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Let the curve with parametric equations x=tan t and y=sec t. Eradicate parameter to determine the relationship between x and y and then explain the curve in words.
Complete square to find conic section, 9y^2+18y=x^2+6x+18. Put conic in standard form and find suitable details like foci, directrix, or whatever is needed.
Find curve 9x^2+4y^2=36 as the parabola, ellipse, or hyperbola. Put te curve into proper form and then draw the curve on th axes. Write foci, vertices, directrix, asymptotes or whatever is needed.
Given triangle ABC with measure of angle A = 120o, length of BC = 10, and length of AC = 20. Find how many solutions are there for measure of angle B?
A cup of coffee is poured at 190·Fahrenheit, and is permitted to cool in the 70`Fahrenheit room. If temperature of coffee is 170`Fahrenheit after half an hour. How long will it take coffee to
How long will it take to decay to 15 mg? Illustrate all algebra leading to the solutions comprising all suitable properties of logarithmic functions.
Find number of dimes will you have stacked on 10th square? Find number dimes will you have stacked on nth square?
Let the function f(x) = |x + 1| (x - 2). Write f(x) as the piecewise defined function. Sketch the graph of f. Find out the domain and range of f.
Find the student's current grade? Determine the lowest final exam grade they can score to have the final grade of at least 65%?
Find out if exponential functions only model phenomena which grow, or if can they also model phenomena which decay.
The wooden artifact recovered from the tomb having 35% of carbon-14 which is present in living trees. Half life of carbon-14 is 5730 years. How long ago was artifact made?
Write down the equation which explains relationship between x and y provided that each point (x,y) is equidistant from point (1,2) and line is y=6. Illustrate the work.
If an area of triangle ABC is 14 square meters, with a = 20 m and b = 8 m, determine all possible measures for angle C.
The bridge is to be built in shape of the semielliptical arch and is to have the span of 100 feet. Height of arch, at the distance of 40 feet from center, is to be 10 feet. Determine height of arch
Reflector of the flashlight is in shape of the paraboloid of revolution. Its diameter is 4 inches and its depth is 1 inch. How far from vertex must light bulb be placed so that rays will be reflect
If c represents a constant force, find the work done if the point of the application of c moves along the line segment from P to Q. c=2j+6j P(0,0), Q(-3,3).
Solve: from 10 names on the ballot, the committee of 3 will be elected to attend the political national convention. Find how many different committees are feasible?
Find all complex cube roots of z=8, write each root in rectangle form. If u=6i+j and v=10i+j, find the magnitude of u+v.
The car is traveling at 31 mph. If its tires have the diameter of 24 inches, how fast are car's tires turning? Write answer in revolutions per minute.
The company manufactures 3 color tv sets, models X,Y, and Z. How many of each model must be produced every week if all available time should be utilized?
The quarterback releasees the football with the speed of 50 ft/sec at the angle of 70 degrees with horizontal. Find horizontal and vertical components of vector which is described.
Magnitudes and directions of two forces are 80lb S 60 degrees E and 50lb N 74 degrees E respectively. Determine magnitude and direction of resultant force.
The luxury liner leaves port on the bearing of N 100 degrees E and travels 12mi. It then turns due East and travels 4mi. How far is liner from port, and determine its bearing from port?
Over the course of 20 years, temperature in the small town is recorded every day. Write the equation which models average temperature of town in terms of days.
At Apple Tree Snacks, the snack mix worth $7/lb is merged with macadamia nuts worth $10/lb to get the 30 lb mixture worth $8.30 per pound. How much of each kind of ingredient was utilized?