Answer:
a) find common ratio = 3
b) calculate 10th term = 78732
c) k = 7
Step-by-step explanation:
A geometric sequence has second term 12 and fifth term 324.
a) find common ratio
Common ratio = r
Hence
We solve for this below:
r = cube root(fifth term/second term)
r = cube root (324/12)
r = cube root (27)
r = 3
Therefore, the common ratio = 3
b) calculate 10th term
The formula for a geometric sequence is given as:
an = ar^n-1
Where
a = First term
r = Common ratio = 3
n = Nth term = 10
Step 1
We have to find the first term
Common ratio = Second term/First term
Common ratio = 3
Second term = 12
Hence:
3 = 12/x
Cross Multiply
3x = 12
x = 12/3
x = 4
Hence , First term = 4
Step 2
We find the 10th term
an = ar^n-1
a10 = 4 × 3^10 - 1
a10 = 4 × 3⁹
a10 = 4 × 19683
a10 = 78732
Therefore, the 10th term = 78732
c) the kth term is the first term that is greater than 2000. Find the value of K
For kth term,
ak = ar^k-1 >2000
a = 4, r = 3
Hence
4 × 3^k-1 > 2000
We divide both sides by 4
4 × 3^k-1/4 > 2000/4
3^k-1 > 500
We take the logarithm of both sides
log 3^k-1 > log 500
k-1 log 3 > log 500
Divide both sides by log 3
k-1 log 3/log 3 > log 500/log 3
k - 1 > 5.6567800693
k > 5.6567800693 + 1
k > 6.6567800693
k = 7
Therefore, k = 7
Remember you can do anything to an equation as long as you do it to both sides
expand by foiling or distributing
4x²-19x-5=-43x-41
add 43x to both sides and add 41 to both sides
4x²+24x+36=0
factor
facotr out of 4
4(x²+6x+9)=0
factor inside
what 2 numbers multiply to get 9 and add to get 6?
3 and 3
4(x+3)(x+3)=0
set to 0
x+3=0
x=-3
x=-3 is answer
Given that 4000 items are checked in one month, let the number of detective items be represented as y.
Quality control finds on average that 0.026% of the items in the factory are detective. This implies that
When 4000 items are checked, we have the number of detective items to be evaluated as
Hence, the number of detective items is 1.04.
Bhjhdgf srhtnrj hjlgon54543tjkl
Answer:
in slope-intercept form y = 5/4x in y-intercept form is b = 0. try to use math___way dot com
Step-by-step explanation:
