作业帮函数 二次方程1.The diagram shows the outdoor pool at Lakeview Park
来源：学生作业帮 编辑：作业帮 分类：英语作业 时间：2024/06/06 12:55:34
函数 二次方程
1.The diagram shows the outdoor pool at Lakeview Park.A cement deck 2 m wide surrounds the outside edge of the pool.Calculate the area of the deck.
2.Determine the maximum area of a triangle,in square centimetres,if the sum of its base and its height is 10 cm.
3.A photograph measuring 12cm by 8cm is to be surrounded by a mat before framing.The width of the mat is to be the same on all sides of the photograph.The area of the mta is to equal the area of the photograph.Find the width of the mat.
1.The diagram shows the outdoor pool at Lakeview Park.A cement deck 2 m wide surrounds the outside edge of the pool.Calculate the area of the deck.
2.Determine the maximum area of a triangle,in square centimetres,if the sum of its base and its height is 10 cm.
3.A photograph measuring 12cm by 8cm is to be surrounded by a mat before framing.The width of the mat is to be the same on all sides of the photograph.The area of the mta is to equal the area of the photograph.Find the width of the mat.
1.The diagram shows the outdoor pool at Lakeview Park.A cement deck 2 m wide surrounds the outside edge of the pool.Calculate the area of the deck.
Solution :
Pool area = 25×30 + 10×15 = 900 (m²)
Deck area = (25+4)×(30+10+4) - 5×10×2 - 900 = 276 (m²)
2.Determine the maximum area of a triangle,in square centimetres,if the sum of its base and its height is 10 cm.
Solution:
Let the base be x,so the height is (10 - x)
Area of triangle = ½x(10-x) = -½(x²-10x) = -½(x²-10x+25-25)
= 12.5 - ½(x-5)²
So,if x = 5,maximum area of triangle = 12.5 (cm²)
3.A photograph measuring 12cm by 8cm is to be surrounded by a mat before framing.The width of the mat is to be the same on all sides of the photograph.The area of the mat is to equal the area of the photograph.Find the width of the mat.
Solution:
Let x be the width of the mat.
Area of photograph = 12×8 = 96 (cm²)
Area of photograph with mat = (12+2x)×(8+2x) = 192
(12+2x)×(8+2x) = 192
(6+x)×(4+x) = 48
x²+10x-24=0
(x+12)(x-2)=0
x₁= 2 (cm); x₂= -12 (cm)(unresonable,rejected)
Ans:Width of the mat is 2 cm.
Solution :
Pool area = 25×30 + 10×15 = 900 (m²)
Deck area = (25+4)×(30+10+4) - 5×10×2 - 900 = 276 (m²)
2.Determine the maximum area of a triangle,in square centimetres,if the sum of its base and its height is 10 cm.
Solution:
Let the base be x,so the height is (10 - x)
Area of triangle = ½x(10-x) = -½(x²-10x) = -½(x²-10x+25-25)
= 12.5 - ½(x-5)²
So,if x = 5,maximum area of triangle = 12.5 (cm²)
3.A photograph measuring 12cm by 8cm is to be surrounded by a mat before framing.The width of the mat is to be the same on all sides of the photograph.The area of the mat is to equal the area of the photograph.Find the width of the mat.
Solution:
Let x be the width of the mat.
Area of photograph = 12×8 = 96 (cm²)
Area of photograph with mat = (12+2x)×(8+2x) = 192
(12+2x)×(8+2x) = 192
(6+x)×(4+x) = 48
x²+10x-24=0
(x+12)(x-2)=0
x₁= 2 (cm); x₂= -12 (cm)(unresonable,rejected)
Ans:Width of the mat is 2 cm.
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