The answer to this question is y' = 10x^2 + 6. You have to use the power rule to bring the exponent down as a coefficient and then reduce the exponent by 1. Do it for all the terms using the sum rule for derivatives (derivative of a sum of the sum of its derivatives).
53= -19z+5+7z
53= -12z+5 (combine -19z and 7z)
48= -12z. ( subract 5 on both sides)
-4=z. (divide by -12 both sides)
Step-by-step explanation:
Cost to make the film : $6500
Cost to set up production: $1500
Additional cost to make each video : $4
Additional cost to make n videos : $4n
total cost to make n videos = $6500 + $1500 + $4n = (8000 + 4n) dollars
overall cost to make each video
= total cost to make n videos ÷ n videos
= (8000 + 4n) / n
by definition, in order to "break even", the selling price for each video must be equal to the cost to make each video. i.e
Price, P(n) = (8000 + 4n) / n
Hence,
P(500) = [8000 + 4 (500)] / 500 = (8000 + 2000) / 500 = $20
This means that in order to break even selling 500 DVD's he has to sell each one for $20
If the triangles are similar then the angles in both are equal. Let's look at each set individually:
(1) Triangle 1: 25°, 35°
Triangle 2: 25°, 120°
Now it may be hard to tell if the triangles are similar at the moment so we must calculate the third angle in each triangle (The angles in a triangle add up to 180°, therefor the missing angle = 180 - (given angle 1 + given angle 2)
Triangle 1: 180 - (25 + 35) = 120°
Triangle 2: 180 - (25 + 120) = 35°
Now writing out the set of angles again we have:
Triangle 1: 25°, 35°, 120°
Triangle 2: 25°, 120°, 35°
So in fact Triangle 1 and 2 are similar.
Now we can repeat this process for (2) - (5):
(2) Triangle 1: 100°, 60°, 20°
Triangle 2: 100°, 20°, 60°
This pair is also similar
(3) Triangle 1: 90°, 45°, 45°
Triangle 2: 45°, 40°, 95°
This pair is not similar
(4) Triangle 1: 37°, 63°, 80°
Triangle 2: 63°, 107°, 10°
This pair is not similar
(5) Triangle 1: 90°, 20°, 70°
Triangle 2: 20°, 90°, 70°
This pair is similar
Therefor pairs (1), (2) and (5) are similar
