標題:
F.5 Maths不等式
發問:
A car travels from town P to town Q in x hours at a speed of 10(3 + x) km/h. If the distance between the two towns is less than 100 km, find the range of possible values of x.It is given that a nsided polygon has n( n - 3) /2diagonals. If a polygon has more than 20 diagonals, find the minimum number of its... 顯示更多 A car travels from town P to town Q in x hours at a speed of 10(3 + x) km/h. If the distance between the two towns is less than 100 km, find the range of possible values of x. It is given that a nsided polygon has n( n - 3) /2diagonals. If a polygon has more than 20 diagonals, find the minimum number of its sides. The product of two consecutive positive even integers is not smaller than 48. Find the least possible value of the smaller integer. The sum of the squares of two consecutive positive integers is less than 41. Find the greatest possible value of the larger integer.
I am STY. The solutions are as follows. Hope can help you~~ 1) distance = time * speed x * 10(x + 3) < 100 x * (10x + 30) < 100 10x^2 + 30x - 100 < 0 x^2 + 3x - 10 < 0 (x + 5)(x - 2) < 0 -5 < x < 2 As this is impossible to have negative speed and time. So, the range of possible value of x is 0 < x < 2 2) n(n - 3) / 2 >20 n(n - 3) > 40 n^2 - 3n - 40 > 0 (n - 8)(n + 5) > 0 n < -5 (rejected) and n > 8 So, the min. no. of sides is 9 3) Let the smaller integer be x then the other no. is x + 2 x(x + 2) >= 48 x^2 + 2x - 48 >= 0 (x + 8)(x - 6) >= 0 x <= -8 (rejected) or x >= 6 So, the least possible value of the smaller integer is 6. 4) Let the larger integer be x then the smaller integer is x - 1 x^2 + (x - 1)^2 < 41 x^2 + x^2 - 2x + 1 < 41 2x^2 - 2x - 40 < 0 x^2 - x - 20 < 0 (x - 5)(x + 4) < 0 -4 < x < 5 So, the greatest possible value of the larger integer is 5
其他解答:
F.5 Maths不等式
發問:
A car travels from town P to town Q in x hours at a speed of 10(3 + x) km/h. If the distance between the two towns is less than 100 km, find the range of possible values of x.It is given that a nsided polygon has n( n - 3) /2diagonals. If a polygon has more than 20 diagonals, find the minimum number of its... 顯示更多 A car travels from town P to town Q in x hours at a speed of 10(3 + x) km/h. If the distance between the two towns is less than 100 km, find the range of possible values of x. It is given that a nsided polygon has n( n - 3) /2diagonals. If a polygon has more than 20 diagonals, find the minimum number of its sides. The product of two consecutive positive even integers is not smaller than 48. Find the least possible value of the smaller integer. The sum of the squares of two consecutive positive integers is less than 41. Find the greatest possible value of the larger integer.
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最佳解答:I am STY. The solutions are as follows. Hope can help you~~ 1) distance = time * speed x * 10(x + 3) < 100 x * (10x + 30) < 100 10x^2 + 30x - 100 < 0 x^2 + 3x - 10 < 0 (x + 5)(x - 2) < 0 -5 < x < 2 As this is impossible to have negative speed and time. So, the range of possible value of x is 0 < x < 2 2) n(n - 3) / 2 >20 n(n - 3) > 40 n^2 - 3n - 40 > 0 (n - 8)(n + 5) > 0 n < -5 (rejected) and n > 8 So, the min. no. of sides is 9 3) Let the smaller integer be x then the other no. is x + 2 x(x + 2) >= 48 x^2 + 2x - 48 >= 0 (x + 8)(x - 6) >= 0 x <= -8 (rejected) or x >= 6 So, the least possible value of the smaller integer is 6. 4) Let the larger integer be x then the smaller integer is x - 1 x^2 + (x - 1)^2 < 41 x^2 + x^2 - 2x + 1 < 41 2x^2 - 2x - 40 < 0 x^2 - x - 20 < 0 (x - 5)(x + 4) < 0 -4 < x < 5 So, the greatest possible value of the larger integer is 5
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