Answer:
slope = 2
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (82, - 96) and (x₂, y₂ ) = (87, - 86)
m = 
= 
= 2
Answer:
y=1/8(-x^2+4x+44
Step-by-step explanation:
In this question the given focus is (2,4) and a directrix of y = 8 and we have to derive the equation of the parabola.
Let (x,y) is a point on the given parabola.Then the distance between the point (x,y) to (2,4) and the distance from (x,y) to diractrix will be same.
Distance between (x,y) and (2,4)
= √(x-2)²+(y-4)²
And the distance between (x,y) and directrix y=8
= (y-8)
Now √(x-2)²+(y-4)² = (y-8)
(x-2)²+(y-4)² = (y-8)²
x²+4-4x+y²+16-8y = y²+64-16y
x²+20+y²-4x-8y = y²-16y+64
x²+20-4x-8y+16y-64=0
x²+8y-4x-44 = 0
8y = -x²+4x+44
From the points you get a slope of -1 using the slope in y=mx+b you get b=1 so y=-x+1
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Assuming that <span>4^2-6(2^x)-16=0 is correct, we can rearrange it as:
</span><span>-6(2^x) + 4^2 - 16=0
Are you sure it's not </span>6(2^x) + 4^2 - 16=0 ?
If 6(2^x) + 4^2 - 16=0 is correct, then
6(2^x) + 4^2 - 16=16 - 16 = 0, that is, 6(2^x) = 0. Then x = 0 (answer)
