Let y be differentiable with respect to x. For the relation x³ + y³ = 9xy, find dy/dx by
implicit differentiation
Answer: (3y² * dy/dx + 3x² * dy/dx - 9y) / 9.
Step-by-step explanation: To find dy/dx for the relation x³ + y³ = 9xy, we can use the chain rule. The chain rule states that if y is a function of x and x is a function of t, then the derivative of y with respect to t is equal to the derivative of y with respect to x times the derivative of x with respect to t.
In this case, we are given that y is a function of x and we want to find the derivative of y with respect to x. To do this, we can rewrite the given equation as follows:
x³ + y³ = 9xy
y³ = 9xy - x³
We can then take the derivative of both sides of the equation with respect to x to find dy/dx as follows:
3y² * dy/dx = 9y + 9x * dy/dx - 3x² * dy/dx
3y² * dy/dx = (9y + 9x * dy/dx) - 3x² * dy/dx
0 = (9y + 9x * dy/dx) - (3y² * dy/dx + 3x² * dy/dx)
0 = 9y + 9x * dy/dx - 3y² * dy/dx - 3x² * dy/dx
We can then solve this equation for dy/dx as follows:
0 = 9y + 9x * dy/dx - 3y² * dy/dx - 3x² * dy/dx
9x * dy/dx = 3y² * dy/dx + 3x² * dy/dx - 9y
9x * dy/dx = 3y² * dy/dx + 3x² * dy/dx - 9y
dy/dx = (3y² * dy/dx + 3x² * dy/dx - 9y) / 9x
dy/dx = (3y² * dy/dx + 3x² * dy/dx - 9y) / 9x
Therefore, the derivative of y with respect to x for the given equation is equal to (3y² * dy/dx + 3x² * dy/dx - 9y) / 9.
Answer
[tex]\frac{dy}{dx}[/tex]
Step-by-step explanation:
Your welcome ;)
f(x) = 3x² + 2x - 20 for x = 3
help please?
When we're given f(x) and x, we can evaluate the function by replacing every x with the given value, and simplifying.
Solving the Question[tex]f(x) = 3x^2 + 2x - 20[/tex]
⇒ Replace every x with 3:
[tex]f(3) = 3(3)^2 + 2(3) - 20\\\\f(3) = 3(9) + 6 - 20\\\\f(3) = 27 + 6 - 20\\\\f(3) = 13[/tex]
Answer[tex]f(3) = 13[/tex]
Step-by-step explanation:
A function is a relationship bound to one output for every single input the value of F(3) for the given function F(x)=3x²+2x-20 is 13.
What is a function?
The function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.
A certain kind of relationship called a function binds inputs to essentially one output.
As per the given function,
F(x)=3x²+2x-20
Substitute, x = 3
F(3) = 3(3)^2 + 2(3) - 20
F(3) = 3(9) + 6 - 20
F(3) = 13
Hence "A function is a relationship bound to one output for every single input the value of F(3) for the given function F(x)=3x²+2x-20 is 13".
For more about the function,
Which statement describes the relationship between the function and its inverse? The range of both f(x) and f–1(x) is all real numbers. The domain of both f(x) and f–1(x) is all real numbers. The range of f(x) is y > 0 and the domain of f–1(x) is x > 0. The domain of f(x) is x > 0 and the range of f–1(x) is y > 0.
The true statement about a function and its inverse is, the range of both f(x) and f⁻¹(x) is all real numbers.
What is an inverse function?The inverse of a function f is denoted by f⁻¹ and it exists only when f is both one-one and onto function.
f⁻¹ isn't the reciprocal of f. The composition of the function f and the reciprocal function f⁻¹ gives the domain value of x.
The true statement about a function and its inverse is,
The range of both f(x) and f⁻¹(x) is all real numbers.
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Explain why the equation cos(x) = x has at least 1 solution
There exists a point c ∈ [0, 2π], therefore, f(c) =0, Hence cos x = x has at least one solution.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given equation is,
cos(x) = x (1)
For the given interval [0, 2π],
By intermediate theorem, for c ∈ [0, 2π], for which f(c) =0
Or we can say that, at x = 0, f(0) = 0
Therefore, cos(x) has at least one solution, in the interval [0, 2π]
So, given equation cos(x) = x has one solution.
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Consider a function f(x) = |x|. A second function g(x) is the result of translating f(x) by 5 units in
the negative y-direction (downward), and 3 units in the positive x-direction (to the right). Write the equation of g(x)
Please Help!!!
The translated function g(x) = | x - 3 | - 5 shifted 3 units along the positive x-axis and 5 units along the negative y-axis.
