Find derivative for 3x³ + 2xy + 4y²=0.
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]Rollin and Sandra want to buy a home priced at $265,000. They plan to finance this amount less the down payment
required. Rollin and Sandra have a combined annual income of $83,600 and have saved $53,000. They have a
recurring debt of $582. Use a 20% down payment and the 28/36 ratio to determine if Rollin and Sandra are eligible for
a loan. What would you advise them to do if they are not eligible?
Answer:
Rollin and Sandra will not be eligible for a loan. Since 20% of $265,000 is $53,000, they have the required down payment.The recurring debt they have exceeds the allowable amount of $557. Rollin and Sandra should work on reducing their recurring debt.
Step-by-step explanation: this is what i put on the practice
Based on the 28/36 rule, the Rollin and Sandra family are eligible for the mortgage loan of $212,000.
Data and Calculations:Price of home = $265,000
Required down payment = 20% or $53,000
Amount saved = $53,000
Combined annual income of Rollin and Sandra = $83,600
Recurring debt = $582 per month
Annual recurring debt = $6,984 ($582 x 12)
The Rollin and Sandra family will need to finance $212,000 ($265,000 - $53,000) of the home price.
At 6% interest rate for 30 years, the Rollin and Sandra household will pay $1,271.05 monthly or $15,252.60 yearly. This gives a total annual debt payment of $22,236.60 ($6,984 + $15,252.60).
Thus, based on the 28/36 rule, the Rollin and Sandra family are eligible for the mortgage loan of $212,000.
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1.) Use the following information to solve the questions. Kay sold 200
tickets for her school auction. Adult tickets cost $8 and child tickets cost
$5. Kay collected $1,225 in all. How many tickets did Kay sell?
8
5
200
O 1,225
9514 1404 393
Answer:
75 adult tickets125 child ticketsStep-by-step explanation:
Let 'a' represent the number of adult tickets sold. Then (200-a) is the number of child tickets sold, and the revenue is ...
8a +5(200 -a) = 1225
3a = 225 . . . . . . . . . . subtract 1000, simplify
a = 75 . . . . . . . . . . . . .divide by 3
200 -a = 125
75 adult ($8) and 125 child ($5) tickets were sold.
__
Additional comment
The question asked here is "how many tickets did Kay sell?" The second line of your problem statement tells you the answer: "Kay sold 200 tickets ...". We have assumed that you are interested in the breakdown of tickets sold, even though that is not the question that is asked here.
Please answer correctly !!!!!!!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!!
Answer:
q = 14
General Formulas and Concepts:
Order of Operations: BPEMDASEquality PropertiesComplementary Angles: Angles that add up to 90°Step-by-step explanation:
Step 1: Set up equation
The 2 angles must add up to 90°.
(4q - 5)° + 39° = 90°
Step 2: Solve for q
Combine like terms: 4q + 34 = 90Subtract 34 on both sides: 4q = 56Divide both sides by 4: q = 14Select all true statements:
Distributive property is multiplication of one term with many terms.
Distributive property is how to solve expressions in the form of 'a(b+c)"
Apply the distributive property requires me to multiply first, before doing addition.
a(b+c) = a(b) + ac)
Answer:
im almost 100% sure that all apply
Step-by-step explanation:
Answer:
Distributive property is how to solve expressions in the form of 'a(b+c)"
and
Apply the distributive property requires me to multiply first, before doing addition.
a(b+c) = a(b) + ac)
The Lakewood wildcats won 5 of their first 7 games this year.There are 28 games in the season.About how many games would you expect the Wildcats to win this season?
Answer:
7 equal to 5
1 equal to 5/7
28 equal to 5/7*28=20
Step-by-step explanation:
if a square has an area of 324 ft what is the length of each side
Answer:
162
Step-by-step explanation:
324/2 because a square has sides that are all equal, so the area is 2 times the length of a side
Answer:
18 ft.Step-by-step explanation:
area = L² where area = 324 ft²
324 = L²
L = √324
L = 18 ft.
