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Basic Calculus

Finding the Optimum

The purpose of this project is to find the values of x and y that will yield the optimum (maximum or minimum) value of a system and the optimum value of a system using algebraic and graphical methods. Follow these ten steps (see mp1.jpg) to determine the optimum value of z and the values of x and y that yield the optimum valu

Rouche's formula

(a) How many roots of the equation z^4 &#8722; 6z + 3 = 0 have their modulus between 1 and 2? (b) Find the number of the roots of the equation z^6 &#8722; 5z^4 + 8z &#8722; 1 = 0 in the annulus {z : 1 < |z| < 2}

Bearings for the laps in a boat racing.

A boat race runs along a triangular course marked by buoys A, B, and C. The race starts with the boats headed west for 3600 meters. The other two sides of the course lie to the north of the first side, and their lengths are 1500 meters and 2800 meters. Draw a diagram that visually represents the problem, and find the bearings fo

Lobster boat is situated due west of a lighthouse

A lobster boat is situated due west of a lighthouse. A barge is 12 km south of the lobster boat. From the barge the bearing to the lighthouse is 63 degrees (12 km is the length of the side adjacent to the 63 degree bearing). How far is the lobster boat from the light house?

Angular Displacement

The flywheel of a gasoline engine rotates at an angular speed of 3240 rpm. Find its angular displacement (in revolution) in 10 sec.

Transportation Cost

For speeds between 40 and 65 mph, a truck gets 480/x miles per gallon when driven at a constant speed of x miles per hour. Diesel gasoline costs 2.23 per gallon, and the driver is paid 15.10 per hour. What is the most economical constant speed between 40 and 65 miles per hour at which to drive the truck.

Buoyancy and Terminal Velocity

Archimedes principal of buoancy states that an object submerged in a fluid is buoyed up by a force equal to the weight of the fluid the object displaces. A rectangular box 1foot X 2 feet X 3 feet and weighing 384 lbs. is dropped into a 100 foot deep freshwater lake (density 62.4 lbs/cubic foot). The box immediately begins to

Velocity, Time and Displacement

A stone is dropped from a high cliff and falls with velocity v = 32t feet per second. How many feet does the stone travel during the first 3 seconds?

Using Rectangles to Approximate Area

Use rectangles to approximate the area bounded by the graph of the function f(x) = x3, the x-axis, and the lines x = 0 and x = 2. Use n = 4 subintervals.

Width of Subintervals

If we break the interval from x = -1 to x = 1 into n = 4 subintervals, what is the width of each subinterval?

Advance Engineering Maths

Please show steps on how you get the answer, type out if possible for easy reading. (See attached file for full problem description)

Suppose a Satellite Travels at a Speed of 12560 mph

Suppose a satellite travels at a speed of 12560 mph about a planet having planetary radius equal to 4000 miles. assuming the satellite makes one full revolution about the planet every 3 hours, find the height of the satellite.

Velocity and Displacement

A toy rocket shot straight up from the ground and travels so that its distance from the ground after t seconds is s(t) = 150t - 16t2 What is the velocity of the rocket after 2 seconds have passed? See the attached file.

Interest and Finding the Equation of an Ellipse

1. An ellipse with major axis of length 1048 ft. and minor axis of length 898 ft. Assuming that a coordinate system is superimposed on the area in such a way that the center is at the origin and the major and minor axes are on the x- and y- axes of the coordinate system, respectively, find an equation of the ellipse. 2. One

Temperature of a Thermometer

The temperature of a thermometer that is x inches from a fire is given by (see attached). T(x) = ___840_ 1 + 0.5x degrees What is lim T(x) x&#61614;0+

Why the Condition is Placed at the End of the Formula

An open container is such that each horizontal cross section is an equilateral triangle. its base has side of a length 10cm and its top has sides length 10x cm. each sloping edge has length 20cm. the surface of the container is modelled by part of an inverted triangular pyramid. the capacity V(x) litres is : V(x)=1/12 (x^2

Equilibrium demand and price

Find the equilibrium demand. Find the equilibrium price (in dollars). supply: p = 2000 / 2000-q supply: p = 7000 - 3q / 2q 2000/2000-q = 7000 - 3q / 2q => (See attached file for full problem description)

Integral calculus

(See attached file for full problem description) Use integral calculus to solve differential equation problems...

Integrate Functions and Use Calculus to Solve

Calculus: Integrate functions and use calculus to solve problems. 1. Find the following integrals a) e^5x dx b) cos x sin 5x dx c) (3x + 4)/(x + 3) dx d) (2x + 5)/(x^2 + 5x) dx 2. The diagram shows the shape of a metal component required in a manufacturing process. The area of the flat metal component is descr

finding area of region, total cost function, midpoint rule

Any help would be appreciated on finding area of region, total cost function, midpoint rule. marginal cost. (See attached file for full problem description) --- A. Find the area of the region bounded by y=1/x and 2x + 2y=5 B. Find the area of the region bounded by the graphs of y= -x^2 + 2x and y=0 C. Find y=f

Concentration, Rate of Flow and Dilution

In a tank containing 100 gallons of fresh water, 10 lbs of salt was added instead of 20 lbs. To correct the mistake, fresh water was added at the rate of 3 gallons per minute while draining off the well stirred salt solution from the tank at the same rate. How long will it take until the tank contains the correct amount of salt?

Solutions of Newtonian Viscous Flow Equations

3-34. A sphere of specific gravity 7.8 is dropped into oil of specific gravity 0.88 and viscosity = 0.15 Pa s. Estimate the terminal velocity of the sphere if ts diameter is (a) 0.1 mm, (b) 1 mm, and (c) 10 mm. Which of these is a creeping motion?