On an algebra test, the highest grade was 42 points higher than the lowest grade. The sum of the two grades was 138. Find the lo
1 answer:
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This question is Incomplete because it lacks the diagram showing the containers as well as the required options. Find attached to this answer the appropriate diagram.
Complete Question
Aluminium coated dewars are cylindrical flasks used to safely store and transport liquid nitrogen, dry ice etc. A company manufactures such dewars of different sizes. Shown here are two dewars, both of the same height but of different diameters. How much aluminium will be required to cover Dewar A compared to that required for Dewar B? (Note: The base and the lid are NOT made up of aluminium.)
A) 1/3 times
B) 3 times
C) 9 times
D) The same amount of aluminum will be required.
Answer:
B) 3 times
Step-by-step explanation:
From the question, we are told that we are to find the amount of aluminum to cover Dewar A and B , we are also told that the base and the lid are not covered with aluminum.
From this information, we can determine that we are to find the curved or Lateral surface area of the cylinder because the base and lid are not included
The curved surface area of a cylinder is calculated as 2πrh
We told that both cylinders have the same height. Hence,
For Dewar A
We have Diameter of 30 cm, radius = Diameter ÷ 2 = 30cm ÷ 2 = 15cm.
Height = h
The curved surface area = 2πrh
= 2 × π × 15 ×h
= 30πhcm²
For Dewar B
We have Diameter of 10 cm, radius = Diameter ÷ 2 = 10cm ÷ 2 = 5cm.
Height = h
The curved surface area = 2πrh
= 2 × π × 5 ×h
= 10πhcm²
When we compare the curved surface Dewar A to the curved surface area of Dewar B
Dewar A : Dewar B
30πhcm² : 10πhcm²
3(10πhcm²) : 10πhcm²
From the above comparison, we can see that 3 times more aluminum is required to cover Dewar A compared to Dewar B.
Answer:
y = 16x/65
Step-by-step explanation:
Given:
Triangle ABE is similar to triangle ACD. AED and ABC are straight lines
EB and DC are parallel
The area of quadrilateral BCDE = xcm²
The area of triangle ABE = ycm²
Find attached the diagram from the above information.
In similar triangles, the ratio of their corresponding angles are equal.
Also, the ratio of the area of the two triangles = square of ratio of the corresponding sides of the two triangles.
Area ∆ACD/area of ∆ABE = (DC/EB)²
Area ∆ACD/area of ∆ABE = [(area of quadrilateral BCDE +
area of ∆ABE)]/(area of ∆ABE)
(x+y)/y = (DC/EB)²
(x+y)/y = (9/4)²
x+y = (81/16)y
x = (81/16)y - y
x = (81y - 16y)/16
x = 65y/16
Making y subject of formula
16x = 65y
y = 16x/65
An expression for y in terms of x:
y = 16x/65