What are some transformations of functions?Suppose we have a function f(x).
f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).
f(x ± c) = Horizontal left/right shift by c units (x - + c, y).
(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).
f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).
f(-x) = Reflection over y axis, (-x, y).
-f(x) = Reflection over x-axis, (x, -y).
Given, A parent function f(x) = | x |.
Now the result of translating f(x) by 5 units in the negative y-direction and 3 units in the positive x-direction g(x) = | x - 3 | - 5.
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Suppose you go to work for a company that pays one penny on the first day, 2 cents on the second day, 4 cents on the third day and so on.
Hint: use an= a1 (r)^n-1 and Sn= a1 (1-r^n) / 1 - r
A. If the daily wage keeps doubling, what would your income be on day 31? Give your answer in dollars NOT pennies.
Income on day 31 = $ __________
B. If the daily wage keeps doubling, what will your total income be for working 31 days? Give your answer in dollars NOT pennies.
Total Income for working 31 days = $ _________
The income on day 31 would be $21,1474,836.48 and the total income for working 31 days would be $42,949,672.94.
The company pays one penny on the first day, 2 cents on the second day, 4 cents on the third day, and so on.
This situation represents the geometry sequence below as
0.02, 0.04, 0.08,..
Here first-term a₁ = 0.02
And common ratio r = 0.04/0.02 = 2
The income on day 31 would be:
⇒ a₁ (r)ⁿ⁻¹
⇒ 0.02 (2)³¹⁻¹
⇒ 0.02 (2)³⁰
⇒ 21,1474,836.48
Total income for working 31 days would be:
⇒ a₁ (1-rⁿ) / 1 - r
⇒ 0.02 (1-2³¹) / (1 - 2)
⇒ 42,949,672.94
Thus, the income on day 31 would be $21,1474,836.48 and the total income for working 31 days would be $42,949,672.94.
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an equation for the direct variation function of the points (-8, -6) and (12, 9)
Answer:
Your answer is [tex]y=0.75x[/tex] or [tex]y=\frac{3}{4} x[/tex]
Step-by-step explanation:
Using the formula [tex]\frac{y1-y2}{x2-x1}[/tex] we get [tex]\frac{3}{4}[/tex]
Using the formula [tex]y=kx[/tex] we get [tex]y=\frac{3}{4} x[/tex]
The first Christmas bell rings every six minutes. The second Christmas bell rings every seven minutes. The third Christmas bell rings every hour. If all the bells ring at 12 noon, at what time will they next all ring together?
Answer:7 PM is whenthey all ring together
Step-by-step explanation:
-6 1/4x= -3 1/8
Whats the value of x
Answer:
Step-by-step explanation:
-25/4(x)= -25/8
x= -(25/8) X (4/-25)= 1/2
What is the slope of the line with equation 2x + 3y = 10?
Answer:
Step-by-step explanation:
-2/3
The coldest temperature ever recorded in Mathville was - 16 deg * F This happened on January 30th, 1978. The normal low for that day is 19 deg * F How much colder was the record temperature than the normal ow temperature?
It was recorded 35°F colder temperature than the normal ow temperature that year in January 30th, 1978.
Explain the term temperature change?Diabatic temperature change is the term used to describe a temperature shift brought on by a heat exchange between two bodies. The term "adiabatic temperature change" refers to another highly significant method of altering the temperature of air. Air undergoes adiabatic temperature change without the addition or subtraction of energy.For the stated data-
Coldest temperature : -16°F
Normal low: 19°F
Thus, the difference in the temperature-
Difference = Normal low - Coldest temperature
Difference = 19°F - (-16°F)
Difference = 35°F
Thus, it was recorded 35°F colder temperature than the normal ow temperature that year in January 30th, 1978.
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Can you please help me with this question
Answer: I can’t read it
Step-by-step explanation:
Find the product.
(wz + 8)³ =
We are given:
Find the product.
[tex](wz+8)^3[/tex]
Solution:
[tex]w^3z^3+24w^2z^2+192wz+512[/tex]
Hope this helps!
Answer:
Step-by-step explanation:
Sandpiper Company has 25,000 shares of cumulative preferred 1% stock, $150 par and 50,000 shares of $5 par common stock. The following amounts were distributed as dividends:
20Y1 $75,000
20Y2 15,000
20Y3 112,500
Determine the dividends per share for preferred and common stock for each year. Round all answers to two decimal places.
If Sandpiper Company has 25,000 shares of cumulative preferred 1% stock.
