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Is there a vector r such that the directional derivative of f at (1,1,0) in the direction of r equals 1? If there is, find one such vector. If not, explain why
Finding angle and length of a post out of alignment using Geometry. A 5 foot post is supposed to be vertical, but it is 4 inches out of alignment at the top.
Prove that the Hyperbolic Rectangle Does Not Exist. Using the Universal Hyperbolic Theorem we can show that the sum of the angles
Use definitions of hyperbolic functions to find each. 1) lim as x approached infinity tanh x
Proof involving congruent triangles. Write a two column proof for the following.
Use logarithmic differentiation to find the derivative of the function.
Proof for the triangle. Prove the following theorem: If the circumcenter of a triangle lies on a median of that triangle
A street light is at the top of a 14 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 7 ft/sec along a straight path.
A student decided to depart from Earth after his graduation to find work on Mars. Before building a shuttle, he conducted careful calculations.
The distance of a body from a point is given by s = xsin(wt + &). Show that the velocity and acceleration are given by v = xwcos(wt + &) and a = -w2s.
Solving Triangles: How Far Apart Are the Girls? A rescue Helicopter at an altitude of 200 m spots two lost girls at the same time.
How to Find 5 Triangles with Integer Sides.Find five triangles with integers sides (without no commun divisors )
Geometry: Angles and Triangles.For the two acute angles, m1=6x -3° and m2 =x + 2°. Solve for x and the measure of each angle.
Triangle Coordinates After Reflection and Mapping.Triangle abc has coordinates a(-1,3), b(-6,5), and c(-4,7):
Both forms of the definitions of the derivative of a function f at number a.
Find the first three derivatives of the function f(x) = 2cos x sin 2x.
Given f(x)= identify a function u of x and an integer n not equal to 1 such that f(x)=(x2+3x+1)5/(x+3)5 . Then compute f'(x)
Area of a Segment of a Circle.In a circle of radius 6 centimeters, find the area of the segment bound by an arc of measure 120 degrees
Tangency of three circles.Create two tangent circles with centers A and B. For convenience sake, let circle A have the larger radius.
Let n be a positive integer a) prove that n is divisible by 5 if and only if it ends with 0,5
write down the centre and radius of circle A.Explain why the distance between the centres of circles A and B is 10.
We've got a cylindrical can with height =h and radius =r. It will hold 4L (4,000 cm cubed) of some liquid. The material for the top and bottom costs 2 cents
Write an expression for the slope of the curve at any point (x,y)
Show that if the tangent to y=ekx at (a, eka) passes through the origin then a=1/k.
Revolutions of a tire.Two cars with new tires are driven at an average speed of 60 mph for a test drive of 2000 miles