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elena55 [62]
2 years ago
14

I need help please!!

Mathematics
1 answer:
astraxan [27]2 years ago
3 0
D
It has 4 spots of lines instead of 3
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Can someone please explain how to get the answer I've watched multiple videos on implicit derivatives and I still cant figure it
Arisa [49]

We're given the implicit equation

x² + 2x + y² - 4y = 12

where "implicit" means that one of the variables is considered a function of the other. In this case, the variable y = y(x) depends on the value of the variable x - in other words, the possible values of y are implied by the value of x. We then say that this equation defines y as an implicit function of x.

We're also given the implicit derivative,

dy/dx = (-2x - 2)/(2y - 4)

which tells us the rate of change y as a function of both x and y. The value of dy/dx corresponds to the slope of the tangent line to the curve defined by the implicit equation above at some point (x, y).

The tangent line is horizontal when its slope is zero. This happens when

(-2x - 2)/(2y - 4) = 0

If y ≠ 2, then we can eliminate the denominator and we're left with

-2x - 2 = 0

Solve for x :

-2x = 2

x = -1

This tells us that the points on the curve with x-coordinate -1 have a tangent line to the curve that is horizontal.

The tangent line is vertical when its slope is undefined/infinite, or equivalently when the denominator of dy/dx is zero:

2y - 4 = 0

Solve for y :

2y = 4

y = 2

So any point on the curve with y-coordinate 2 will have a tangent line there that is vertical.

By completing the square in the implicit equation, we can easily identify where these points are located.

x² + 2x + y² - 4y = 12

x² + 2x + 1 + y² - 4y + 4 = 17

(x + 1)² + (y - 2)² = 17

This equation defines a circle centered at (-1, 2) with radius √17. When x = -1, we have

(y - 2)² = 17   ⇒   y = 2 ± √17

and when y = 2, we have

(x + 1)² = 17   ⇒   x = -1 ± √17

See the attached plot to see the circle and the tangents at these points.

7 0
2 years ago
Solve the equation by completing the square. round to the nearest hundredth if necessary. x^2+3x-5=0
elena55 [62]
X=0.85 and -5.85 is the answer, that's all of the work

3 0
3 years ago
Which two inequalities to compare |-5| and 4?
lilavasa [31]

Answer:

|-5|>4

Step-by-step explanation:

Negative 5 in absolute value is 5 since any number in absolute value turns out positive or at the very least 0. 5 is greater than 4, so |-5|>4.

7 0
3 years ago
Tim and his family want to place a flower bed in the backyard and have a pretty border around it. They have chosen to make it a
abruzzese [7]

Answer:

Area = 60

Step-by-step explanation:

(h b)/2

h = 10

b = 12

12 x 10 = 120

120/2 = 60

(h = height and b = base)

6 0
3 years ago
Read 2 more answers
What is the equation of a line with a slope of 6 and a y-intercept of -8
kirill [66]

Answer:

COULD BE Y=6x-8

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
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