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Complex conjugate roots: Suppose that the equation ax^2+bx+c=0 has real coefficients and the complex roots. Why must the roots be complex conjugates of each other?
Find the lengths of both circular arcs of the unit circle connecting the point (1,0) and the endpoint of the radius that makes an angle of 3.90 radians with the positive horizontal axis.
Each function graphed is of the form y=a sin bx or y=a cos bx, where b greater than 0. Determine the equation of the graph.
The leaf then floats down the river at 3ms-1 FOR 20 seconds until it gets caught on a rock. How far and in what direction from the base of the tree is the rock?
Prove the sine, cosine, and tangent sum formulas for all real values, and derive special applications of the sum formulas (i.e half angle, double angle).
The angle of elevation from the top of a house to a jet flying 2 miles above the house is x radians. If d represents the horizontal distance, in miles, of the jet from the house, express d in terms
The vertices of Triangle ABC are the points A(4,-3), B(2,1), and C(-2,4). Find the measure of the largest angle in the triangle to the nearest tenth of a degree.
Change all trig functions to sines and cosines and simplify. Write the answer using s for sin(x) and c for cos(x). cos (-x)/sec(x) + tan(-x)
Find the terminal point on the unit circle determined by 3π/4. Use exact values.
Find all solutions of the equation. Use a calculator to solve the equation in the interval [0, 2pi].
Give exact values (fractions and square roots) for the fallowing problems. Please show work so i can understand it better(just only 1 for each different sin, cos, etc.)
Which of the following relations in 0,1,2,3 are equivalence relations? If the given relation is an equivalence relation, then verify the properties of equivalence relation. If the given relation is
Calculate the length of the perppendicular from a poit p on the curve defined by ax= y^2, by=z^2, to the xz plane, where the perpendicular is also perpendicular to the plane defined by the tangent
Use vector techniques to prove that a triangle and its medial triangle have the same centroid, stating each step of the proof.
I am given a quad. and asked what values x and y must be to make the quad. a parallelogram. One side says 26 and the opposite side of that says 3x-y.
The magnitudes of the four displacement vectors shown in the drawing are A = 15.0 m, B = 11.0 m, C = 11.0 m, and D = 23.0 m. Determine the (a) magnitude and (b) direction for the resultant that occu
Lee is explainig the lesson on minimum perimeters to Greg. He says to construct a rectangle with the lowest possible perimeter from 38cm of material, the dimensions have to be 18cm and the width 1cm
The manager of a small business receives a shipment of five hard drives. Three hard drives are good and 2 are defective. If a computerrepairshop purchases 3 of this stock of hard drives from the sm
Bats can produce and hear sounds w/ frequencies up tp 100000 Hz. a) what is the wavelength of the sound?
Discuss the discrete and orthogonal polynomials to least square approximations. Provide at least one example on each case to support your discussion.
An empty beaker weighs 41.19 g. When it is completely filled with water (density = 1.0 g/mL), the beaker weighs 92.92 g. (a) How many grams of water have been added to the beaker?
A saleswoman is working on a 3% commission basis. If she wants to make $3,000 in one month, how much must she sell?
One day, a person went to horse racing area, Instead of counting the number of human and horses, he instead counted 74 heads and 196 legs. Yet he knew the number of humans and horses there. How did
The crowd that heard the President speak was estimated to be 10,000 people. The actual crowd could be 750 people more or less than this. What are the possible varibles for the actual crowd size?
The management of MACU Corporation is trying to determine the amount of each of two products to produce over the coming planning period. The following information concerns labor availability, labor