Need help with geometry!!!!!!! hurryyyy!!

Mathematics

1 answer:

MakcuM [25]2 years ago

6 0

Answer:

#8 - substitution property of equality

hop this helps! <3

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If the acceleration of an object is given by dv/dt = −2v, Find the position function s(t) if v(0) = 7 and s(0) = 0.

kirill [66]

Answer:

Step-by-step explanation:

Given that acceleration of an object is

$\frac{dv}{dt} =-2v\\\frac{dv}{v} =-2dt\\ln v = -2t+C\\$

is the solution to the differential equation

Since v(0) =7

we get ln 7 = C

Hence $lnv = -2t+ln 7\\v=7e^{-2t}$

since velocity is rate of change of distance s we have

$v=\frac{ds}{dt} =7e^{-2t}\\s= [tex]s(t) =\frac{-7}{2} (e^{-2t})+C)[$

substitute t=0 and s=0

$C=7/2$

So solution for distance is

$s(t) =\frac{-7}{2} (e^{-2t}-1)$

4 0

3 years ago

Ella and jade both ran a marathone ella finished 4 hours 6 mins and 13 seconds jade finished in 4 hours and 3 mins and 18 second

spin [16.1K]

Answer:

Jade is faster than Ella by 2 minutes and 55 seconds.

Step-by-step explanation:

We are told that Ella and Jade both ran a marathon. Ella finished marathon in 4 hours 6 mins and 13 seconds. Jade finished marathon in 4 hours and 3 mins and 18 seconds.

We can write 4 hour 6 minutes 13 seconds as 4 hour 5 minutes 73 seconds. 1 minute has been borrowed to the seconds side, and seconds become 13+60 = 73 seconds.

We can see that Ella took more time than Jade. Let us find how much more time Ella took than Jade by subtracting time taken by Jade from time taken by Ella.

$4\text{ hr }5\text{ min }73\text{ sec }-4\text{ hr }3\text{ min }18{ sec }= 2\text{ min }55\text{ sec }$