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3 years ago

Niamh runs 6 km in 30-minutes what is the average speed in km h

Mathematics

2 answers:

mylen [45]3 years ago

6 0

Answer:

12 km/hr

Step-by-step explanation:

SIZIF [17.4K]3 years ago

4 0

Step-by-step explanation:

Speed = Distance / Time

given distance = 6km

time = 30 minutes = 30/60 hr = 1/2hr

speed =

$\frac{6}{\frac{1}{2} } \\ = 6 \div \frac{1}{2} \\ = 6 \times 2 \\ = 12 \frac{km}{h}$

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A polynomial asymptote is a function $p(x)$ such that

$\displaystyle\lim_{x\to\pm\infty}(f(x)-p(x))=0$

$(y+1)^2=4xy\implies y(x)=2x-1\pm2\sqrt{x^2-x}$

Since this equation defines a hyperbola, we expect the asymptotes to be lines of the form $p(x)=ax+b$ .

Ignore the negative root (we don't need it). If $y=2x-1+2\sqrt{x^2-x}$ , then we want to find constants $a,b$ such that

$\displaystyle\lim_{x\to\infty}(2x-1+2\sqrt{x^2-x}-ax-b)=0$

We have

$\sqrt{x^2-x}=\sqrt{x^2}\sqrt{1-\dfrac1x}$
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since $x\to\infty$ forces us to have $x>0$ . And as $x\to\infty$ , the $\dfrac1x$ term is "negligible", so really $\sqrt{x^2-x}\approx x$ . We can then treat the limand like

$2x-1+2x-ax-b=(4-a)x-(b+1)$

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$\displaystyle\lim_{x\to\infty}(2x-1+2\sqrt{x^2-x}-4x-b)=0$

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We write

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The other asymptote is obtained similarly by examining the limit as $x\to-\infty$ .

$\displaystyle\lim_{x\to-\infty}(2x-1+2\sqrt{x^2-x}-ax-b)=0$

$\displaystyle\lim_{x\to-\infty}(2x-2x\sqrt{1-\frac1x}-ax-(b+1))=0$

Reduce the "negligible" term to get

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Now we take $a=0$ , and again we're careful to not pick $b=-1$ .

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