The length of a rectangle is 5m greater than its width and its area is 6m2. Find its dimensions.
1 answer:
Answer:
Width = 1 m and length = 6 m
Step-by-step explanation:
Let b is the width of the rectangle.
Length = 5+b
The area of the rectangle, A = 6 m²
We need to find the dimensions of the rectangle. We know that, the area of a rectangle is given by :
A = lb
Width of the rectangle = 1 m
Length of the rectangle = 5+b = 6 m
Hence, this is the required solution.
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Answer: mass (m) = 4 kg
center of mass coordinate: (15.75,4.5)
Step-by-step explanation: As a surface, a lamina has 2 dimensions (x,y) and a density function.
The region D is shown in the attachment.
From the image of the triangle, lamina is limited at x-axis: 0≤x≤2
At y-axis, it is limited by the lines formed between (0,0) and (2,1) and (2,1) and (0.3):
<u>Points (0,0) and (2,1):</u>
y =
y =
<u>Points (2,1) and (0,3):</u>
y =
y = -x + 3
Now, find total mass, which is given by the formula:
Calculating for the limits above:
where a = -x+3
m = 2(-4+6)
m = 4
<u>Mass of the lamina that occupies region D is 4.</u>
<u />
Center of mass is the point of gravity of an object if it is in an uniform gravitational field. For the lamina, or any other 2 dimensional object, center of mass is calculated by:
and
are moments of the lamina about x-axis and y-axis, respectively.
Calculating moments:
For moment about x-axis:
Now to find the x-coordinate:
x =
x =
x = 15.75
For moment about the y-axis:
63
To find y-coordinate:
y =
y =
y = 4.5
<u>Center mass coordinates for the lamina are (15.75,4.5)</u>
