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(a) Consider the circle that has its center at the point (2, -3) and passes through the point (5, -1). Find the radius of this circle, and find the point-slope and slope-intercept forms of the equation of the line which is tangent to this circle at the point (5, -1). In your solution, use only algebra and the fact that a line which is tangent to a circle is perpendicular to the line that passes through the center of the circle and the point of tangency.
(b) Do the same for a circle that has its center at the point (h, k) and passes through the point (x_0, y_0), where h, k, x_0, y_0 are real numbers such that the conditions h = x_0 and k = y_0 are not both satisfied.
(c) In part (b) above, why do we specify that the conditions h = x_0 and k = y_0 are not both satisfied?
estimate the drying time of the varnish when 3.5 grams of the chemical are added.
Find the equation of the straight line perpendicular to the line 2x - 3y + 5 = 0 and passing through the point (3, - 4). Please write the answer in three forms.
Gram-Schmidt Orthogonalization - Maple plot - , Calculate ?P and ?N by the formulas given above. Use Step I of the Maple supplement to plot your results and to check your calculations.
Find the interval(s) on which f(x) increases, given that f(x) = x3 - 12x + 1. Find the interval(s) on which f(x) increases, given that f(X) =- 2x (25x2 + 75 + 72).
For an integer n, define the graph Tn as follows: Vertices are 2-element subsets of {1,2,...,n}. Two vertices are adjacent if they have one element in common.
Create an equation or inequality that could be used for analysis, prediction, or decision making. Then, draw a graph to depict the variables in the situation.
Problems on time and distance.
Finding the vertex and axis of symmetry
If k = L = m = 0, explain why the system must be consistent. What can be said about the point of intersection of the three lines if the system has exactly one solution?
Find the LCM from the following denominators
A production process fill bags to a mean weight of 1010 grams, with a standard deviation of 20 grams. Each bag is labelled with a weight of 1 kg. What is the chance a bag is produced that is 2% or more underweight?
Express as a polynomial
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