Dividends per share for preferred
Year 1 = $3 per shareYear 2 = $4.5 per shareYear 3 = $1 per shareCommon stock
Year 1 = $0Year 2 = $1.95Year 3 =$1.75How to find the dividends per share and common stock?The arrear $75,000 of unpaid dividends from year 1 will be paid to preferred stockholders in year 2
= ($150 x 1% x 25,000) +$75,000
= ($37,500 + $75,000)
= $112,500
Year 1 Year 2 Year 3
Distributed $75,000 $15,000 $112,500
Preferred $75,000 $112,500 $25,000
Common $0 $97,500 $87,500
Dividends per share for preferred
Year 1 = $75,000/25,000 shares
Year 1 = $3 per share
Year 2 = $112,500 /25,000 shares
Year 2 = $4.5 per share
Year 3 = $25,000/$25,000 shares
Year 3 = $1 per share
Common stock
Year 1 = 0/ 50,000 shares
Year 1 = $0
Year 2 =$97,500 / 50,000 shares
Year 2 = $1.95
Year 3 = $87,500 /50,000 shares
Year 3 =$1.75
Therefore the dividends per share for preferred is $3 per share, $4.5 per share, $1 per share and the common stock $0, $1.95, $1.75.
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What is x when x=2-4+5
can sum1 help i got no teachers near
Answer:
Option C : x-6
Step-by-step explanation:
since tina’s brother height is X we start there
x
And tine is 6 less than her bother so we subtract 6
x-6
and that’s it
Hopes this helps please mark brainliest
Which of the following sentences uses homophones incorrectly?
a
The baker is required to knead the dough every hour.
b
The celebrity thought it would be best to have a plain plane
c
The artist erased the whole drawing and made a large hole.
d
The principle of the school makes decisions based on principals.
Help plss
Answer:
Answer: D. The principle of the school makes decisions based on principals.
A ball is thrown from a height of 3 meters with an initial downward velocity of 5 m/s The ball's height h (in meters) after t seconds is given by the following. how long after the ball is thrown does it hit the ground
The ball hits the ground at a time of 1.433 seconds.
How to calculate the time until the ball hits the ground
In this problem we have the case of a ball that experiments a free fall, that is, an uniform accelerated motion due to gravity. The position of the ball in time is described by a quadratic equation:
y = y' + v' · t + 0.5 · g · t²
Where:
y' - Initial position, in meters.v' - Initial speed, in meters per second. t - Time, in seconds. g - Gravitational acceleration, in meters per square second.y - Final position, in meters.If we know that y' = 3 m, v' = 5 m / s, g = - 9.807 m / s², y = 0 m, then the time of the ball until it hits the ground is:
0 = 3 + 5 · t - 4.904 · t²
Then, by the quadratic formula:
t = - v' / g ± (1 / g) · √[v'² - 2 · g · y']
t = - 5 / (- 9.807) ± [1 / (- 9.807)] · [5² - 2 · (- 9.807) · 3]
t₁ = 1.433 s. or t₂ = - 0.424 s.
The hitting time of the ball is 1.433 seconds.
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The function f(x) = –x3 – 7x2 – 7x + 15 has zeros located at –5, –3, 1. Verify the zeros of f(x) and explain how you verified them. Describe the end behavior of the function.
The zeros of the function f(x) = -x³ - 7x² - 7x + 15 are -5, -3 and 1
Zeros of a FunctionThe zeros of a function are defined as the values of the variable of the function such that the function equals 0. Graphically, the zeros of a function are the points on the x-axis where the graph cuts the x-axis. In other words, we can say that the zeros of a function are the x-intercepts of its graph. The number of zeros of a polynomial function is equal to the degree of the polynomial.
To verify if the zeros are for the function, we simply need to plug the values in for x and solve.
f(x) = -x³ - 7x² - 7x + 15
f(-5) = -5³ - 7(-5)² - 7(-5) + 15
f(-5) = 0
When x = - 3
f(-3) = -3³ - 7(-3)² -7(-3) + 15
f(-3) = 0
when x = 1
f(1) = 1³ -7(1) - 7(1) + 15
f(1) = 0
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stop charging me immediately
Answer:
what do you mean
Step-by-step explanation:
Please help me I need help
Answer:
El intercepto en y es 6,1
Step-by-step explanation:
Espero que esto ayude
Graph the function (fx) = 2√ + 3 on the coordinate plane
The graph of the function y = 2√x + 6 is plotted and attached.
What is the general equation of a Straight line? What are the points of intersection of the graph of y = x and y = √x? Which curve is more diverged?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.
The points of intersection of the graph of y = x and y = √x are (0, 0) and (1, 1). The curve y = √x diverges more.
We have the following equation -
y = 2√x + 6
Given is the following equation as -
y = 2√x + 6
Refer to the graph of the function attached.
Therefore, the graph of the function y = 2√x + 6 is plotted and attached.
