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:
about 78.539 meters. smallest diameter = 50. plug that into the equation C = πd
Step-by-step explanation:
AngleA= angle D
5x+2=87
5x=85
X=17
180-87-42=51
Angle C= angle F
3y=51
Y=17
Answer:
y=11
Step-by-step explanation:
Answer:
The maximum number of gumballs you can buy is 10
Step-by-step explanation:
Let
x ---->represents the number of gumballs you can buy
we know that
The number of gumballs you can buy multiplied by it cost must be less than or equal to $2.50 (two dollars and 50 cents)
so
The inequality that represent this situation is
solve for x
Divide both sides by 0.25
therefore
The maximum number of gumballs you can buy is 10
