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In the figure there are infinitely many circles approaching the vertices of an equilateral triangle, each circle touching other circles and sides.
At what rate is the angle between the string and the horizontal decreasing when 200ft of string has been let out?
Let f(x)=c/x+x^2. Determine all values of the constant c such that f has a relative minimum, but no relative maximum.
How large must a trust fund that pays 7.5% compounded continuously be, in order for a child on her 8th birthday to ensure sufficient funds at age 18?
Use the mean value theorem to show that at some time between 2:00 and 2:10 the acceleration is exactly 120 mi/h^2.
A model rocket is fired vertically upward from rest. It's acceleration for the first three seconds is a(t)=60t at which time the fuel is exhausted.
A rectangular lot, 54 square yds. in area with a perimeter fence, is divided into 2 rectangular sections by a single connecting fence costing $2.00/yd.
Prove that the point p is a limit point of the point set X if and only if each open point set containing p contains a point in X which is different from p.
A highway patrol helicopter hovers 3/10 mile above a level, straight interstate highway which has a posted speed limit of 65 miles per hour.
Finding the derivative. Calculating derivative from mathematical expressions.
One is tangent to the to the parabola at (A, A^2 + 3) and the other at (-A, A^2 + 3). Find (the positive number) ?
Each chicken produces the same amount of eggs on one 24hr period.how many chickens are there if each chicken can produce 20 eggs per day.
When the balloon is 75 ft above the road, a car moving at 55 ft/s passes directly under the balloon.
A rectangular field is going to be enclosed and divided into two separate rectangular areas. (Areas do not have to be equal).
A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle.
A Farmer wants to construct a fence. The area that he is going to enclose is rectangular, but one of the sides is a river (assumed to be straight).
At 10:00 AM, an object is removed from a furnace and placed in an environment with a constant temperature of 68 degrees.
If the perimeter is 16 feet, what dimensions will admit the most light? (hint: Area of equilateral triangle = the square root of 3/4 times x squared.)
She noted that the body temperature of the deceased was 85.5 deg. while the air temperature was 78 deg.
Due to pollutants, it gets contaminated with 'P(t)' kilograms of chemical waste at time 't' which is evenly distributed throughout the tank.
But the theory of Taylor (Maclaurin) expansions is a part of more general theory developed in the course of the functions of complex variable.
Find the vertex, focus, and directrix of the parabola described by the above equations.
Find the dimensions of a cylinder with a surface area of 300 cm^2 with a maximum volume.
A certain rational function f(x) contains quadratic functions in both its numerator and denominator.
An iron ball with radius R/2 centimeters is placed in the bowl and water is poured in to a depth of 2R/3 centimeters. How much water was poured in?