A group of 8 friends went to lunch and spent a total of $76, which included the food bill and a tip of $16. They decided to split the bill and tip evenly among themselves.
Which equations and solutions describe the situation? Select two options.
Answer:
$11.50 is being split among the 8 friends
Step-by-step explanation:
76 + 16 = 92
92/8 = 11.5
Answer:
A and C
Step-by-step explanation:
1) The equation 1/8(x+16)=76/8 represents the situation, where x is the food bill.
2) The solution x=60 represents the total food bill.
Tickets for the school play cost $7 each. Each member of the cast gets 1 free ticket for a family member. For the run of the play, 210 tickets are collected, including all the free tickets, and the box office makes $1,358 from ticket sales. The equation that models this situation is7(210 – c) = 1,358 where c is the number of cast members. How many cast members are in the play?
Answer:
there are 16 cast members.
Step-by-step explanation:
7(210-c)=1358 multiply everything in the parentheses by 7
1470-cx=1358
-7c=-112 subtract 1470 from both sides
c=16 divide -112 by -7
c=16
Solve by making a proportion. If seven movie tickets cost $57.40, how much would 5 tickets cost?
PLSSS i need help
Answer: $41
work out what one ticket is:
$57.40/7=$8.20
and then multiply by 5
$8.20*5=41
Answer:
$41
Step-by-step explanation:
Rewrite the product as a power: [tex]x^{7} y^{7}[/tex]
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[tex] {x}^{7} {y}^{7} = ({x \times y})^{7} = ({xy})^{7} [/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Answer: ❤️❤️(x*y) 7
=(xy) 7
Yo could someone help...
Answer:
42
Step-by-step explanation:
2(4x+2)=4x+44 THE MIDSEGMENT IS ALWAYS HALF OF THE BASE
8x+4=4x+44
4x=40
x=10
4(10)+2
40+2
42 Hope this helped!
find area and perimeter
pls show work
Step-by-step explanation:
ok so first you can split the object into 2 different shapes like the first picture.
next you can start with shape labeled 1
and the perimeter of that would be 5+5+4+4 =14
so the perimeter is shape 1 is 14
the area would be5×4 which is 20
now shape 2 the perimeter of that would be 8+8+2+2 which is 20
the area would be 8×2 which would be 16
so then you add the are and perimeter of each shape together
p= 14+20=34
a= 20+16= 36
Need help ASAP!! Plz help me
Determine whether each quadrilateral must be a parallelogram & justify your answer.
please help! thank you
Solve for x.
Here is the set up:
11x - 2 = 75
Take it from here.
Answer:
7
Step-by-step explanation:
11x-2=75
11x=77
x=7
explanation:
The given information lets us know that 11x-2 is equal to 75 because it is corresponding with the top left exterior angle.
Geometry help don’t take points if I get 70%+ I’ll give some away!!
What is the value of x?
What is the value of y?
answer:
y=4
Step-by-step explanation:
given
DG=GF
10y-4=7y+8
3y-4=8 (subtract both side by 7y)
3y=12 (add both side by 4)
y=12/3
y=4 (ans)
Solve the following equation.
150 - x - 2x = 120 +2x
Answer:
X = 6
Step-by-step explanation:
150 - 3x = 120 + 2x
150 = 120 + 5x
30 = 5x
6 = x
x = 6
The solution to the equation is x = 6.
To solve this equation 150 - x - 2x = 120 +2x , we need to isolate the variable x.
To simplify the equation ;
Distribute the negative sign to the terms inside the parentheses:
150 - x - 2x = 120 + 2x
150 - 3x = 120 + 2x
Combine like terms on both sides of the equation:
-3x - 2x = 120 - 150
-5x = -30
Divide both sides of the equation by -5 to solve for x:
-5x / -5 = -30 / -5
x = 6
Therefore, the solution to the equation is x = 6.
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For those who are good with equations....(unlike me when it comes to this)
Answer:
a = 5
Step-by-step explanation:
When the coefficients of the variables are equal with different constants, then you will get an equation which is never true.
For this particular equation, when a on the right side has a coefficient of 5, you will get the equation: 4(a - 2) + a = 5a - 4.
