Answer:
65.45
Step-by-step explanation:
Answer:
The 96th term of the arithmetic sequence is -1234.
Step-by-step explanation:
first term (a)=1
second term (t2)=-12
common difference (d)= t2-a
d=-12-1
d=-13
96th term (t96)=?
We know that,
t96=a+(n-1)d
t96=1+(96-1)(-13)
t96=1+95(-13)
t96=1-1235
t96=-1234
Answer:
Area = πr², where "r" is some distance "y" and/or the function "(1/6)x"; depending on the situation
Step-by-step explanation:
If I'm picturing this correctly, you'll have conical shape after revolving the function about the x-axis. If you took some generic slice and wanted to find the area of the resulting cross-section, then you would have a circle whose radius is some arbitrary value of the line that matches the slice.
For example:
y = (1/6)x right?
If you took a slice at x = 2, then the radius of the resulting cross-sectional circle would be equal to y = (1/6)•2 =1/3.
From here you just plug it into the area of a circle, πr², to get an area of π/3.
Except with an integral you need to take all the points on the interval, so the radius comes out to be the function itself.
Assuming your integral is in terms of dx, r=y. But in order to integrate in terms of dx you must replace "y" with its function (1/6)x. So ultimately r=(1/6)x and Area = π(1/6)x.
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
