An artist mixes 4 mL of red paint with every 9 mL of yellow paint to create the perfect shade of orange paint. Which ratio of milliliters of red paint to milliliters of yellow paint will result in the same shade of orange paint?
Answers
Step-by-step explanation:
Join oa <br /><br /><br /><br />
1. Pa = (pn-an) , pb = (pn+bn ) <br /><br /><br /><br />
pa.Pb = (pn-an)(pn+bn) <br /><br /><br /><br />
on perpendicular ab so an = bn <br /><br /><br /><br />
pa.Pb = (pn-an)(pn+an) = pn^2-an^2 <br /><br /><br /><br />
2. Pn^2-an^2 = <br /><br /><br /><br />
in ∆ona <br /><br /><br /><br />
oa^2 = on^2+an^2 <br /><br /><br /><br />
an^2 = oa^2-on^2 <br /><br /><br /><br />
pn^2-(oa^2-on^2)= pn^2+on^2-oa^2 <br /><br /><br /><br />
in ∆ onp <br /><br /><br /><br />
op^2 = on^2+pn^2 <br /><br /><br /><br />
so. Op^2- oa^2 <br /><br /><br /><br />
oa= ot <br /><br /><br /><br />
pn^2-an^2= op^2-ot^2 <br /><br /><br /><br />
3. From 1 & 2 <br /><br /><br /><br />
pa.Pb = op^2-ot^2 <br /><br /><br /><br />
in ∆ otp <br /><br /><br /><br />
op^2 = pt^2+ot^2 <br /><br /><br /><br />
op^2-ot^2= pt^2 <br /><br /><br /><br />
so pa.Pb = pt^2 <br /><br /><br /><br />
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