(a) converges; consider the function <em>f(x)</em> = <em>a</em> ˣ, which converges to 0 as <em>x</em> gets large for |<em>a</em> | < 1. Then the limit is 2.
(b) converges; we have
4ⁿ / (1 + 9ⁿ) = (4ⁿ/9ⁿ) / (1/9ⁿ + 9ⁿ/9ⁿ) = (4/9)ⁿ × 1/(1/9ⁿ + 1)
As <em>n</em> gets large, the exponential terms vanish; both (4/9)ⁿ → 0 and 1/9ⁿ → 0, so the limit is 1.
(c) converges; we know ln(<em>n</em> ) → ∞ and arctan(<em>n</em> ) → <em>π</em>/2 as <em>n</em> → ∞. So the limit is <em>π</em>/2.
Answer:
In total, they will be able to cut 7 posters.
Step-by-step explanation:
Mr. Parker's class has 7 feet of white paper and 8 feet of yellow paper to make posters.
If they cut the paper into 2-foot posters, then from 8 feet of yellow paper they will make
posters.
Now, from the 7 feet white paper if they cut 2-foot posters then they will make 3 posters maximum as
.
Therefore, in total, they will be able to cut (4 + 3) = 7 posters. (Answer)
Answer:
True.
Step-by-step explanation:
The explicit form for an arithmetic sequence is:

where
is the first term and
is the common difference.
The common difference here is 2 because the y's are going up by 2 while the x's are going up by 1.
Yes, the common difference is the slope.
So we have d=2.
The first term is 9.5 because that is what happens when x=1.
x is n.
y is
.
So the answer is true.
----
You can also verify by plugging in numbers for n and see if you get the outputs mentioned in the pairs given:
Let n=1:




Let n=2:




Let n=3:




Let n=4:




Let n=5:




Let n=6:




We have confirmed that we get all 6 of the mentioned points using the equation they gave.
Answer:
180°
Step-by-step explanation:
Supplementary angles are angles whose sum is 180°. If L and M are supplementary, the sum of their measures is 180°.
Answer:
y= 7x-73
Step-by-step explanation:
the equation form is y=mx+c where m is the slope and c a constant
m= (25-(-10))/14-9 = 35/5 = 7
so y= 7x+c
replace x and y by 14 and 25 respectively
25 = 7*14+c
c= 25-7*14
c = -73
so y= 7x-73