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Marrrta [24]
2 years ago
5

Find the 11th term of the geometric sequence 2, -6, 18, ...

Mathematics
1 answer:
Sergeeva-Olga [200]2 years ago
5 0
R = a₂/a₁ = -3
a₁₁ = a₁r¹⁰ = 2×(-3)¹⁰ = 118,098
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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
Help if you’re feeling generous today!! thank youu
ra1l [238]

Answer:

<h3>The answer is option 3 </h3>

Step-by-step explanation:

4x² - 2y

when

x = - 2 and y = - 1

Substitute the values of x and y into the expression and simplify

That's

4( - 2)^{2}  - 2( - 1) \\  = 4(4) + 2 \\  = 16 + 2

We have the final answer as

<h2>18</h2>

Hope this helps you

5 0
3 years ago
What is the factorization of 3x^2 – 8x + 5?
hodyreva [135]
3x^2 - 8x + 5
3x^2 - 3x - 5x + 5
3x(x - 1) - 5(x - 1)
(x - 1)(3x - 5)

The answer is: (x - 1)(3x - 5).
5 0
3 years ago
Read 2 more answers
The y -intercept of the line whose equation is 2 x + 5 y = 8 is
Anastaziya [24]

Answer:

8/5

Step-by-step explanation:

4 0
3 years ago
Help and I will give brainliest alot
Nikitich [7]

Answer:

dude i cant read it its to small

Step-by-step explanation:

8 0
2 years ago
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