Answer:
60
Step-by-step explanation:
Cot is the same as 1/tan so:

By rearranging the equation, we get:

By taking the inverse tan, we get:

Answer:
x = -4.59, -7.41.
Step-by-step explanation:
x^2 + 12x + 34 = 0
(x + 6)^2 - 36 +34 = 0
(x + 6)^2 = 36 - 34 = 2
x + 6 = +/-√2
x = +/-√2 - 6
x = -4.59, -7.41
2.75 cups were in the punch bowl before felicia refilled it .
<u>Step-by-step explanation:</u>
Here we have , the punch bowl at felicia's party is getting low so she adds 12 cups of punch to the bowl two guests serve themselves 1.25 cups and 2 cups and 2 cups of punch the punch bowl now contains 11.5 cups of punch . We need to find how many cups were in the punch bowl before felicia refilled it let n=number of cups bowl before felicia refilled it. Let's find out:
Initially we have , n number of cups of punch ! Than 12 additional cups were added , given below is the equation framed for the number of cups present:
⇒ 
Now , After this 1.25 and 2 cups were served by guests themselves and remaining cups were 11.5 i.e.
⇒ 
⇒ 
Equating both we get :
⇒ 
⇒ 
⇒ 
Therefore , 2.75 cups were in the punch bowl before felicia refilled it .
Answer: Please see explanation column for answer
Step-by-step explanation:
According to sequence 2, 6, 18, 54, 162
--we can see that it is a geometric sequence since to go from one term to the next requires us to multiply by 3 which is called the common ratio which is gotten by dividing the next by the previous.
ie term 2/ term 1= 6/2 = 3
term 3/ term 2= 18/6= 3
term 4/ term 3= 54/28= 3
term 5 / term 4= 162/54=3
term 6 will therefore be 162 x3 = 486
and term 7 = 486 x 3=1,458 and so on
Recall that nth term of GP is
Tn = ar^n-1
Where a= first term
r= common ratio
n= term
such that to easily find particular term, we plug in the values and calculate
for example the 10th term of the above sequence
Tn = ar^n-1
= 2 X 3 ^(10-1)
2 X 3^9
T10 =39,366