When you distribute the factors in the parenthesis and add the like terms of a together, 4(a - 2) + a will become 5a - 8. This is because 4(a - 2) + a = 4(a) + 4(-2) + a = 4a - 8 + a = 5a - 8.
Now when you simplify 5a - 8 = 5a - 4 by subtracting 5a from both sides, you will get an equation with unlike constants. For instance 1 = 0.
Now:
5a - 8 = 5a - 4
-5a -5a
-8 = -4
This is never true, so therefore, there is no solution.
Answer:
It is 5
Step-by-step explanation:
What is the tip answer?
Answer:
100.60
Step-by-step explanation:
15% of 87.48 is 13.12
[tex]a/87.48[/tex] x [tex]15/100[/tex]
cross multiply, you get 13.12
add up 13.12 and 87.48, you get 100.60
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What is the coefficient of the second term in this expression?
a2c3+a3c+1+ac2
Answer:
1
Step-by-step explanation:
I assume the term is , and since there is no visible coefficient the coefficient is implied to be 1
Nathan took his car in for service and repairs. He had a coupon for 10% off.
Original Prices
• Labor $254.58
• Parts $333.90
• Other $64.42
Which amount is closest to Nathan's total costs after the 10% discount and including 6% sales tax? [Assume tax is applied after the discount is applied.]
Answer:
$594.21
Step-by-step explanation:
Because 254.58 + 333.90+ 64.42= $622.87
and 10 off of $622.87 = $560.58
and 6% sales tax to $560.58 = $594.21
What is the slope of the line that passes through these two points (8, 4) and (5, 3)?
Answer:
Equation for the slope of the line is, m=y2−y1x2−x1
∵ the point B(5, 8) is above A(3, 4), hence, and B(x2,y2),∵ the point B(5, 8) is above A(3, 4), hence,
A(x1,y1)→A(3,4) and B(x2,y2)→B(5,8)A(x1,y1)→A(3,4) and B(x2,y2)→B(5,8)
m=8−45−3=2⇒m=8−45−3=2
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Related
The slope is the intensity of inclination thus the slope of the line that passes through points (8, 4) and (5, 3) is 1/3.
What is the slope?A slope is a tangent or angle at a point and a slope is the intensity of inclination of any geometrical lines.
Slope = Tanx where x will be the angle from the positive x-axis at that point.
The slope of a line that passes through (x₁, y₁) and (x₂, y₂) is,
Slope = (y₂ - y₁)/(x₂ - x₁)
Since, the given line is passing through (8, 4) and (5, 3).
Slope = (3 - 4)/(5 - 8)
Slope = -1/-3 = 1/3
Hence "The slope is the intensity of inclination thus the slope of the line that passes through points (8, 4) and (5, 3) is 1/3".
To learn more about slopes,
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What is the value of the underlined digit?
5,682, 450,003
A. eighty thousand
B. eighty million
C. eighty-two million
D. eighty billion
\begin{aligned} &y \leq 2x \\\\ &y < -\dfrac{3}{4}x-2 \end{aligned} y≤2x y<− 4 3 x−2 Which graph represents the system of inequalities?
Answer:
what in the world is that
Step-by-step explanation:
lol
Answer:
Step-by-step explanation:
A square with a side length of 4 inches is dilated by a scale factor of 3/2. What is the length of a side of the dilated
square?
Write the equation of the line that passes through the points (-6, 9) and (0, -9).
Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal
line.
Help‼️
Answer:
slope(m)= -3
Step-by-step explanation:
Pierre, an art dealer, earns 25% commission of the art pieces he sells. He earned $10,800 this month. What is the total amount of the art pieces he sold?
Answer:
2700
Step-by-step explanation:
25 percent of 10800 is 2700. hope this helped, this was a bit rushed!xx
Answer:
sry I need points
Step-by-step explanation: If you hadn't done it to me I wouldn't do it to you
What vector describes the transition depicted below !! Please help !!!
Answer:
vector v(4;-3)
Step-by-step explanation: