The slope of the curve x²y-xy²=4 is defined everywhere except for points where x = 2y. This conclusion is reached by using implicit differentiation and the product rule to find the derivative (slope), and then determining where the slope is undefined.
Explanation:To find where the slope of the curve is defined for the equation x²y-xy²=4, we first need to find the derivative of the equation. The derivative will give us the slope of the tangent line at a specific point. This process involves using the Product Rule of differentiation. The Product Rule states that the derivative of two functions multiplied together is the first function times the derivative of the second function plus the second function times the derivative of the first function.
For the given equation, we first need to rewrite it in the form: y = f(x). However, as y cannot be easily expressed solely as a function of x in this case, we will need to use implicit differentiation. Implicit differentiation assumes that y is a function of x, even if it's not explicitly stated. By using the product rule, we get 2xy + x² × (dy/dx) - y² - 2xy × (dy/dx) = 0; simplifying this, we get (x² - 2xy) × (dy/dx) = y² - 2xy. So dy/dx = (y² - 2xy) / (x² - 2xy).
Thus, the slope of the curve is defined wherever the denominator, x² - 2xy, does not equal zero, since division by zero is undefined. Hence, we need to solve x² - 2xy ≠ 0. Solving this inequality, we find that the slope of the curve is defined for all (x,y) except where x = 2y.
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In what position would you find the 'leading' runner in a race? In what position do you suppose you would find the 'leading coefficient' in a polynomial?
what is 3 fourths equal to n tenths
At a farmer’s market, a basket of strawberries costs $20 and a basket of peaches costs $18. On Saturday, $430 worth of strawberries and peaches were sold, and a total of 23 baskets were sold. If x represents baskets of strawberries and y represents baskets of peaches, how many baskets of peaches were sold on Saturday?
20x+18y=430
x+y=23
8 baskets
11 baskets
12 baskets
15 baskets
Final answer:
To find the number of baskets of peaches sold on Saturday, we can set up a system of equations and solve it using elimination or substitution. The answer is 15 baskets Option Dof peaches.
Explanation:
To solve this problem, we need to use a system of equations. Let's call the number of baskets of strawberries x and the number of baskets of peaches y. We can set up the following equations:
20x + 18y = 430 (equation 1)
x + y = 23 (equation 2)
We can solve this system of equations using substitution or elimination. Let's use elimination:
Multiply equation 2 by 18 to make the coefficients of y in both equations cancel:
18x + 18y = 414 (equation 3)
Subtract equation 3 from equation 1 to eliminate y:
(20x + 18y) - (18x + 18y) = 430 - 414
2x = 16
Divide both sides of the equation by 2:
x = 8
Substitute x = 8 into equation 2 to find y:
8 + y = 23
y = 23 - 8
y = 15
Therefore, 15 baskets of peaches were sold on Saturday.
A quiz has 1 true-false question and 2 multiple choice questions that each have 4 answers. What is the probability that someone guessing all 3 answers will get 100% on the quiz?
...?
Answer:
1/32
Step-by-step explanation:
You're welcome
If g(x)+xsin(g(x))= x^2 find g'(0) ...?
We want to find the g'(0) by knowing that:
g(x) + x*sin(g(x)) = x^2
We will get:
g'(0) = 0
First, we can see that:
g(0) is given by:
g(0) + 0*sin(g(0)) = 0^2
g(0) = 0.
Now let's derive this, we can rewrite:
g(x) = x^2 - x*sin(g(x))
Now we just differentiate to get:
g'(x) = 2*x - sin(g(x)) - x*cos(g(x))*g'(x)
Now we need to move all the terms with g'(x) to the left side:
g'(x) + x*cos(g(x))*g'(x) = 2x - sin(g(x))
g'(x)*(1 + x*cos(g(x)) = 2x - sin(g(x))
g'(x) = ( 2x - sin(g(x)) )/(1 + x*cos(g(x))
Now we just need to evaluate this in x = 0, so we get:
g'(0) = (2*0 - sin(g(0)))/(1 + 0*cos(g(0)) = -sin(g(0))
And remember that g(0) = 0 then:
g'(0) = -sin(0) = 0
g'(0) = 0
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In the number 956 ,783,529 how does the value of the digit 5 in the ten millones place compare to the digit 5 in the hundred place?
increase 160km by 30%
What is the value of x in the equation 4x − 17 = 65? start fraction 41 over two end fraction −12 12 −start fraction 41 over two end fraction
(11a^3+6)-(-7a^3+7) Solve
12 less than the quotient of a number and seven is negative two find the number
how does a balance sheet work?
Step-by-step explanation: A balance sheet is a statement of financial condition at a point in time. It includes assets, liabilities, and equity. The balance sheet demonstrates the overall health of a company. It can be used to obtain loans and more financing.
last question for today i promise xD
If the parent function is 3√x , describe the translation of the function y =3√x-4 +3
A. Three units to the left and four units down from 3√x
B. Four units to the right and three units up from 3√x
C. Three units to the right and four units down from 3√x
D. Four units to the left and three units up from 3√x
The correct translation of the function is,
⇒ Four units to the right and three units up from 3√x
Option B is true.
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The parent function is,
⇒ f (x) = 3√x
And, the translation of the function is,
y = 3√x- 4 + 3
Now, We get;
The parent function is,
⇒ f (x) = 3√x
After translated Four units to the right we get;
⇒ f (x) = 3√x - 4
And, After translated three units up from 3√x;
f (x) = 3√x- 4 + 3
Thus, The correct translation of the function is,
⇒ Four units to the right and three units up from 3√x
Option B is true.
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Pam is looking for a new car. She has test-driven two cars but can only purchase one. The probability that she will purchase car A is 0.46, and the probability that she will purchase car B is 0.34. What is the probability that she will not purchase either car A or car B?
0.12
0.40
0.20
0.80
The probability that Pam will not purchase either car A or car B is 0.20.
What is probability?Probability deals with the occurrence of a random event. The chance that a given event will occur. It is the measure of the likelihood of an event to occur.The value is expressed from zero to one.
For the given situation,
Probability that she will purchase car A = 0.46
Probability that she will purchase car B = 0.34
The probability that she will purchase either car A or car B is
⇒ [tex]0.46+0.34[/tex]
⇒ [tex]0.80[/tex]
Thus the probability that she will not purchase either car A or car B is
⇒ [tex]P(A)=1-0.80[/tex]
⇒ [tex]P(A)=0.20[/tex]
Hence we can conclude that the probability that Pam will not purchase either car A or car B is 0.20.
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A triangle has side lengths measuring 3x cm, 7x cm, and h cm. Which expression describes the possible values of h, in cm?
4x < h < 10x
10x < h < 4x
h = 4x
h = 10x
Answer with explanation:
In a triangle sum of two sides , should always be greater than the third side.
Sides of the given triangle are, 3 x cm, 7 x cm and h cm.
1.
3 x + 7 x > h
→ 10 x > h
2.
3 x+ h > 7 x
→h > 7 x -3 x
→h> 4 x
3.
7 x + h > 3 x, which will be always true.
Combining 1, 2 and 3 we get
→4 x < h < 10 x
Option A
The solution to w/-7 = -21 is 3.
True
False
You are having a family-barbeque. in attendance are a grandfather, a grandmother, two fathers, two mothers, four children, three grandchildren, one brother, two sisters, two sons, two daughters, one father-in-law, one mother-in-law and one daughter-in-law. if every person is eating two burgers, what’s the minimum amount of burgers you will need?
Final answer:
To calculate the minimum amount of burgers you will need, count the number of individuals who will be eating and multiply it by 2. The Total burgers needed is 50 .
Explanation:
To calculate the minimum amount of burgers you will need, you need to count the number of individuals who will be eating. Let's count:
1 Grandfather
1 Grandmother
2 Fathers
2 Mothers
4 Children
3 Grandchildren
1 Brother
2 Sisters
2 Sons
2 Daughters
1 Father-in-law
1 Mother-in-law
1 Daughter-in-law
Adding all of these individuals, we get a total of 25 people. Since every person will be eating 2 burgers, we can calculate the minimum amount of burgers we will need by multiplying the total number of people by 2:
Total burgers needed = 25 people * 2 burgers per person = 50 burgers
When a number is raised to the 6th power, it equals 90. What is this number, and write it using the root symbol ...?
Is there any rational numbers between 5/7 and 6/7 and why? ...?
The reference angle for an angle whose measure is -440 is _____. 60 80 100
The reference angle for an angle whose measure is -440 is 80.
Step-by-step explanation:Reference angle--
It is the angle which is made from the terminal side of the given angle and it is always made by taking x-axis as a reference.
Here we are given a angle whose measure is:
-440.
This means that the angle covers more than one rotation and ends in the fourth quadrant.
Hence, the reference angle is:
-440+360=80
a city bus company sold 39 one-way tickets and 20 round-trip tickets from west elmwood to east elmwood. one-way tickets cost $14. round trip tickets cost $35. how much money did the bus company collect
What are the first 20 digits of pi?
The first 20 digits of pi are 3.1415926535897932384. It's an irrational number used in many mathematical calculations and its decimal representation never ends or repeats.
Explanation:The first 20 digits of the mathematical constant pi (π) are 3.1415926535897932384. Pi is an irrational number, meaning it cannot be expressed exactly as a fraction, and its decimal representation never ends or repeats.It not only appears in geometry and trigonometry, but also in various fields of mathematics and science. Its value is usually approximated as 3.14 or 3.14159 in most mathematical and scientific calculations.Learn more about pi here:https://brainly.com/question/23320385
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Solve the problem.
When granular materials are allowed to fall freely, they form conical (cone-shaped) piles. The naturally occurring angle of slope, measured from the horizontal, at which the loose material comes to rest is called the angle of repose and varies for different materials. The angle of repose θ is related to the height h and base radius r of the conical pile by the equation θ = cot-1(r/h). A certain granular material forms a cone-shaped pile with a height of 19 feet and a base diameter of 30 feet. What is the height of a pile that has a base diameter of 104 feet?
The angle of repose is calculated using the equation θ = cot-1(r/h). For a pile with a height of 19 feet and a base diameter of 30 feet, the angle of repose is approximately 38.03 degrees. Using this angle and the base diameter of 104 feet, we can find that the height of the new pile is approximately 77.07 feet.
The angle of repose θ is related to the height h and base radius r of the conical pile by the equation θ = cot-1(r/h).
Given a pile with a height of 19 feet and a base diameter of 30 feet, we can find its base radius by dividing the diameter by 2, which gives us a radius of 15 feet.
Now, we can substitute the given values into the equation to find the angle of repose θ.
θ = cot-1(15/19)
Using a calculator, we find that the angle of repose is approximately 38.03 degrees.
Next, we can use the height of the new pile and the known angle of repose to find its base radius.
Given a base diameter of 104 feet, the radius is half of the diameter, so the radius is 52 feet.
Now, we can use the equation θ = cot-1(r/h) and solve for h to find the height of the new pile.
h = r / tan(θ)
Substituting the known values, we get:
h = 52 / tan(38.03)
Using a calculator, we find that the height of the pile with a base diameter of 104 feet is approximately 77.07 feet.
A projectile is thrown upward so that its distance above the ground after t seconds is h(t)=-16t^2 + 570t. After how many seconds does it reach its maximum height?
What is 12 345 to the nearest thousand
Convert the radical below into a fractional exponent The square root of 4^3
What is the total area of a covered box with a length of 4 ft, a width of 3 ft, and a height of 6 ft?
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Wet-cell batteries are typically used to supply eletrical energy to
which is bigger 0.07 or 0.005?
Consider the function y=x^2+5x-2 . What would happen to the graph if (x + 5) was substituted in place of the x?
A. The graph would shift 5 units to the right.
B. The graph would shift down 5 units.
C. The graph would shift up 5 units.
D. The graph would shift 5 units to the left.
Consider the function y=x^2+5x-2 . What would happen to the graph if (x + 5) was substituted in place of the x?
A. The graph would shift 5 units to the right.
B. The graph would shift down 5 units.
C. The graph would shift up 5 units.
D. The graph would shift 5 units to the left.
Option: D is the correct answer.
D. The graph would shift 5 units to the left.
Step-by-step explanation:We know that the transformation of a function f(x) to f(x+a) is a shift of the function either to the left or to the right by a units depending on the sign of a i.e. if a>0 then the shift is a units to the left
and if a<0 then the shift is a units to the right.
Here we have:
[tex]y=x^2+5x-2[/tex] is converted to:
[tex]y=(x+5)^2+5(x+5)-2[/tex]
Here we have a=5>0
Hence, the shift is 5 units to the left.