Answer: f(g) = 895 + 30g
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He paid $2065. Number of games he played:
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2065 = 895 + 30g
30g = 2065 - 895
30g = 1170
g = 39
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Answer: He played 39 games.
Step-by-step explanation:
So we have a rectangle, whose area is A=bh. We don't know any of those, so we've got a bit of thinking to do. (Wish I could draw a picture....) First of all, we only need to consider half the rectangle. Since it is bounded by a parabola that is symmetric over the y-axis (ie not moved left or right), the rectangle has the same area on the right and left. So let's just consider the first quadrant. Note that if we maximize this area, we maximize the entire rectangle's area. The width of this half rectangle is x (it's the x coordinate). The height of this rectangle is whatever the y coordinate of the corner is. That corner is directly above the x coordinate, and is on the rectangle. So the upper corner must have coordinates of (x, y), or (x, 8-x2). Those will serve as our base and height. A = x (8 - x2)A = 8x - x3 Maximize implies derivative = 0, so... dA = 8 - 3x20 = 8 - 3x23x2 = 8x2 = 8/3x = ±1.633 Notice that this is giving us two answers -- one of them is on the left (second quadrant), while the other is on the right. The y coordinates will be the same for both, due to the nature of this parabola. y = 8 - (1.633)2y = 8 - (8/3)y = 5.333 Our upper corners are (±1.633, 5.333). The dimensions are: Height: 5.333Width = (2 · 1.633) = 3.266 :)
The answer would be true because 4+5 is > 8
Answer:
Unit Rate of Machine A = 2.5 square feet per hour
Unit Rate of Machine B = 3.333 square feet per hour.
The unit rate of Machine B is greater than unit rate of machine A.
Step-by-step explanation:
The unit rates for both machines need to be calculated first.
The unit rate will be calculated as:
<u>For Machine A:</u>
Area Covered = 5/8
Time = 1/4
The unit rate will be:
<u>For Machine B:</u>
Area Covered = 2/3
Time = 1/5
As it can be seen that unit rate for Machine B is greater than Unit Rate of Machine A.
Hence,
Unit Rate of Machine A = 2.5 square feet per hour
Unit Rate of Machine B = 3.333 square feet per hour.
The unit rate of Machine B is greater than unit rate of machine A.