Write the equation of the line passing through point (4, -1) and perpendicular to the line whose equation is 2 x - y - 7 = 0.

1 answer:

6 0

2 x - y - 7 = 0
y =2x - 7 slope = 2
perpendicular slope = -1/2
line passing through point (4, -1)
y = mx + b
-1=-1/2(4) + b
-1 = - 2 + b
b = 1

equation
y =-1/2(x) + 1

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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.

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