Herleid tot de gevraagde vorm.
3p
Herleid de formule \(y = \sqrt{35 x} + \sqrt{6 x}\) tot de vorm \(y = a \sqrt{x} \text{.}\)
Rond \(a\) af op twee decimalen.
○
(herleiden)
\(y = \sqrt{35 x} + \sqrt{6 x}\)
\(\text{} = \sqrt{35} ⋅ \sqrt{x} + \sqrt{6} ⋅ \sqrt{x}\)
1p
○
(wortels berekenen)
\(y = 5{,}916... ⋅ \sqrt{x} + 2{,}449... ⋅ \sqrt{x}\)
1p
○
\(y = 3{,}47 \sqrt{x}\)
1p
Herleid tot de gevraagde vorm.
3p
Maak \(x\) vrij bij de formule \(y = 3{,}8 \sqrt{{x \over 38}} \text{.}\)
Rond af op twee decimalen.
○
(balansmethode)
\(3{,}8 \sqrt{{x \over 38}} = y\)
\(\sqrt{{x \over 38}} = {1 \over 3{,}8} ⋅ y\)
\(\sqrt{{x \over 38}} = 0{,}263... ⋅ y\)
1p
○
(kwadrateren)
\({x \over 38} = (0{,}263... ