A ramp has a horizontal distance of 10 feet and a vertical rise of 3 feet. Find the length of the ramp. Round to the nearest ten
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Answer:
Figure 1's surface area: 550
Figure 2's surface area: 530
Figure 3's surface area: 790
So, the order of the figures' surface areas is: Figure 2 < Figure 1 < Figure 3.
Step-by-step explanation:
Bearing in mind that the surface area of a 3D object is the total area of its surface (that is the sum of the areas of its faces), we can count the number of distinct shapes in each figure, calculate their areas and add them up. Be careful not to add the faces that are "inside".
<u>Figure 1</u>
Its surface area consists of 13 squares of 5x5and 3 rectangles of 15x5
. So, its surface area is (13x25 + 3x75)
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<u>Figure 2</u>
Its surface area consists of 6 squares of 5x5, 3 rectangles of 17x5
, 1 rectangle of 13x5
and 2 triangles of base 12 feet and height 5 feet. So, its surface area is (17x5x3+6x5x5+13x5+12x5x2:2)
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<u>Figure 3</u>
Its surface area consists of 2 rectangles of 12.5x5, 1 rectangle of 11x5
, 2 triangles of base 12 feet and height 5 feet, 1 rectangle of 11x13
, 2 rectangles of 12.5x11
and 1 rectangle of 12x11
.
So, its surface area is (2x12.5x5+11x5+2x12x5:2+11x13+2x12.5x11+12x11)
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Solution :
Let the distance of the stick from one break be X
And let us assume that .
Here, l = length of stick
Therefore,
We know that, , so by definition we get
The cumulative distribution function for R is
When it starts at zero, then r =0. It ends at one when the r has a maximum
value of one.
The probability density function is given by
Now integrating, we find E(R) and gives :
Therefore, Var(R)=