if D(t)=√400+t^2 and R(x)=20x, find (DºR)(x)?
Can someone explain this to me? by the way the º is supposed to be a small "o" on the bottom but I don't know how to put it.
Update:by the way the answer is 20x√x²-1 but I dont understand how I get to that conclusion
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D(t) = √(400 + t²) ... assuming that's what you mean
R(x) = 20x
(D o R)(x) = D[R(x)] = √[400 + (20x)²] ... [just replace t in D(t) with 20x]
= √[400 + 400x²]
= √[400(1 + x²)]
= √400 * √(1 + x²)
= 20 √(1 + x²) ... I think the given answer is wrong ... there's no way there can be an x outside the radical sign and everything is positive ... so who knows where they get the x² - 1 from ... so I'm pretty sure their answer is wrong