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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?
If the rope is pulled in at a rate of 1m/s, how fast is the boat approaching the dock when it is 8m from the dock?
If the trough is being filled with water at a rate of 0.2m3/min, how fast is the water level rising when the water is 30cm deep?
Write the equations. Provide complete and step by step solution for the question and show calculations and use formulas.
Find if the planes are parallel, perpendicular or neither. If they are not parallel then find the equation for the line of intersection.
Find the angle between a cube's diagonal and one of its sides. (use the vector calculus to get your answer) give detailed response.
Find the Taylor polynomial of degree 4 at c=1 for the equation and determine the accuracy of this polynomial at x=2.
The quarterback of a football team releases a pass at a height of 7feet above the playing field, and the football is caught by a receiver 30 yrds .
Find the points at which the function has a horizontal tangent line. f(x)=x^2+4x+5
The inverse cosine function has domain [-1,1] and range [0, pi]. Prove that (cos^-1)'(x) = -1 / sqrt(1-x^2)
If I be an open interval containing the point x. (x0) and suppose that the function f:I->R has two derivatives.
Let I be an open interval and n be a natural number. Suppose that both f:I->R and g:I->R have n derivatives.
The equation x2 - 3x + 1 = 0 has a solution for x = 0. Give the third approximationby using Newton's method. Your first approximation is to be 1.
Let f: I ?R where I is an open interval containing the point c, and let k ? R. Prove the following.
Differentiate to derive the equation for instantaneous velocity, which would be represented by the gradient of a graph.
Determine whether the function is homogenous. If it is, state the degree.Provide complete and step by step solution for the question and show calculations.
Find the mass and centroid of the plane lamina with the indicated shape and density.