If you show me a picture of the problem I could help you, but I can’t see the circle sooo I can’t help u unless I see it
Answer: sin u = -5/13 and cos v = -15/17
Step-by-step explanation:
The nice thing about trig, a little information goes a long way. That’s because there is a lot of geometry and structure in the subject. If I have sin u = opp/hyp, then I know opp is the opposite side from u, and the hypotenuse is hyp, and the adjacent side must fit the Pythagorean equation opp^2 + adj^2 = hyp^2.
So for u: (-5)^2 + adj^2 = 13^2, so with what you gave us (Quad 3),
==> adj of u = -12 therefore cos u = -12/13
Same argument for v: adj = -15,
opp^2 + (-15)^2 = 17^2 ==> opp = -8 therefore sin v = -8/17
The cosine rule for cos (u + v) = (cos u)(cos v) - (sin u)(sin v) and now we substitute: cos (u + v) = (-12/13)(-15/17) - (-5/13)(-8/17)
I am too lazy to do the remaining arithmetic, but I think we have created a way to approach all of the similar problems.
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
7*x-4-(21)=0
Solve : 7x-25 = 0
Add 25 to both sides of the equation :
7x = 25
Divide both sides of the equation by 7:
x = 25/7 = 3.571
The number of different three-digit numbers that can be set for the combination lock is 125
<h3>How to determine the number of different locks?</h3>
The digits are given as
Digit = 1, 2, 3, 4, 5
Each digit can be repeated on the number lock.
So, the individual digit of the lock can be any of the 5 digits.
So, we have:
Locks = 5 * 5 * 5
Evaluate
Locks = 125
Hence, the number of different three-digit numbers that can be set for the combination lock is 125
Read more about combination at:
brainly.com/question/11732255
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![72^{\circ}](https://tex.z-dn.net/?f=72%5E%7B%5Ccirc%7D)
1) In this question, we are going to make use of the formula for the area of that sector, to find the central angle.
2) So, let's write it out an expression involving the area of a circle, the unshaded area, and the shaded one and then plug into that the given data:
![\begin{gathered} A=\frac{\alpha}{360^{\circ}}\times\pi r^2 \\ A_{Unshaded}+A_{shaded}=A_{Circle} \\ 500\pi+\frac{\alpha}{360}\times\pi r^2=\pi r^2 \\ \\ 500\pi+\frac{α}{360}\pi25^2=25^2\pi \\ \\ 500\pi+\frac{125\piα}{72}=625\pi \\ \\ 500\pi +\frac{125\pi α}{72}-500\pi =625\pi -500\pi \\ \\ \frac{125\pi α}{72}=125\pi \\ \\ \frac{72\times \:125\pi α}{72}=72\times \:125\pi \\ \\ \frac{125\pi α}{125\pi }=\frac{9000\pi }{125\pi } \\ \\ α=72^{\circ} \\ \\ \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20A%3D%5Cfrac%7B%5Calpha%7D%7B360%5E%7B%5Ccirc%7D%7D%5Ctimes%5Cpi%20r%5E2%20%5C%5C%20A_%7BUnshaded%7D%2BA_%7Bshaded%7D%3DA_%7BCircle%7D%20%5C%5C%20500%5Cpi%2B%5Cfrac%7B%5Calpha%7D%7B360%7D%5Ctimes%5Cpi%20r%5E2%3D%5Cpi%20r%5E2%20%5C%5C%20%20%5C%5C%20500%5Cpi%2B%5Cfrac%7B%CE%B1%7D%7B360%7D%5Cpi25%5E2%3D25%5E2%5Cpi%20%5C%5C%20%20%5C%5C%20500%5Cpi%2B%5Cfrac%7B125%5Cpi%CE%B1%7D%7B72%7D%3D625%5Cpi%20%5C%5C%20%20%5C%5C%20500%5Cpi%20%2B%5Cfrac%7B125%5Cpi%20%CE%B1%7D%7B72%7D-500%5Cpi%20%3D625%5Cpi%20-500%5Cpi%20%20%5C%5C%20%20%5C%5C%20%5Cfrac%7B125%5Cpi%20%CE%B1%7D%7B72%7D%3D125%5Cpi%20%20%5C%5C%20%20%5C%5C%20%5Cfrac%7B72%5Ctimes%20%5C%3A125%5Cpi%20%CE%B1%7D%7B72%7D%3D72%5Ctimes%20%5C%3A125%5Cpi%20%20%5C%5C%20%20%5C%5C%20%5Cfrac%7B125%5Cpi%20%CE%B1%7D%7B125%5Cpi%20%7D%3D%5Cfrac%7B9000%5Cpi%20%7D%7B125%5Cpi%20%7D%20%5C%5C%20%20%5C%5C%20%CE%B1%3D72%5E%7B%5Ccirc%7D%20%5C%5C%20%20%5C%5C%20%20%5Cend%7Bgathered%7D)
Thus, the centra angle of that shaded area is 72º