90-7 =83 degrees
height = 3 miles
divide 3 by the cos of 83 degrees
3/cos(83) = 24.6165
rounded to nearest mile = 25 miles
The second one. 4/6 and 2/3
The question as presented is incomplete, here is the complete question with the multiple choice:
The sequence a1 = 6, an = 3an − 1 can also be
written as:
1) an = 6 ⋅ 3^n
2) an = 6 ⋅ 3^(n + 1)
3) an = 2 ⋅ 3^n
4) an = 2 ⋅ 3^(n + 1)
The correct choice is option 3) an = 2⋅3^n.
If we look at the initial sequence an = 3⋅an-1, and
a1 = 3⋅a0 = 6
a0 = 6/3
a0 = 2
We can now look at the sequence.
a0 = 2
a1 = 6
a2 = 18
a3 = 54
etc...
A common factor in each of those numbers is 2, so we can rewrite the sequence by factoring out 2.
a0 = 2⋅1
a1 = 2⋅3
a2 = 2⋅9
a3 = 2⋅27
The numbers being multiplied by 2 are all factors of 3. So we can rewrite the sequence again as:
a0 = 2⋅3^0
a1 = 2⋅3^1
a2 = 2⋅3^2
a3 = 2⋅3^3
This sequence can now be rewritten as an = 2⋅3^n.
Answer:
D
Step-by-step explanation:
x²-4x-12≤0
x²-6x+2x-12≤0
x(x-6)+2(x-6)≤0
(x-6)(x+2)≤0
x=6,-2
∴ value of x lies between -2 & 6
Answer : The substances half life in days is, 5.6 days.
Step-by-step explanation :
Half life : It is defined as the amount of time taken by a radioactive material to decay to half of its original value.
All radioactive decays follow first order kinetics.
The relation between the half-life and rate constant is:
where,
k = rate constant = 0.1235 per days
= half-life
Now put all the given values in the above formula, we get:
Thus, the substances half life in days is, 5.6 days.
