10. from the question; the circle theorem obeyed is "angled formed by semi-circle"
The angle formed in a semicircle is 90 degrees, hence
This gives
But
Substituting values we get
hence, x =12
If the length of each side of a triangle is cut to 1/3 of its original size, what happens to the area of the triangle?
1 answer:
Answer:
The new area of the triangle is (1 / 9) th of the original area.
That is to say the original area of the triangle is decreased to (1/9) th of its value.
Step-by-step explanation:
The area of a triangle is given by, Area = 1/2 base
height
If each side of a triangle is cut to 1/3 of its original size then the base will also become one third and the height will also become one third.
Therefore the new area will be given by = 1/2 (1/3
base)
(1/3
height)
= 1/9 1/2
base
height
= 1/9 Area.
The new area of the triangle is 1 / 9 th of the original area.
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Answer:
the rate of change of the water depth when the water depth is 10 ft is;
Step-by-step explanation:
Given that:
the inverted conical water tank with a height of 20 ft and a radius of 8 ft is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec.
We are meant to find the rate of change of the water depth when the water depth is 10 ft.
The diagrammatic expression below clearly interprets the question.
From the image below, assuming h = the depth of the tank at a time t and r = radius of the cone shaped at a time t
Then the similar triangles ΔOCD and ΔOAB is as follows:
( similar triangle property)
h = 2.5r
The volume of the water in the tank is represented by the equation:
The rate of change of the water depth is :
Since the water is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec
Then,
Therefore,
the rate of change of the water at depth h = 10 ft is:
Thus, the rate of change of the water depth when the water depth is 10 ft is;
