Question

英文数学题

1.A sketch is drawn that is 4 inches by 6 inches. It is put in a frame of uniform width. If the area of the sketch is equal to the area of the frame, what is the width of the frame?
2.The sum of a number and it's square is 56. Find the number(s).
3.A smart-phone is thrown upwards from the top of a 560-foot building with an initial velocity of 32 feet per second. The height h of the smart-phone after t seconds is given by the quadratic equation h=-16t2+32t+560. When will the smart-phone hit the ground?

Answer 1

1. 一幅素描长6英寸宽4英寸。把它放到一个等宽的画框中。如果画框的面积和素描相同，那么画框有多宽？

   解：素描的面积为：4×6=24平方英寸

   画框的面积为24平方英寸，边长为√24，化简后为2√6

   Answer: The area of sketch: 4×6=24 square inches

   The area of frame=24 square inches, the width of frame=√24=2√6

2. 一个数和它的平方之和是56，这个数是

   解：设这个数为X,

   X+X²=56

   X²+X-56=0

   (X+8)(X-7)=0

   X=7或-8

   Answer: Regard this number as X,

   X+X²=56

   X²+X-56=0

   (X+8)(X-7)=0

   X=7 OR -8

3. 智能手机从560英尺高的建筑物顶部向上投掷，初始速度为每秒32英尺。高度h的智能手机t秒后符合二次方程h=-16t²+2t+560。智能手机什么时候能落地？

   解：手机落地时，高度h=0，所以：

   -16t²+32t+560=0

   16t²-32t-560=0

   t²-2t-35=0

   (t-7)(t+5)=0

   t=7或-5

   因为t≥0

   所以t=7

   7秒后手机落地

   Answer: When smart-phone hit the ground, h=0

   -16t²+32t+560=0

   16t²-32t-560=0

   t²-2t-35=0

   (t-7)(t+5)=0

   t=7 or -5

   As t≥0. so t=7

   Smart-phone will hit the ground after 7 seconds.