1. Observe that the f(t) is change by 4 per time t => there's a acceleration of 4 => f''(t) = 4; Take the derivative of it we can get a velocity function. f'(t) = 4t + c. Since the velocity from 100 to 80 is -20 (average), this means at t = 0, f'(0) = -22 => f'(t) = 4t - 22; Take the derivative again to get the position function: f(t) = 2t^2 - 22t + d, here d = 100 should be trivial. So, the function that models the relationship is f(t) = 2t^2 - 22t + 100.
2. By the compound interest formula:
A = P (1 + r/n)^(nt) , since it's yearly, so n = 1;
results A(t) = 100 (1+0.12)^t.
3. The average rate of change is basically finding the slope, m = y1 - y2 / x1 - x2.
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Answer:
The triangle is not acute because 2² + 4² < 5²
Step-by-step explanation:
The square of the hypotenuse of a right triangle with the given short sides would be 2² +4² = 20. So, that hypotenuse would be √20, about 4.47. The long side of this triangle is longer than that, so the angle opposite is larger than 90°. The triangle with sides 2, 4, 5 is an obtuse triangle.
The triangle is not acute because 2² + 4² < 5²
There are 30 rocks in Willy's collection.
Since the number of rocks in Willy's collection is x, the number in Billy's collection is (2 2/3)x or 8/3x.
x+(2 2/3)x = 110
(3 2/3)x=110
11/3x = 110
Dividing both sides by 11/3,
(11/3x)÷11/3 = 110÷11/3
x = 110÷11/3 = 110/1 ÷ 11/3 = 110/1 × 3/11 = 330/11 = 30
