Let us check series : -10 /-2 = 5 -50/-10 = 5
so it is a geometric series with a= -2 and r= 5
sum formula for n terms of geometric series = a ( r^n -1 ) /( r-1)
here we find S5 that is n= 5 = -2 ( 5^ 5 - 1) /( 5-1)
= -2 ( 3125 -1) / 4 = -1562
second series is : 1.5/1 = 1.5 2.25/1.5 = 1.5
this is also geometric series but n = 12 a= 1 and r= 1.5
we use same formula
S12 = 1 ( (1.5) ^12 -1) /( 1.5-1) =
128.74 / 0.5 = 257.49
Last is 2/1= 2 4/2 = 2 8/4 = 2 so r = 2 a = 1 and n = 12
we use same formula 1 ( 2^12 - 1) / (2-1)
= 4095
Answers : -1562 , 257.49 , 4095
Answer:
A. Cos2x
Step-by-step explanation:
f(x) = sin(x)cos(x) = (1/2) sin(2x) using double angle formula.
f'(x) = ( (1/2)sin(2x) )' = 2(1/2)cos(2x) = cos(2x)
Answer:
Step-by-step explanation:
6 = 2(y+2)
6 = 2y+4
2 = 2y
y = 1
An embryo is an unborn or unhatched offspring
Let d = # of dimes
Let q = # of quarters
equation #1: number of coins
d + q = 1234
equation #2: value of coins
0.10d + 0.25q = 290.05
Solve #1 for d:
d=1234-q
Sub #1 into #2 and solve for q:
0.10d + 0.25q = 290.05
0.10(1234-q) + 0.25q = 290.05
123.4 - 0.10q + 0.25q = 290.05
0.15q = 166.65
q = 1111
Now go back to d=1234-q and sub in 1111 for q to find d:
d = 1234 - 1111
d = 123
1111 quarters and 123 dimes.
