Area of the parabolic region = Integral of [a^2 - x^2 ]dx | from - a to a =
(a^2)x - (x^3)/3 | from - a to a = (a^2)(a) - (a^3)/3 - (a^2)(-a) + (-a^3)/3 =
= 2a^3 - 2(a^3)/3 = [4/3](a^3)
Area of the triangle = [1/2]base*height = [1/2](2a)(a)^2 = <span>a^3
ratio area of the triangle / area of the parabolic region = a^3 / {[4/3](a^3)} =
Limit of </span><span><span>a^3 / {[4/3](a^3)} </span>as a -> 0 = 1 /(4/3) = 4/3
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Answer:
See explanation below
Step-by-step explanation:
Archimedes was able o obtain the actual volume of the supposedly gold made object by collecting the water displaced by the object as it was sunk on a bowl filled with water to the rim. Then knowing the volume displaced and therefore the volume of the object, he could find the object's density (mass over volume). The mass he could get just by weighting the object. and compare that with the density of any other object made of real gold (like for example a coin) and see if the quotient was the same. The density of both objects should be the same if they are made of the same material.
Answer:
f(x)= (x^2 - 63) + 76
Step-by-step explanation:
Danielle earned $951.25
Step-by-step explanation:
Multiply her commission by her sales and add her base rate
x=7.25%($4500)+625 or x=0.0725(4500)+625
distribute
x=326.25+625
simplify
x=951.25
Answer:
m= -3
Step-by-step explanation:
