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 pa ewdlq4y4fm, dju oda+/+ib,c,/ 7iwy 2fv.efa.efatr9 3(0ba7y r4nvju9 sx -2mlfrom a slingshot into the air. Each time he launches a stone, he records the 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 belo.eafy2ref4t9as bl v (a- j 9n0um7r3xw 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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