki charges the same rate,
many cars must she wash to earn $35? *
plz help me solve this
