Solve equation with square roots k^2+6=6

Mathematics

1 answer:

il63 [147K]4 years ago

3 0

Answer:

k = 0

Step-by-step explanation:

Note the equal sign. What you do to one side, you do to the other. Do the opposite of PEMDAS. First, subtract 6 from both sides

k² + 6 (-6) = 6 (-6)

k² = 0

Isolate the k. Root both sides

√(k²) = √(0)

k = 0

0 is your answer for k

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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.

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