First off, let's notice that the angle is in the IV Quadrant, where sine is negative and the cosine is positive, likewise the opposite and adjacent angles respectively.
Also let's bear in mind that the hypotenuse is never negative, since it's simply just a radius unit.
![\bf cot(\theta )=\cfrac{\stackrel{adjacent}{6}}{\stackrel{opposite}{-7}}\qquad \impliedby \textit{let's find the \underline{hypotenuse}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{6^2+(-7)^2}\implies c=\sqrt{36+49}\implies c=\sqrt{85} \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbf%20cot%28%5Ctheta%20%29%3D%5Ccfrac%7B%5Cstackrel%7Badjacent%7D%7B6%7D%7D%7B%5Cstackrel%7Bopposite%7D%7B-7%7D%7D%5Cqquad%20%5Cimpliedby%20%5Ctextit%7Blet%27s%20find%20the%20%5Cunderline%7Bhypotenuse%7D%7D%20%5C%5C%5C%5C%5C%5C%20%5Ctextit%7Busing%20the%20pythagorean%20theorem%7D%20%5C%5C%5C%5C%20c%5E2%3Da%5E2%2Bb%5E2%5Cimplies%20c%3D%5Csqrt%7Ba%5E2%2Bb%5E2%7D%20%5Cqquad%20%5Cbegin%7Bcases%7D%20c%3Dhypotenuse%5C%5C%20a%3Dadjacent%5C%5C%20b%3Dopposite%5C%5C%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5C%5C%20c%3D%5Csqrt%7B6%5E2%2B%28-7%29%5E2%7D%5Cimplies%20c%3D%5Csqrt%7B36%2B49%7D%5Cimplies%20c%3D%5Csqrt%7B85%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
Answer:
Step-by-step explanation:
12d - 7 = 41
12d = 48
d = 4
<span>You are given volume of 6 US
quart. You are required to convert this into liters and be rounded off to the
nearest hundredth. Keep in mind that for
volume, every one liter is equal to 1.05669 US quart. So you need to divide the
6 US quart. This is equal to 6.34014 liters. To round of the nearest hundredth,
the ocation of the hundredth is the four in 6.3<u>4</u>014. since after four is
zero, the round off rule states that from 0-4, the preceding number remains
unchanged. So the final answer is 6.34 liters.</span>
Answer:
<h2>She gave her brother 6 tickets</h2>
Step-by-step explanation:
This problem is on fractional numbers.
given that she has 60 tickets
1.She used 3/4 of her tickets to play game
=(3/4)*60
=180/4
=45
She is left with (60-45)= 15 tickets
2. She used 1/5 of her remaining tickets for rides
=(1/5)*15
=15/5
=3
She is left with (15-3)= 12 tickets
3. She gave half of her tickets to her brother.
= (1/2)*12
=12/2
= 6
She gave her brother 6 tickets
