都很简单的题目
1.Ben has four more than twice as many CDs as Jack .If they have a total of 31 CDs ,how many CDs does Jack have
Ben 的CD是Jack的2倍还多4张,如果他们一共有31张CD,那问Jack有几张CD?
x+2x+4=31 ===> x = 9
2.Jack wants to replace the flooring in his rectangular Kitchen .He calculates the area of the floor to be 12.8 square meters ,The actual area of the floor is 13.5 square meters .What is the relative error in calculating the area of the floor ,to the nearest thousandth?
Jack想重新装修一下他家厨房的地板,他算了一下他家的地板面积是12.8平米,可实际上正确答案是13.5平米.Jack测量的相对误差是多少,答案精确到千分之一.
(13.5-12.8)/13.5 = 0.051851851851851816 = 0.052
3.A right triangle contains a 38° angle whose adjacent side measures 10 centimeters.What is the length of the hypotenuse ,to the nearest hundredth of a centimeter
一个直角三角形有一个角是38度,对边是10cm,问斜边的长度.
sin (38*3.14/180) = 对边 / 斜边
====> 斜边 = 16.2427 cm
这个题如果是不准带计算器的话,有点难度,要用三角函数的近似
sin[38] = sin[30+8] = sin[30]cos[8] + sin[8]cos[30]
sin[30] = 1/2
cos[30] = sqrt(3)/2
角度比较小的时候
sin[x] = x-x^3/6,cos[x] = 1-x^2/2,x=角度*3.1416/180=0.14
带入到前面的式子中
sin[38] = ((1 - x^2/2)/2 + 1.732/2*(x - x^3/6))
10/sin[38] = 16.235 cm
4 画图 我用Mathematica 一句话搞定
Plot[{Abs[x],Abs[3 x]},{x,-3,3},PlotStyle -> Thick]
5 画图 还是Mathematica 一句话搞定
Plot[{x^2 + 6 x - 3,7 - x},{x,-12,4},PlotStyle -> Thick]