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Sketch and describe the following sets and their images under the function z → z2.
(a) The set of all points of the form z = x + 2i.
(b) The set of all points of the form z = x + 2xi.
(c) The set of all points on the upper half of the unit circle centred at the origin, that is, points z with polar coordinates (r, ?) such that r = 1 and 0.
find the terminal point on the unit circle determined by 3pi4. use exact
Find the directional derivative at P(-2,2,-1) in the direction of Q(18,-2,4). Find the direction of maximum decrease at P. (your answer does not have to be unit vector.) What is the maximum rate of decrease?
rapid city is having its annual citywide celebration. the city wants to rent a bumper-car ride. the pieces used to make
Explain why a decision maker might feel uncomfortable with the expected value approach, and decide to use a non-probabilistic approach even when probabilities are available.
use slope-intercept form to create a graph that shows these earnings and estimate the company's earnings for the next year if the compnay continues to grow at the same rate?
If a rock is thrown upward on the planet Mars with a velocity of 23 m/s, its height (in meters) after t seconds is given by H = 23t - 1.86t2. (Round all numbers to two decimal places.)
23% of the seniors at a high school failed pre-calculus. If 1138 students failed pre-calculus, how many seniors are at this high school?
If a skateboarder leaves a ramp at 25 feet per second and attains a height of 4.7 feet after one sec what is the angle of her ramp?
How far did the messenger travel by land and how far by water?
Explain what is meant by a function. Give two real-world examples of relationships that are functions and two real-world examples that are not functions.
A graph has six vertices, every two of which are joined by an edge. Each edge is colored red or white. Show that the graph contains a monochromatic triangle (a triangle all of whose vertices have the same color.) Is the result ttrue for a graph wi..
A pizza, heated to a temperature of 350 degrees Fahrenheit, is taken out of an oven and placed in a 75 degree room at time t = 0 minutes.
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