F.5 Maths inequalities 20 mark
2017/06/13 00:46
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標題:
F.5 Maths inequalities 20 mark
發問:
1) One side of a rectangular field is bounded by a river. A farmer has 100m of fencing and wants to fence the other three sides of the field. If he wants to enclose an area of at least 800m^2, what will be the maximum length of the field along the river?2)When heating up an aluminium pipe of 15m long from a... 顯示更多 1) One side of a rectangular field is bounded by a river. A farmer has 100m of fencing and wants to fence the other three sides of the field. If he wants to enclose an area of at least 800m^2, what will be the maximum length of the field along the river? 2)When heating up an aluminium pipe of 15m long from a temperature of 20 degree Celsius to x degree Celsius, its length (L m) is given by the formula below: L=15+0.00585(x-20) A researcher is going to explore the properties of the pipe due to heating when the percentage increase of the length is less then 0.5% or greater than 2%. What is the possible range of values of x under this condition?(Give the answer correct to the nearest integer) 3) a)If 2x^2-4x+k>=0 for all real values of x, find the minimum value of k. b)If -x^2-4x+k<=8 for all real values of x, find the maximum value of k. 4)If 2cos A =3x-1, where A is any angle, find the range of values of x. Please show ALL steps. Thank you very much.
最佳解答:
1 Let x m be the length of the field y m be the width of the field x+2y <=100........(1) xy>=800..........(2) from (2) y>= 800/x 2y >=2(800/x) 100 >=x+2y>= x+2(800/x) 100>= x+2(800/x) 100x>=x^2+1600 x^2-100x+1600<=0 (x-80)(x-20)<=0 x<=80 & x>=20 or x>80 & x<20 (rejected) so 20 <= x <=80 maximum length of the field is 80m width of the field is 10m 2)A researcher is going to explore the properties of the pipe due to heating when the percentage increase of the length is less then 0.5% or greater than 2%. What is the possible range of values of x under this condition?(Give the answer correct to the nearest integer) [15 + 0.00585(x-20) -15 ]/15 <0.5% (0.00585x -0.117)<0.075 x<32.82 x<32 (corr to the nearest integer) [15+0.00585(x-20)-15]/15 > 2% (0.00585x-0.117) >0.3 x> 71.28 x>72 (corr to the nearest integer) 2010-09-22 12:36:38 補充： 2) 20 <= x <32 x>72 3) a)the coefficient of x^2 is 2 (>0) the graph opens upward, the vertex is the minimum, when 2x^2-4x+k=0, then there is only one real root, b^2-4ac=0 16-4(2)k=0 2K=-16/-4 K=2 2010-09-22 12:37:10 補充： b)-x^2-4x+k-8<=0 the coefficient of x^2 is -1 (<0) the graph opens downward, the vertex is the maximum, when –x^2-4x+(k-8)=0, thenf there is only one real root b^2-4ac=0 16-4(-1)(k-8)=0 16+4(k-8)=0 K=-4+8 K=4 2010-09-22 15:31:03 補充： 2) 20 < x <=32 or x>= 72 2010-09-22 15:37:33 補充： 4) -1 <=cosA <= 1 -2<= 2cosA <= 2 -2<=3x-1 <=2 -1<=3x <=3 -1/3 <=x <=1
其他解答:
F.5 Maths inequalities 20 mark
發問:
1) One side of a rectangular field is bounded by a river. A farmer has 100m of fencing and wants to fence the other three sides of the field. If he wants to enclose an area of at least 800m^2, what will be the maximum length of the field along the river?2)When heating up an aluminium pipe of 15m long from a... 顯示更多 1) One side of a rectangular field is bounded by a river. A farmer has 100m of fencing and wants to fence the other three sides of the field. If he wants to enclose an area of at least 800m^2, what will be the maximum length of the field along the river? 2)When heating up an aluminium pipe of 15m long from a temperature of 20 degree Celsius to x degree Celsius, its length (L m) is given by the formula below: L=15+0.00585(x-20) A researcher is going to explore the properties of the pipe due to heating when the percentage increase of the length is less then 0.5% or greater than 2%. What is the possible range of values of x under this condition?(Give the answer correct to the nearest integer) 3) a)If 2x^2-4x+k>=0 for all real values of x, find the minimum value of k. b)If -x^2-4x+k<=8 for all real values of x, find the maximum value of k. 4)If 2cos A =3x-1, where A is any angle, find the range of values of x. Please show ALL steps. Thank you very much.
最佳解答:
1 Let x m be the length of the field y m be the width of the field x+2y <=100........(1) xy>=800..........(2) from (2) y>= 800/x 2y >=2(800/x) 100 >=x+2y>= x+2(800/x) 100>= x+2(800/x) 100x>=x^2+1600 x^2-100x+1600<=0 (x-80)(x-20)<=0 x<=80 & x>=20 or x>80 & x<20 (rejected) so 20 <= x <=80 maximum length of the field is 80m width of the field is 10m 2)A researcher is going to explore the properties of the pipe due to heating when the percentage increase of the length is less then 0.5% or greater than 2%. What is the possible range of values of x under this condition?(Give the answer correct to the nearest integer) [15 + 0.00585(x-20) -15 ]/15 <0.5% (0.00585x -0.117)<0.075 x<32.82 x<32 (corr to the nearest integer) [15+0.00585(x-20)-15]/15 > 2% (0.00585x-0.117) >0.3 x> 71.28 x>72 (corr to the nearest integer) 2010-09-22 12:36:38 補充： 2) 20 <= x <32 x>72 3) a)the coefficient of x^2 is 2 (>0) the graph opens upward, the vertex is the minimum, when 2x^2-4x+k=0, then there is only one real root, b^2-4ac=0 16-4(2)k=0 2K=-16/-4 K=2 2010-09-22 12:37:10 補充： b)-x^2-4x+k-8<=0 the coefficient of x^2 is -1 (<0) the graph opens downward, the vertex is the maximum, when –x^2-4x+(k-8)=0, thenf there is only one real root b^2-4ac=0 16-4(-1)(k-8)=0 16+4(k-8)=0 K=-4+8 K=4 2010-09-22 15:31:03 補充： 2) 20 < x <=32 or x>= 72 2010-09-22 15:37:33 補充： 4) -1 <=cosA <= 1 -2<= 2cosA <= 2 -2<=3x-1 <=2 -1<=3x <=3 -1/3 <=x <=1
其他解答:
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- F.5 Maths 列式 (數列)
- 3,3,7,7, (+,-,x,÷)點先可以等於24@1@
- 我要21-2-08有誰共鳴`!
- 1968年2月2日(23-00)男,問詳細性格八字與運程,唔該
- 14吋車胎幾錢一條
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