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nalin [4]
4 years ago
8

An equation of the horizontal line that passes through the point (-2,5)

Mathematics
1 answer:
Greeley [361]4 years ago
8 0
Y=5 it's a horizontal lines so b in y=mx+b would have to be 5 and since it's horizonal, it doesn't have a slope so it's just y=5
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What is the equation of the line that represents the horizontal asymptote of the function f(x)=25,000(1+0.025)^(x)?
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Answer:

The answer is below

Step-by-step explanation:

The horizontal asymptote of a function f(x) is gotten by finding the limit as x ⇒ ∞ or x ⇒ -∞. If the limit gives you a finite value, then your asymptote is at that point.

\lim_{x \to \infty} f(x)=A\\\\or\\\\ \lim_{x \to -\infty} f(x)=A\\\\where\ A\ is\ a\ finite\ value.\\\\Given\ that \ f(x) =25000(1+0.025)^x\\\\ \lim_{x \to \infty} f(x)= \lim_{x \to \infty} [25000(1+0.025)^x]= \lim_{x \to \infty} [25000(1.025)^x]\\=25000 \lim_{x \to \infty} [(1.025)^x]=25000(\infty)=\infty\\\\ \lim_{x \to -\infty} f(x)= \lim_{x \to -\infty} [25000(1+0.025)^x]= \lim_{x \to -\infty} [25000(1.025)^x]\\=25000 \lim_{x \to -\infty} [(1.025)^x]=25000(0)=0\\\\

Since\  \lim_{x \to -\infty} f(x)=0\ is\ a\ finite\ value,hence:\\\\Hence\ the\ horizontal\ asymtotes\ is\ at\ y=0

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Step-by-step explanation:

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PLEASE HELP Word problem involving average rate of change
oee [108]

Answer:

(a): 26.1

(b): 27.9

Please see below for the steps.

Step-by-step explanation:

(a):

Use points (0,0) and (3, 78.3)

Use slope formula. The slope formula is also used to find average rate of change (just so you know).

y2-y1/x2-x1

78.3-0/3-0=78.3/3=26.1

Answer for (a) is 26.1

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Use points (4, 147.6) and (9, 287.1)

Use slope formula.

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The answer for (b) is 27.9

Hope this helps!

Please mark as brainliest if correct!

Have a great day!

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