The expression to find the perimeter of a rectangle is 2(length + width). What is the perimeter, in units, of a rectangle of len
2 answers:
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Answer:
22670.8 cm³/min
Step-by-step explanation:
Given:
Radius of the balloon at a certain time (r) = 19 cm
Rate of growth of radius is,
The rate at which the air is pumped in the balloon can be calculated by finding the rate of increase in the volume of the balloon.
So, first we find the volume of the sphere in terms of 'r'. As the balloon is spherical in shape, the volume of the balloon is equal to the volume of a sphere. Therefore,
Volume of balloon is given as:
Now, rate of increase of volume is obtained by differentiating both sides of the equation with respect to time 't'.
Differentiating both sides with respect to time 't', we get:
Now, plug in 19 cm for 'r', 5 cm per minute for and solve for
. This gives,
Therefore, the rate at which the air is being pumped into the balloon is 22670.8 cm³/min.
Answer:
Circumscribed circle: Around 80.95
Inscribed circle: Around 3.298
Step-by-step explanation:
Since C is a right angle, when the circle is circumscribed it will be an inscribed angle with a corresponding arc length of 2*90=180 degrees. This means that AB is the diameter of the circle. Since the cosine of an angle in a right triangle is equivalent to the length of the adjacent side divided by the length of the hypotenuse:
To find the area of the circumscribed circle:
To find the area of the inscribed circle, you need the length of AC, which you can find with the Pythagorean Theorem:
The area of the triangle is:
The semiperimeter of the triangle is:
The radius of the circle is therefore
The area of the inscribed circle then is .
Hope this helps!