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Derivatives to Physical Systems:
A stone is dropped into a quiet lake, & waves move within circles outward from the location of the splash at a constant velocity of 0.5 feet per second. Determine the rate at that the area of the circle is increasing when the radius is 4 feet.
Solution:
Using the formula for the area of a circle,
A = πr2
obtain the derivative of both sides of this equation along with respect to time t.
dA/dt = 2πr (dr/dt)
But, dr/dt is the velocity of the circle moving outward which equals 0.5 ft/s and dA /dt is the rate at which the area is increasing, that is the quantity to be determined. Set r equal to 4 feet, substitute the known values into the equation, and solve for dA /dt.
dA/dt = 2πr(dr/dt)
dA/dt = (2)(3.1416)(4 ft)(0.5 ft/s)
dA/dt = 12.6 ft2/s
Therefore, at a radius of 4 feet, the area is raising at a rate of 12.6 square feet per second.
Evaluate each of the following. (a) 25 1/2 (b) 32 1/5 Solution (a) 25 1/2 Thus, here is what we are asking in this problem. 2
-2-1
1.A manufacturing facility consists of five departments, 1, 2, 3, 4 and 5. It produces four components having the manufacturing product routings and production volumes indicated in
3x2+5x-2
( a+2b)x + (2a - b)y = 2, (a - 2b)x + (2a +b)y = 3 (Ans: 5b - 2a/10ab , a + 10b/10ab ) Ans: 2ax + 4ay = y , we get 4bx - 2by = -1 2ax+ 4ay = 5 4bx- 2by = - 1
273.98 convert it into BCD code?
what is (x-y)(x+y)
The base of an isosceles triangle and the altitude drawn from one of the congruent sides are equal to 18cm and 15cm, respectively. Find the lengths of the sides of the triangle.
Infinite limits : Let's now move onto the definition of infinite limits. Here are the two definitions which we have to cover both possibilities, limits which are positive infinity
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