Answer:
Its 67.9 but technically its 67.912 *hope this helps
Step-by-step explanation:
Right scalene triangle.
Sides: a = 66 b = 16 c = 67.912
Area: T = 528
Perimeter: p = 149.912
Semiperimeter: s = 74.956
Angle ∠ A = α = 76.373° = 76°22'23″ = 1.333 rad
Angle ∠ B = β = 13.627° = 13°37'37″ = 0.238 rad
Angle ∠ C = γ = 90° = 1.571 rad
Height: ha = 16
Height: hb = 66
Height: hc = 15.55
Median: ma = 36.674
Median: mb = 66.483
Median: mc = 33.956
Inradius: r = 7.044
Circumradius: R = 33.956
Vertex coordinates: A[67.912; 0] B[0; 0] C[64.142; 15.55]
Centroid: CG[44.018; 5.183]
Coordinates of the circumscribed circle: U[33.956; 0]
Coordinates of the inscribed circle: I[58.956; 7.044]
Exterior (or external, outer) angles of the triangle:
∠ A' = α' = 103.627° = 103°37'37″ = 1.333 rad
∠ B' = β' = 166.373° = 166°22'23″ = 0.238 rad
∠ C' = γ' = 90° = 1.571 rad
Answer:
f'(1)=150ln(1.5)
Step-by-step explanation:
I'm not sure why you would need a table since the limit definition of a derivative (from what I'm remembering) gives you the exact formula anyway... so hopefully this at least helps point you in the right direction.
My work is in the attachment but I do want to address the elephant on the blackboard real quick.
You'll see that I got to the point where I isolated the h's and just stated the limit equaled the natural log of something out of nowhere. This is because, as far as I know, the way to show that is true is through the use of limits going to infinity. And I'm assuming that you haven't even begun to talk about infinite limits yet, so I'm gonna ask you to just trust that that is true. (Also the proof is a little long and could be a question on it's own tbh. There are actually other methods to take this derivative but they involve knowing other derivatives and that kinda spoils a question of this caliber.)
Consider, please, this solution. If it is possible, check it in the alternative sources.
Let width be W
Then length = 5W
P=2L+2W
P< 96cm
Then the Perimeter of the rectangle is equal to
(2L+2W)< 96
2*(5W)+2W)≤96
Therefore, 2w+2⋅(5w)≤96
should be your answer