(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:
y = -7/5x
Step-by-step explanation:
First, we need to use the two points to find the slope.
m = y₁ - y₂ / x₁ - x₂
m = -7 - 0 / 5 - 0
m = -7/5
Now we know that the slope is -7/5. Now we'll substitute the information we've gathered into the point-slope form equation to get an equation.
y - y₁ = m(x - x₁)
y - (-7) = -7/5(x - 5)
y + 7 = -7/5x + 7
y = -7/5x
Therefore, the equation of the line is y = -7/5x.
Expanding the parentheses:-
-6x + 30 = -6x + 13
+6x + 6x
30 = 13
which is obviously absurd so the answer is No Solution.
Answer:
- $2.49 each shirt
- $3.99 each slacks
- $7.49 each sports coat
Step-by-step explanation:
If we let s, p, c represent the cost of cleaning the shirts, pants, and coats, respectively, the problem information lets us write three equations:
3s +1p +0c = 11.46
5s +2p +1c = 27.92
5s +0p +1c = 19.94
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A variety of methods and tools are available for solving these equations. We can do it "by hand" using elimination and substitution.
Subtracting the 3rd equation from the 2nd, we get ...
(5s +2p +c) -(5s +c) = (27.92) -(19.94)
2p = 7.98
p = 7.98/2 = 3.99
Substituting this value into the first equation gives ...
3s +1(3.99) = 11.46
3s = 7.47 . . . . . . . . . . subtract 3.99
s = 7.47/3 = 2.49
Substituting this value into the last equation gives ...
5(2.49) +c = 19.94
c = 7.49 . . . . . . . . . . . subtract 12.45
Rachel was charged ...
$2.49 for each shirt
$3.99 for each pair of slacks
$7.49 for each sports coat
