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Basic Calculus

Rate of Flow

A fluid has a density 1500 and velocity field of: v = -yi + xj + 2z k. Find the rate of flow outward through the sphere x^2 + y^2 + z^2 = 25.


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

Help setting up problem

I would like some help seting up this problem. I am doing some extra learning and the problem is a bit confusing The angle is 22 degrees and the book gives the answer as .50636 Thank You

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

Distance across a canyon Find RS

To determine the distance RS across a deep canyon. Joanna lays off a distance TR=582 yards. She then finds that T=32degrees50' and R=102degrees20' findRS? please show me the steps Thank U

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