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2:8=12:_____________
48 let the unknown part be x. And make it 2/8=
3. Find the length of the bridge.
20 ft
160 ft
32.5 ft
Malik deposited $2,439 in an account earning 7% interest compounded annually.
To the nearest cent, how much interest will he earn in 3 years?
Answer: $548.00
Step-by-step explanation: In order to find out how much interest Malik will earn in 3 years, we need to first calculate the amount of interest earned each year. We can do this by multiplying the initial amount he deposited by the interest rate, which is 7%. So, the amount of interest earned each year is $2,439 * 7% = $169.73.
Since the interest is compounded annually, this means that the amount of interest earned in the first year is added to the initial deposit to form the new balance. This new balance will then earn interest in the second year, and so on.
Therefore, the amount of interest earned in the second year is 7% of the new balance, which is $2,439 + $169.73 = $2,608.73. So, the interest earned in the second year is $2,608.73 * 7% = $182.61.
In the third year, the interest is again compounded, so the new balance is $2,608.73 + $182.61 = $2,791.34. The interest earned in the third year is 7% of this new balance, which is $2,791.34 * 7% = $196.48.
In total, Malik will earn $169.73 + $182.61 + $196.48 = $548.82 in interest over 3 years. To the nearest cent, this is $548.00.
When you apply the method to complete the square to find the solution to the equation
2x^2 +3x +3=4
What term should we sum/add on both sides of the equation?
A. 9
B. 9/4
C. 3/2
D. 9/16
Answer:
B
Step-by-step explanation:
2x²+3x=4-3=1
2x²+3x=1
to make it a perfect square we divide the coeff of X by 2 then square it and add it to both sides
=(3/2)²=9/4
A rectangle has a length of 72cm and a width of 56cm. A second rectangle has the same area as this one, but its width is 21cm. What is the constant of variation.
192 cm is the length of rectangle.
What is rectangle?
An example of a quadrilateral with opposite sides that are both equal and parallel is a rectangle.
There are four 90-degree angles on its four sides, making it a four-sided polygon. A rectangle is a shape with only two dimensions.
Area of rectangle = 72 * 56
= 4032 cm²
the second rectangle's area is same as first rectangle .
4032 = x * 21
x = 4032/21
x = 192 cm
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● 4.Harsh purchased 6kg 025g of fruits and 4 kg 325of vegetables and put them in a bag. The bag with its contents weighs 12 kg. What is the weight of the empty bag?
Step-by-step explanation:
6kg025g = 6025g
4kg 325g = 4325 g
6025+4325= 10350 g
12kg = 12000g
12000-10350 = 1650g = 1 kg 650 g
An investor needs $18000 in 10 years.
(a) What amount should be deposited in a fund at the end of each quarter at 9% compounded quarterly so that there will be enough money in the fund?
(b) Find the investor's quarterly deposit if the money is deposited at 4.5% compounded quarterly.
(a) Let P be the amount deposited at the end of each quarter. Then, the future value F after n quarters is given by
F = P(1 + 0.09)^n
Given that there must be enough money in the fund, we can set F = A, the amount required. Therefore,
A = P(1 + 0.09)^n
Solving for P,
P = A(1 + 0.09)^-n
(b) Let P be the amount deposited at the end of each quarter. Then, the future value F after n quarters is given by
F = P(1 + 0.045)^n
Given that there must be enough money in the fund, we can set F = A, the amount required. Therefore,
A = P(1 + 0.045)^n
Solving for P,
P = A(1 + 0.045)^-n
Find the HCF of 2, 4 and 4/5.
(A) 1/20 (B) 1/40 (C) 20 (D) 15
Answer:
1/20
Step-by-step explanation:
You can find the HCF (Highest Common Factor), also known as GCF, by dividing the numbers by the list of answers. And, if they all come out as whole numbers, then the answer you chose will be the answer. But, if there is another answer that also comes out as whole numbers for all of them, we choose the biggest one (HCF):
2 ÷ 1/20 = 40
4 ÷ 1/20 = 80
4/5 ÷ 1/20 = 16
So, 1/20 is definitely one of the answers, but we should check the other ones too:
2 ÷ 1/40 = 80
4 ÷ 1/40 = 160
4/5 ÷ 1/40 = 32
So, even though we also got whole numbers for this one, it isn't the answer because 1/20 is bigger than 1/40 so far. Let's try the last two answers:
2 ÷ 20 = 0.1
So, we already got our answer. We don't need to check the rest of the numbers, because the first one is already not a whole number. Let's try the final answer:
2 ÷ 15 = 0.13333333
This is not the right one either. So, our answer is 1/20 because it is the biggest one that came out as all whole numbers.
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