A cyclist rides down a long straight road at a velocity (in m/min) given by v(t)equals400minus20t, for 0less than or equalstless than or equals10. a. How far does the cyclist travel in the first 6 min? b. How far does the cyclist travel in the first 10 min? c. How far has the cyclist traveled when his velocity is 290 m/min?

a. 2040 m

b. 3000 m

c. 1697.5 m

Explanation:

Given that:

v(t) = 400 - 20t

0 ≤ t ≤ 10

We can get the formula for distance traveled by integrating the velocity, v(t), with respect to time:

=> s(t) = 400t - 10t²

a. First 6 mins:

t = 6 mins

s(t) = 400(6) - 10(6)²

s(t) = 2400 - 360

s(t) = 2040m

b. First 10 mins:

t = 10 mins

s(t) = 400(10) - 10(10)²

s(t) = 4000 - 1000

s(t) = 3000 m

c. When v(t) =290 m/mins

We insert this into the v(t) equation so we can find time t.

v(t) = 400 - 20t

290 = 400 - 20(t)

20t = 400 - 290

20t = 110

t = 110/20 = 5.5 mins

Now we insert that into the s(t) equation:

s(t) = 400(5.5) - 10(5.5)²

s(t) = 2200 - 302.5

s(t) = 1697.5 m

does anyone know or what?

bacteria that live on the ocean floor are sustained by phytoplankton. phytoplankton, microscopic marine photosynthetic organisms, have a vastly significant role to play not only in the marine food web of which they’re part of, but also on a more global scale. despite their infinitely small size in comparison to other marine organisms, these tiny creatures occupy an immensely important ecological niche: they are the foundation of the marine food web, and as primary producers, play key roles in supporting all other organisms in the marine environment, as well as in the regulation of the earth’s climate through the sequestration of carbon, oxygen production, and other related processes. phytoplankton account for roughly half of all global primary productivity; therefore, their significance extends far beyond the marine environment alone. there is an intriguing sense of irony in the realization that these tiny living beings that often live out their existence unnoticed and undetected by the rest of the world, have such a far-reaching impact on the lives of virtually all other living organisms on the planet, particularly on those in the marine environment. the world that we have become accustomed to has been and is continuously shaped by the workings of these miniscule yet vital “plants of the sea”.

hope this !