IB MAI HL Calculus Topic 5.2 Integration (id: d30249847)

本题目来源于试卷: IB MAI HL Calculus Topic 5.2 Integration，类别为 IB数学

[填空题]
Kai launches stones from a slingshot into the air.h-tys prh .,- 9vde3bi Each time he launches a stoaay71det:uo6 ncqb0+f 3gx 6gne, he records tyg7c1 b adna3xg:euo0+66 tfq he angle, \theta , in degrees, at which the stone is launched, and the horizontal distance, L , in metres, which the stone travels from his shooting position to where it first lands. The diagram below illustrates how the stones travel in the air when launched at different angles.


Kai analyses his results and concludes:

$\frac{\mathrm{d} L}{\mathrm{~d} \theta}=-0.08 \theta+3.3, \quad 0^{\circ} \leq \theta \leq 90^{\circ}$ .

1. Determine whether the graph of L versus \theta is  ----待选择----increasing decreasing  at $\theta= 50^{\circ}$ .

Kai observes that when the angle is $30^{\circ} $, the sling stone will travel a horizontal distance of $90 \mathrm{~m}$ .
2. Find an expression for L in terms of $\theta$ .
L= -0.04$\theta$$^2$+ a$\theta$+b ;a=  ,b=  .

参考答案:
空格1: decreasing  空格2: 3.3  空格3: 27 


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