Hope this helps. and that you understand
The answer would be 168 :)
Answer:
I believe it is 34.1 x 10^1
Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the
10
. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
Answer:
Angle J <em>is</em><em> </em><em>congruent</em><em> </em><em>to</em><em> </em>Angle G
Answer:
A.
miles
Step-by-step explanation:
Given two Cartesian coordinates
, the distance between the points is given as:
![d = \sqrt{((x_1-x_2)^2+(y_1-y_2)^2)}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%28%28x_1-x_2%29%5E2%2B%28y_1-y_2%29%5E2%29%7D)
Converting to polar coordinates
![(x_1,y_1) = (r_1 cos \theta_1, r_1 sin \theta_1)\\(x_2,y_2) = (r_2 cos \theta_2, r_2 sin \theta_2)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%28r_1%20cos%20%5Ctheta_1%2C%20r_1%20sin%20%5Ctheta_1%29%5C%5C%28x_2%2Cy_2%29%20%3D%20%28r_2%20cos%20%5Ctheta_2%2C%20r_2%20sin%20%5Ctheta_2%29)
Substitution into the distance formula gives:
![\sqrt{((r_1 cos\theta_1-r_2 cos \theta_2)^2+(r_1 sin \theta_1-r_2 sin \theta_2)^2}\\=\sqrt{(r_1^2+r_2^2-2r_1r_2(cos \theta_1 cos \theta_2+sin\theta_1 sin \theta_2) }\\= \sqrt{r_1^2+r_2^2-2r_1r_2cos (\theta_1 -\theta_2)}](https://tex.z-dn.net/?f=%5Csqrt%7B%28%28r_1%20cos%5Ctheta_1-r_2%20cos%20%5Ctheta_2%29%5E2%2B%28r_1%20sin%20%5Ctheta_1-r_2%20sin%20%5Ctheta_2%29%5E2%7D%5C%5C%3D%5Csqrt%7B%28r_1%5E2%2Br_2%5E2-2r_1r_2%28cos%20%5Ctheta_1%20cos%20%5Ctheta_2%2Bsin%5Ctheta_1%20sin%20%5Ctheta_2%29%20%7D%5C%5C%3D%20%5Csqrt%7Br_1%5E2%2Br_2%5E2-2r_1r_2cos%20%28%5Ctheta_1%20-%5Ctheta_2%29%7D)
In the given problem,
![(r_1,\theta_1)=(8 mi, 63^0) \:and\: (r_2,\theta_2)=(8 mi, 123^0 ).](https://tex.z-dn.net/?f=%28r_1%2C%5Ctheta_1%29%3D%288%20mi%2C%2063%5E0%29%20%5C%3Aand%5C%3A%20%20%28r_2%2C%5Ctheta_2%29%3D%288%20mi%2C%20123%5E0%20%29.)
![Distance=\sqrt{8^2+8^2-2(8)(8)cos (63 -123)}\\=\sqrt{128-128cos (-60)}\\=\sqrt{64}=8 mile](https://tex.z-dn.net/?f=Distance%3D%5Csqrt%7B8%5E2%2B8%5E2-2%288%29%288%29cos%20%2863%20-123%29%7D%5C%5C%3D%5Csqrt%7B128-128cos%20%28-60%29%7D%5C%5C%3D%5Csqrt%7B64%7D%3D8%20mile)
The closest option is A.
miles