The slope is 2/3. hope that helps
To find the tangent line we will need the slope of the tangent at x=-1 (the x-coordinate of the point given). We find the slope by using the derivative of the curve.
Th curve given is
which can be solved for y by taking the root of both sides. We obtain
We find the derivative using the chain rule. Bring down the exponent, keep the expression in the parenthesis, raise it to 1/2 - 1 and then take the derivative of what is inside.
Next we evaluate this expression for x=-1 and obtain:
So we are looking for a line through (-1,2) with slope equal to -9/2. We use y=mx+b with m=-9/2, x=-1 and y=2 to find b.
2-(9/2)=b
b=-5/2
So the tangent line is given by y=(-9/2)x+(-5/2)
Mixed number form: h = - 1 2/13 Hope that helps :))
To find f(-7), just plug -7 in for all x
2(-7) + 8
-14 + 8
-6 is the answer!
h(t) = -16t² + 50t + 5
The maximum height is the y vertex of this parabola.
Vertex = (-b/2a, -Δ/4a)
The y vertex is -Δ/4a
So,
The maxium height is -Δ/4a
Δ = b² - 4.a.c
Δ = 50² - 4.(-16).5
Δ = 2500 + 320
Δ = 2820
H = -2820/4.(-16)
H = -2820/-64
H = 2820/64
H = 44.0625
So, the maxium height the ball will reach is 44.0625