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
Answer: Make an equation explaining how blue fire hydrant "b" relates to green fire hydrant "g". Once you have your equation choose the one on the multiple choice that matches your work.
Step-by-step explanation:
Step-by-step explanation:
a 12 miles per hour * 45/60 = 9 miles
b I mean he can't ride negative speed, unless he's going backwards??
-8 * 45/60 = -6 miles
c they would be abs(-6) + 9 = 15 miles apart
11/12 hours left. 1 2/3 - 3/4 = 11/12. First, find the common denominator (12) . The problem is now 1 8/12 - 9/12. Use the 1 in (1 8/12) to borrow. Multiply the denominator by 1 (12) and add that to the numerator. The question is now 20/12 - 9/12. I assume that you can finish it off from there.
