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
She could have hiked one 2 mile trail and one 1 mile trail or she could’ve hiked one 2.5 mile trail and another 0.5 mile trail
Need to see more instructions.
Answer:
375 = 3 · 5³
1000 = 2³ · 5³
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Cube root 1000x^6 = 10x^2
Cube root of - 27 = 3
So the first part of the factorization process is 10x^2 - 3. There is no help here because all of the answers give this binomial as the first factor.
The second factor is (10x^2)^2 + (3)*10x^2 + 3^2)
Expanding you get 100x^4 + 30x^2 + 9
Be very careful when looking at 100x^4 because that is where the answer is found.
It has to be B
