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Step2247 [10]
3 years ago
9

PLZ HELP ASAP FEATURES OF A CIRCLE FROM ITS EXPANDED EQUATION LAST ONE

Mathematics
1 answer:
pantera1 [17]3 years ago
5 0
We have the following equation:
 x2 + y2 + 6y - 72 = 0
 Rewriting we have:
 x2 + y2 + 6y = 72
 Complete squares we have:
 x2 + y2 + 6y + (6/2) ^ 2 = 72 + (6/2) ^ 2
 x2 + y2 + 6y + (3) ^ 2 = 72 + (3) ^ 2
 x2 + y2 + 6y + 9 = 72 + 9
 x2 + (y + 3) 2 = 81
 So, the center is:
 (0, -3)
 The radio is:
 r = 9
 Answer:
 
(0, -3)
 
r = 9
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In a certain region, about 6% of a city's population moves to the surrounding suburbs each year, and about 4% of the suburban po
Sedbober [7]

Answer:

City @ 2017 = 8,920,800

Suburbs @ 2017 = 1, 897, 200

Step-by-step explanation:

Solution:

- Let p_c be the population in the city ( in a given year ) and p_s is the population in the suburbs ( in a given year ) . The first sentence tell us that populations p_c' and p_s' for next year would be:

                                  0.94*p_c + 0.04*p_s = p_c'

                                  0.06*p_c + 0.96*p_s = p_s'

- Assuming 6% moved while remaining 94% remained settled at the time of migrations.

- The matrix representation is as follows:

                         \left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] \left[\begin{array}{c}p_c\\p_s\end{array}\right] =  \left[\begin{array}{c}p_c'\\p_s'\end{array}\right]          

- In the sequence for where x_k denotes population of kth year and x_k+1 denotes population of x_k+1 year. We have:

                         \left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] x_k = x_k_+_1

- Let x_o be the populations defined given as 10,000,000 and 800,000 respectively for city and suburbs. We will have a population x_1 as a vector for year 2016 as follows:

                          \left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] x_o = x_1

- To get the population in year 2017 we will multiply the migration matrix to the population vector x_1 in 2016 to obtain x_2.

                          x_2 = \left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right]\left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] x_o

- Where,

                         x_o =  \left[\begin{array}{c}10,000,000\\800,000\end{array}\right]

- The population in 2017 x_2 would be:

                         x_2 = \left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right]\left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] \left[\begin{array}{c}10,000,000\\800,000\end{array}\right] \\\\\\x_2 = \left[\begin{array}{c}8,920,800\\1,879,200\end{array}\right]

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