Answer:
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Step-by-step explanation:
ripppppppppppp
Answer:
k=24
Step-by-step explanation:
The tangent of the function f at x=a, can be found by differentiating f w.r.t. x and then replacing x with a.
f=-x^2+8x+20
Differentiating both sides:
f'=(-x^2+8x+20)'
By sum rule:
f'=(-x^2)'+(8x)'+(20)'
By constant multiple rule:
f'=-(x^2)'+8(x)'+(20)'
By constant rule:
f'=-(x^2)+8(x)'+0
By power rule:
f'=-2x+8
f' at x=a is -2a+8
This is the slope of any tangent line to the curve f.
The slope of g is 4 if you compare it to slope intercept form y=mx+b.
So we gave -2a+8=4.
Subtracr 8 on both sides: -2a=-4
Divide both sides by -2: a=2
The tangent line to the curve at x=2 is y=4x+k.
To tind y we must first know the y-coordinate of the point of tangency.
If x=2, then
f(2)=-(2)^2+8(2)+20=-4+16+20=12+20=32
So the point is (2,32).
g(x)=4x+k and we know g(2)=32.
This gives us:
32=4(2)+k
32=8+k
k=32-8
k=24
P ≥ 53.
p (the number of people) is at least (so, greater than or equal to) 53
*Hint: When you have two y's, they could equal each other in order to solve for the x value.
|x^2 -3x + 1| = - (x - 1)
x^2 -3x + 1 = -x + 1
x^2 - 2x + 1 = 1
x^2 - 2x = 0
x (x - 2)
x = 2 and x = 0
Once both of them are plugged in, only x = 2 works so that's the value for x. Now we just plug it in order to solve for y.
y = x - 1
y = 2 - 1
y = 1
(2, 1)
The answer would be C.
