1. Find the equation of a normal to the curve y= 2² - 2x +3 at the point (3,0)

Mathematics

1 answer:

Gala2k [10]1 year ago

5 0

I think you meant to say the equation is

y = 2x² - 2x + 3

Differentiate both sides with respect to x :

dy/dx = 4x - 2

At the point (3, 0), the slope of the tangent line is dy/dx(3) = 4•3 - 2 = 10. Then the normal line to the curve at (3, 0) has slope -1/10.

Using the point-slope formula, the equation of the normal line is

y - 0 = -1/10 (x - 3) ⇒ y = (3 - x)/10

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4^(x-1)+4^(x)+4^(x-1)=84

creativ13 [48]

Answer:

7.66

Step-by-step explanation:

Just open the parenthesis.

4x-4+4x+4x-4=84

Now simplify and solve

12x-8=84

12x=92

x= 7.66

3 0

3 years ago

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.

Alexandra [31]

Answer: y-axis.

Explanation:

The equation r = 3 - 4 sin θ may be graphed using cartesian coordinates (i.e. x and y) or polar coordinates.

The logical way is to graph in polar coordinates. I did it using a graphing software and obtained the attached graph.

Also, I attached the graph in cartesian coordinates.

Here you have a table that you can build by your self and use the pairs to draw the graph (either cartesian or polar coordinates).

 θ (rad) r = 3 - 4 sin θ 

0 3 
π/8 2.61731657 
 π/4 2.29289322 
3π/8 2.07612047
 π/2 2
 5π/8 2.07612047 
3π/4 2.29289322 
7π/8 2.61731657 
π 3 
9π/8 3.38268343 
5π/4 3.70710678 
11π/8 3.92387953 
3π/2 4 
13π/8 3.92387953 
7π/4 3.70710678 
15π/8 3.38268343 
2π 3 

In both of the attached graphs you can see that the left side is equal to the right side, but the upper side is not equal to the bottom side.

Therefore, the graph is symmetric about the y-axis.