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3 years ago

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How long will it take an object to travel 5 1/5 when it travels 8 2/3 miles per hour

2 answers:

lorasvet [3.4K]3 years ago

6 0

let's first convert the mixed fractions to improper, and then proceed.

$\bf \stackrel{mixed}{5\frac{1}{5}}\implies \cfrac{5\cdot 5+1}{5}\implies \stackrel{improper}{\cfrac{26}{5}}~\hfill \stackrel{mixed}{8\frac{2}{3}}\implies \cfrac{8\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{26}{3}}\\\\[-0.35em]\rule{34em}{0.25pt}\\\\\begin{array}{ccll}miles&hours\\\cline{1-2}\\\frac{26}{3}&1\\[0.8em]\frac{26}{5}&h\end{array}\implies \cfrac{~~\frac{26}{3}~~}{\frac{26}{5}}=\cfrac{1}{h}\implies \cfrac{26}{3}\cdot \cfrac{5}{26}=\cfrac{1}{h}\implies \cfrac{5}{3}=\cfrac{1}{h}$

$\bf h=\cfrac{3\cdot 1}{5}\implies h=\cfrac{3}{5}\impliedby \textit{36 minutes}$

timama [110]3 years ago

3 0

I alkeast need 20 characters long.

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3 years ago

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Answer:

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Step-by-step explanation:

Given information: |a| = 80, |b| = 50, the angle between a and b is 3π/4.

We need to find the dot product a · b.

The formula of dot product is

$a\cdot b=|a||b|\cos \theta$

where, θ is the angle between a and b.

Substitute the given values in the above formula.

$a\cdot b=(80)(50)\cos (\frac{3\pi}{4})$

$a\cdot b=4000\cos (\pi-\frac{\pi}{4})$

$a\cdot b=-4000\cos (\frac{\pi}{4})$ $[\because \cos (\pi-\theta)=-\cos \theta]$

$a\cdot b=-4000\frac{1}{\sqrt{2}}$

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Rationalize the above equation.

$a\cdot b=-\frac{4000}{\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}}$

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