The general form of a parabola when using the focus and directrix is:
(x - h)² = 4p(y - k) where (h, k) is the vertex of the parabola and 'p' is distance between vertex and the focus. We use this form due to the fact we can see the parabola will open up based on the directrix being below the focus. Remember that the parabola will hug the focus and run away from the directrix. The formula would be slightly different if the parabola was opening either left or right.
Given a focus of (-2,4) and a directrix of y = 0, we can assume the vertex of the parabola is exactly half way in between the focus and the directrix. The focus and vertex with be stacked one above the other, therefore the vertex will be (-2, 2) and the value of 'p' will be 2. We can now write the equation of the parabola:
(x + 2)² = 4(2)(y - 2)
(x + 2)² = 8(y - 2) Now you can solve this equation for y if you prefer solving for 'y' in terms of 'x'
Answer:
1) 2x^3-2x^2+4x+20
Step-by-step explanation:
line up the equations, having each variable aligned with the similar variable, and distribute the minus sign across the parenthesis
7x^3 + 4x + 13
-(5x^3 + 2x^2 - 7)
---------------------------------
2x^3 - 2x^2 +4x +20
The value of x is 2 and the length of JK is 4
<h3>How to solve the unknown variables?</h3>
The given parameters from the circle are:
- Center = Point S
- Segment JK = 8
- Segment LK = 2x + 4
- Congruent SN = SP = 7
The lines SR and SQ are the radii of the circle P
This means that lines JK and JL are congruent
So, we have:
JK = KL
Substitute LK = 2x + 4 and JK = 4
4 = 2x + 4
Rewrite the above equation as:
2x + 4 = 8
Subtract 4 from both sides
2x + 4 - 4 = 8 - 4
Evaluate the difference
2x = 4
Divide both sides by 2
2x = 4/2
This gives
x = 2
Substitute x = 2 in LK = 2x + 4
LK = 2*2 + 4
Evaluate the product of 2 and 2
LK = 4 + 4
This gives
LK = 8
The point N divides JK into 2 equal segments
So, we have
JN = JK/2
JN= 8/2
JN = 4
Hence, the value of x is 2 and the length of JK is 4
Read more about circles at:
brainly.com/question/11833983
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The periodicity of function is 
<em><u>Solution:</u></em>
Given that we have to find the period of function
<em><u>Given function is:</u></em>
<em><u>Use the below formula:</u></em>
Thus,
Now find the periodicity of cos(x)
We know that,
periodicity of cos(x) = 
Therefore,
Thus the periodicity of function is
Answer:
xy^4 z^3 ( 16x + 33y^4 z^2)
Step-by-step explanation:
step 1 : see what variable you can take out , start with x see if there is x in the left and right side. and how many time you can take it out
next y same thing and then last z
with x = left side you x^2 and right side you have x = so u can take x out once left you with x
with y = left side y^4 and right side y^8 so you can take out y ^4 out left you with y^4
with z = left side z^3 and right side z ^5 you can take out z^3 left you with z^2
