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If r varies jointly as p and q and inversely as t, then how do you find an equation for r if r=6 when p=8, q=−3, and t=3?

Answer 1

The equation for r can be found by using the formula for joint variation and inverse variation. The equation is r = k(pq/t), where k is the constant of variation. To find the value of k, substitute the given values into the equation and solve for k. In this case, k = r(pt/q) = 6(8*−3/3) = -48. Therefore, the equation for r is r = -48(pq/t).

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Answer 2

Eva Adamson

#r=-(3pq)/(4t)#

#"the initial statement is "rprop(pq)/t#

#"to convert to an equation multiply by k the constant"# #"of variation"#

#rArrr=(kpq)/t#

#"to find k use the given condition"#

#r=6" when "p=8,q=-3" and "t=3#

#r=(kpq)/t#

#rArrkpq=rtlarrcolor(blue)" cross-multiplying"#

#rArrk=(rt)/(pq)=(6xx3)/(8xx-3)=18/(-24)=-3/4#

#rArr" equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(r=-(3pq)/(4t)color(white)(2/2)|)))#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.