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2 years ago

The time it takes to travel a fixed distance varies inversely with the speed traveled. It takes

1 answer:

6 0

first off, let's notice that Purple's time is in minutes, whilst the rate is in miles per hour, the units of both must correspond, so, we can either change the time from minutes to hours or the rate from hours to minutes, hmmm let's change the time to hours.

so 40 minutes, we know there are 60 minutes in 1 hour, so 40 minutes will be 40/60 of an hr, or namely 2/3.

$\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill$

$\stackrel{\begin{array}{llll} \textit{\tiny "t"ime varies}\\ \textit{\tiny inversely with "s"peed} \end{array}}{t = \cfrac{k}{s}}\qquad \textit{we know that} \begin{cases} t=\stackrel{minutes}{40}\to \stackrel{hrs}{\frac{2}{3}}\\ s=\stackrel{m/h}{9} \end{cases} \implies \cfrac{2}{3}~~ = ~~\cfrac{k}{9} \\\\\\ 18=3k\implies \cfrac{18}{3}=k\implies 6=k~\hfill \boxed{t=\cfrac{6}{s}} \\\\\\ \textit{when s = }\stackrel{m/h}{12}\textit{ what is "t"?}\qquad t=\cfrac{6}{12}\implies t=\cfrac{1}{2}$

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40, 10, 5/2 5/8... (fractions) is it arithmetic or geometric and what are the next two terms PLZ HELP DUE IN 10 MINS

patriot [66]

Answer:

Please check the explanation.

Step-by-step explanation:

Given the sequence

$40,\:10,\:\frac{5}{2},\:\frac{5}{8}$

A geometric sequence has a constant ratio 'r' and is defined by

$\:a_n=a_0\cdot r^{n-1}$

Computing the ratios of all the adjacent terms

$\frac{10}{40}=\frac{1}{4},\:\quad \frac{\frac{5}{2}}{10}=\frac{1}{4},\:\quad \frac{\frac{5}{8}}{\frac{5}{2}}=\frac{1}{4}$

The ratio of all the adjacent terms is the same and equal to

$r=\frac{1}{4}$

Thus, the given sequence is a geometric sequence.

As the first element of the sequence is

$a_1=40$

Therefore, the nth term is calculated as

$\:a_n=a_0\cdot r^{n-1}$

$a_n=40\left(\frac{1}{4}\right)^{n-1}$

Put n = 5 to find the next term

$a_5=40\left(\frac{1}{4}\right)^{5-1}$

$a_5=40\cdot \frac{1}{4^4}$

$a_5=\frac{40}{4^4}$

$=\frac{2^3\cdot \:5}{2^8}$

$a_5=\frac{5}{2^5}$

$a_5=\frac{5}{32}$

now, Put n = 6 to find the 6th term

$a_6=40\left(\frac{1}{4}\right)^{6-1}$

$a_6=40\cdot \frac{1}{4^5}$

$a_6=\frac{40}{4^5}$

$=\frac{2^3\cdot \:5}{2^{10}}$

$a_6=\frac{5}{2^7}$

$a_6=\frac{5}{128}$

Thus, the next two terms of the sequence 40, 10, 5/2, 5/8... is:

$a_5=\frac{5}{32}$

$a_6=\frac{5}{128}$

7 0

2 years ago

I Need help. Thanks.

PIT_PIT [208]

Answer:

Step-by-step explanation:

$-2(5y-5)-3y\leq -7y+22$

Expand parentheses:

$-10y+10-3y\leq -7y+22$

Move all y's to one side and numbers to the other:

$-6y\leq 12$

Divide both sides by -6. Since you are dividing both sides by a negative number, you need to flip the comparator:

$y\geq -2$

Hope this helps!

5 0

3 years ago

Read 2 more answers

A biker travels 5 feet in 0.5 seconds. At this exact speed, how far will the biker travel in a minute?

Pavel [41]

A minute has 60 seconds, therefore we will deal with seconds now And since we have it that the biker travels 5 feet every 0.5 seconds, lets multiply that by 2 to get the traveled distance per second to make it easier 5*2=10 Finally, multiply 10 feet by 60 seconds(1 minute) = 600 feet

3 0

3 years ago

Mark did 2/5 of a job and Alan did 1/3 of the remainder. The fraction of the job left undone

Evgesh-ka [11]

2/5=4/10=12/30 1/3=10/30 12/30+10/30=22/30 22/30=11/15

4 0

2 years ago

What is the volume of this sphere <br> Use π=3.14 and round your answer to the nearest hundredth

Alina [70]

The answer is 523.6 and all you have to do is round it to the nearest hundredth

7 0

2 years ago