4/16, 5/20, 6/24, 7/28, 8/32...
The length of his territory is 12 square miles long, just divide 96 and 8, in which you get 12
Depending on what the clock says yes and no.
Answer:
<em>A.</em>
<em>The student made an error in step 3 because a is positive in Quadrant IV; therefore, </em>
<em />![cos\theta = \frac{a\sqrt{a^2 + b^2}}{a^2 + b^2}](https://tex.z-dn.net/?f=cos%5Ctheta%20%3D%20%5Cfrac%7Ba%5Csqrt%7Ba%5E2%20%2B%20b%5E2%7D%7D%7Ba%5E2%20%2B%20b%5E2%7D)
Step-by-step explanation:
Given
![P\ (a,b)](https://tex.z-dn.net/?f=P%5C%20%28a%2Cb%29)
![r = \± \sqrt{(a)^2 + (b)^2}](https://tex.z-dn.net/?f=r%20%3D%20%5C%C2%B1%20%5Csqrt%7B%28a%29%5E2%20%2B%20%28b%29%5E2%7D)
![cos\theta = \frac{-a}{\sqrt{a^2 + b^2}} = -\frac{\sqrt{a^2 + b^2}}{a^2 + b^2}](https://tex.z-dn.net/?f=cos%5Ctheta%20%3D%20%5Cfrac%7B-a%7D%7B%5Csqrt%7Ba%5E2%20%2B%20b%5E2%7D%7D%20%3D%20-%5Cfrac%7B%5Csqrt%7Ba%5E2%20%2B%20b%5E2%7D%7D%7Ba%5E2%20%2B%20b%5E2%7D)
Required
Where and which error did the student make
Given that the angle is in the 4th quadrant;
The value of r is positive, a is positive but b is negative;
Hence;
![r = \sqrt{(a)^2 + (b)^2}](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%7B%28a%29%5E2%20%2B%20%28b%29%5E2%7D)
Since a belongs to the x axis and b belongs to the y axis;
is calculated as thus
![cos\theta = \frac{a}{r}](https://tex.z-dn.net/?f=cos%5Ctheta%20%3D%20%5Cfrac%7Ba%7D%7Br%7D)
Substitute ![r = \sqrt{(a)^2 + (b)^2}](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%7B%28a%29%5E2%20%2B%20%28b%29%5E2%7D)
![cos\theta = \frac{a}{\sqrt{(a)^2 + (b)^2}}](https://tex.z-dn.net/?f=cos%5Ctheta%20%3D%20%5Cfrac%7Ba%7D%7B%5Csqrt%7B%28a%29%5E2%20%2B%20%28b%29%5E2%7D%7D)
![cos\theta = \frac{a}{\sqrt{a^2 + b^2}}](https://tex.z-dn.net/?f=cos%5Ctheta%20%3D%20%5Cfrac%7Ba%7D%7B%5Csqrt%7Ba%5E2%20%2B%20b%5E2%7D%7D)
Rationalize the denominator
![cos\theta = \frac{a}{\sqrt{a^2 + b^2}} * \frac{\sqrt{a^2 + b^2}}{\sqrt{a^2 + b^2}}](https://tex.z-dn.net/?f=cos%5Ctheta%20%3D%20%5Cfrac%7Ba%7D%7B%5Csqrt%7Ba%5E2%20%2B%20b%5E2%7D%7D%20%2A%20%5Cfrac%7B%5Csqrt%7Ba%5E2%20%2B%20b%5E2%7D%7D%7B%5Csqrt%7Ba%5E2%20%2B%20b%5E2%7D%7D)
![cos\theta = \frac{a\sqrt{a^2 + b^2}}{a^2 + b^2}](https://tex.z-dn.net/?f=cos%5Ctheta%20%3D%20%5Cfrac%7Ba%5Csqrt%7Ba%5E2%20%2B%20b%5E2%7D%7D%7Ba%5E2%20%2B%20b%5E2%7D)
So, from the list of given options;
<em>The student's mistake is that a is positive in quadrant iv and his error is in step 3</em>