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
(a) How many roots of the equation z^4 − 6z + 3 = 0 have their modulus between 1 and 2? (b) Find the number of the roots of the equation z^6 − 5z^4 + 8z − 1 = 0 in the annulus {z : 1 < |z| < 2}
The following table shows the average number of hours worked per week at a place of... Calculus Functions. See attached file for full problem description.
See attached file for full problem description. Do only the 4th problem.
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
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?
The flywheel of a gasoline engine rotates at an angular speed of 3240 rpm. Find its angular displacement (in revolution) in 10 sec.
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.
Find the value of cot 35.2 degree rounded to four significant digits.
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
See attached file for full problem description. Can you show more steps in the problems how you got the answer?
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?
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.
If we break the interval from x = -1 to x = 1 into n = 4 subintervals, what is the width of each subinterval?
Calculus engineering math, Lagranges Interpolation, Quadratic Interpolation, Interpolating polynomial. See attached file for full problem description.
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 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.
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.
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
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0+
Determine which elements of Z_7 (Z sub 7) are primitive roots.
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
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)
Verify each equation is an identity (double angle used in this chapter). See attached file for full problem description.
(See attached file for full problem description) Use integral calculus to solve differential equation problems...
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
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
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?
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?
Please see the attached file for the fully formatted problems. Please redo showing all steps.