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Tems11 [23]
3 years ago
14

Consider the following equation. 9x2 − y2 = 6 (a) Find y' by implicit differentiation. y' = (b) Solve the equation explicitly fo

r y and differentiate to get y' in terms of x. y' = ±
Mathematics
1 answer:
qaws [65]3 years ago
6 0

Answer:

Step-by-step explanation:

Given is an equation in x and y as

9x^2 - y^2 = 6

We use implicit method to differentiate the above equation

18x-2yy'=0

y' = 9x/y

b) to solve the equation explicitly for y and differentiate to get y' in terms of x. y' = ±

We separate the variables as

yy' =9x\\\frac{y^2}{2} =\frac{9x^2}{2} +C\\y^2 =9x^2+2C

Take square root

y=\sqrt{9x^2+2C} \\y=-\sqrt{9x^2+2C}

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4 0
3 years ago
Which of the following is the maximum value of the function y = −x^2 + 2x + 1?
azamat

Answer:

Step-by-step explanation:

We don't need choices to find out the correct answer. Solve this problem by completing the square. Begin by setting the quadratic equal to 0 and moving over the constant, like this:

-x^2+2x=-1 and factor out the -1 in front of the x-squared, since the leading coefficient HAS to be a 1:

-1(x^2-2x)=-1 Now take half the linear term, square it, and add it to both sides. Our linear term is -2. Half of -2 is -1, and squaring that gives us 1. So we add a 1 into both sides. But that -1 out front there on the left is a multiplier, so what we actually added in was -1(1) which is -1:

-1(x^2-2x+1)=-1-1

On the left side we have a perfect square binomial, which is why we do this, and on the right side we have -2:

-1(x-1)^2=-2 and we can move that constant back over and set the quadratic back equal to y:

y=-1(x-1)^2+2  which gives us a max height of 2.

(If this was modeling parabolic motion, we would know that the time it takes to get to that max height is 1 second. The vertex of this parabola is (1, 2))

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4 years ago
Subtract.
kobusy [5.1K]
Is it 729 lol why would you put it as mixed number
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Answer:

m= -5.5

Step-by-step explanation:

Mark me braniliest plzz

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3 years ago
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