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Basic Calculus

Finding cylindrical coordinates

(See attached file for full problem description) --- Given a point P with spherical coordinates (4, pi/6, pi/4). Find the xyz coordinates and cylindrical coordinates for P. ---

Business Calculus : Come up with an original optimization project.

I would like for you to complete an optimization project. Examples include: the optimum number of hours to study for an exam, the best time to leave for work to avoid traffic, the optimum speed to drive a dirt bike up a hill to achieve the longest jump. I would like you to follow "The Process of Problem Solving" found below

Math problems:Algebra, Economics and some Calculus

Please see attached. 1. A factory working at 83% of capacity produces 231 widgets per day. How many widgets would it produce if it worked at full capacity? 2. Solve for X: x - 2.4 = 1.5 .3 3. Simplify: (Recall: x-3 = 1/x3) 91/2 a2/3 b-1/5 b4/5 4. PROTRAC, Inc. produces two line

Calculus: Four good word problems in calculus

#1 A tumor may be regarded as a population of multiplying cells. It is found empirically that the "Birth Rate" of the cells in the tumor decrease exponentially with time, so that B(t)=B0e^(-at)... find the limiting population of the tumor. (See attachment for full questions)

Business Calculus : Rate of Change, Slope of Tangent

1. Consider the following table: X 0 1 2 3 4 5 Y 1.5 2.4 3.6 4.5 5.6 6.7 For each of the following intervals, find the average rate of change: (a) [0,1] (b) [0,3] (c) [2,5] (d) [0,5] 2. Consider the following table: X 1 2 3 4 5 6 Y 24 26 28 27 25 23 For each of the following intervals, find the average rat

Minimum possible width

A long rectangular sheet of metal strip is to be made into a rain gutter by turning up two sisdes at right angles to the remaining center strip. The rectangular cross-section of the gutter is to have an area of 18 in^2. Find the minimum possible width of the strip. Could you please show all work so I can better grasp the co

Related rates

A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 24 ft/s. (a) At what rate is his distance from second base decreasing when he is halfway to first base? (b) At what rate is his distance from third base increasing at the same moment?

Related rates

A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 1.6 m/s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building?

Tunnel Problem

In the summer of 1999, construction will begin on a 3000 ft. tunnel that will pass under the Mississippi River, connecting the cities of East St. Louis, Illinois and St. Louis, Missouri. A Missouri-based company has been contracted to begin excavating the tunnel from the Missouri side, while an Illinois-based company will begin

Integer Linear Regression

ASW Publishing Inc., a small publisher of textbooks, must make a decision regarding which books to publish next year. The books under consideration are listed in the following table, along with the projected three year sales expected from each book: Book Subject Type of Book Projected Sales (1000's) Business Calculus Ne


30) If f(x) = ln(sin(x^2)), then f''(x)=? Explain. 31) The college is making parking lot, rectangular and enclose 6000 sq meters. A fence will surround the lot and on parallel to one of the sides will divide the lot into two sections. What are the dimensions in meters of the rectangle lot using the least amount of fen

Practical Calculus Problem for the Design of Water Guttering

Please see the attached file for the fully formatted problems. MAX FLOW A company is constructing guttering to carry water. The cross section of the guttering is below: Each side is the same length and the angle between each side and the hosizontal are equal. That is, the cross section is symmetrical about the vertical

Seven Calculus Problems

Please see the attached file for the fully formatted problems. 1. Use an iterated integral to find the area of a region... 2. Evaluate the double integral... 3. Use double integral to find the volume of a solid... 4. Verify moments of inertia... 5. Limit of double integral... 6. Surface area... 7. Triple integral...

10 Calculus Problems

Please see the attached file for the fully formatted problems. Problems involve: parametric equation of line segment, volume of a parallelipiped, sketching a plane gven the equation, finding rectangular equations, center and radius of a sphere using the equation of a sphere, force vector problems.


#1 Write an equation of the line tangent to the curve y=f(x) at the given point P on the curve. Express the answer in the form ax+by=c. 1)y=3x^2-4; P(1,-1) 2)y=2x-1/x; P(0.5,-1) #2 Give the position function x=f(t) of a particle moving in a horizontal straight line. Find its location x when its velocity v is zero. 1)x=-1

A related rates calculus problem in regards to a cone.

A waffle cone has a height of 6in with a radius at the top being 1 inch. A spherical scoop of ice cream is placed on top of the cone and melts into the cone. At a particular instant of time, the radius of the ice cream is 3/2 inch and is decreasing by 1/100 in/min. At this same time, the height of the melted ice cream in the