Answer:
9r
Step-by-step explanation:
1.5r - 3r + 10.5r
10.5r + 1.5r = 12r
12r - 3r = 9r
Final Answer = 9r
Answer:
d = 17
Step-by-step explanation:
The given arithmetic sequence is :
31, 48, 65, 82, ...
We need to find the common difference for this sequence.
First term, a₁ = 31
Second term, a₂ = 48
Common difference = a₂-a₁
= 48-31
= 17
So, the common difference for this arithmetic sequence is equal to 17.

![\bf 2sin(x)cos(x)=sin(x)\sqrt{2}\implies 2sin(x)cos(x)-sin(x)\sqrt{2}=0 \\\\\\ sin(x)~[2cos(x)-\sqrt{2}]=0\\\\ -------------------------------\\\\ sin(x)=0\implies \measuredangle x=0~~,~~\pi \\\\ -------------------------------\\\\ 2cos(x)-\sqrt{2}=0\implies 2cos(x)=\sqrt{2}\implies cos(x)=\cfrac{\sqrt{2}}{2} \\\\\\ \measuredangle x=\frac{\pi }{4}~~,~~\frac{7\pi }{4}](https://tex.z-dn.net/?f=%5Cbf%202sin%28x%29cos%28x%29%3Dsin%28x%29%5Csqrt%7B2%7D%5Cimplies%202sin%28x%29cos%28x%29-sin%28x%29%5Csqrt%7B2%7D%3D0%0A%5C%5C%5C%5C%5C%5C%0Asin%28x%29~%5B2cos%28x%29-%5Csqrt%7B2%7D%5D%3D0%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C%0Asin%28x%29%3D0%5Cimplies%20%5Cmeasuredangle%20x%3D0~~%2C~~%5Cpi%20%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C%0A2cos%28x%29-%5Csqrt%7B2%7D%3D0%5Cimplies%202cos%28x%29%3D%5Csqrt%7B2%7D%5Cimplies%20cos%28x%29%3D%5Ccfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Cmeasuredangle%20x%3D%5Cfrac%7B%5Cpi%20%7D%7B4%7D~~%2C~~%5Cfrac%7B7%5Cpi%20%7D%7B4%7D)
now, we're not including the III and II quadrants, where the cosine has an angle of the same value, but is negative, because the exercise seems to be excluding the negative values of √(2).
Answer:
Criag have left with 4 tickets .
Step-by-step explanation:
Criag have total no. of ride tickets = 232
Each ride of the Feris Wheel cost no. of tickets = 6
6 tickets are required to cover each ride of Feris wheel
So, 232 tickets are required to cover no. of rides of Feris wheel = 
232 tickets are required to cover no. of rides of Feris wheel = 
1 ride of Ferris wheel cost no.of tickets = 6
38 rides of Ferris wheel cost no.of tickets =
So, Tickets left = 232-228=4
Hence Criag have left with 4 tickets .