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So, we know the center is at -3,-1, ok
hmmm what's the radius anyway? well, we know that there's a point at 1,2 that is on the circle's path...hmmmm what's the distance from the center to that point? well, is the radius, let's check then.
![\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -3}}\quad ,&{{ -1}})\quad % (c,d) &({{ 1}}\quad ,&{{ 2}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ r=\sqrt{[1-(-3)]^2+[2-(-1)]^2}\implies r=\sqrt{(1+3)^2+(2+1)^2} \\\\\\ r=\sqrt{16+9}\implies r=\sqrt{25}\implies r=5](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bdistance%20between%202%20points%7D%5C%5C%20%5Cquad%20%5C%5C%0A%5Cbegin%7Barray%7D%7Blllll%7D%0A%26x_1%26y_1%26x_2%26y_2%5C%5C%0A%25%20%20%28a%2Cb%29%0A%26%28%7B%7B%20-3%7D%7D%5Cquad%20%2C%26%7B%7B%20-1%7D%7D%29%5Cquad%20%0A%25%20%20%28c%2Cd%29%0A%26%28%7B%7B%201%7D%7D%5Cquad%20%2C%26%7B%7B%202%7D%7D%29%0A%5Cend%7Barray%7D%5Cqquad%20%0A%25%20%20distance%20value%0Ad%20%3D%20%5Csqrt%7B%28%7B%7B%20x_2%7D%7D-%7B%7B%20x_1%7D%7D%29%5E2%20%2B%20%28%7B%7B%20y_2%7D%7D-%7B%7B%20y_1%7D%7D%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0Ar%3D%5Csqrt%7B%5B1-%28-3%29%5D%5E2%2B%5B2-%28-1%29%5D%5E2%7D%5Cimplies%20r%3D%5Csqrt%7B%281%2B3%29%5E2%2B%282%2B1%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0Ar%3D%5Csqrt%7B16%2B9%7D%5Cimplies%20r%3D%5Csqrt%7B25%7D%5Cimplies%20r%3D5)
so, what's the equation of a circle with center at -3, -1 and a radius of 5?
![\bf \textit{equation of a circle}\\\\ (x-{{ h}})^2+(y-{{ k}})^2={{ r}}^2 \qquad \begin{array}{lllll} center\ (&{{ h}},&{{\quad k}})\qquad radius=&{{ r}}\\ &-3&-1&5 \end{array} \\\\\\\ [x-(-3)]^2+[y-(-1)]^2=5^2\implies (x+3)^2+(y+1)^2=25](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bequation%20of%20a%20circle%7D%5C%5C%5C%5C%20%0A%28x-%7B%7B%20h%7D%7D%29%5E2%2B%28y-%7B%7B%20k%7D%7D%29%5E2%3D%7B%7B%20r%7D%7D%5E2%0A%5Cqquad%20%0A%5Cbegin%7Barray%7D%7Blllll%7D%0Acenter%5C%20%28%26%7B%7B%20h%7D%7D%2C%26%7B%7B%5Cquad%20%20k%7D%7D%29%5Cqquad%20%0Aradius%3D%26%7B%7B%20r%7D%7D%5C%5C%0A%26-3%26-1%265%0A%5Cend%7Barray%7D%20%0A%5C%5C%5C%5C%5C%5C%5C%0A%5Bx-%28-3%29%5D%5E2%2B%5By-%28-1%29%5D%5E2%3D5%5E2%5Cimplies%20%28x%2B3%29%5E2%2B%28y%2B1%29%5E2%3D25)
hmmm what's the radius anyway? well, we know that there's a point at 1,2 that is on the circle's path...hmmmm what's the distance from the center to that point? well, is the radius, let's check then.
so, what's the equation of a circle with center at -3, -1 and a radius of 5?
Option B
We can store a total of 360 songs in 60 megabytes of space.
<u>Solution:</u>
It is given to us that It takes 24 megabytes to store 144 songs on a music player. We have been asked to find out what is the greatest number of songs that 60 megabytes could store.
To solve this question we can use the unitary method.
We will first find out how many songs can be stored in 1 megabyte. This can be done as follows:
Therefore, we can store 6 songs in 1 megabyte.
So, in 60 megabyte we can store the following number of songs:
So, we can store a total of 360 songs in 60 megabytes.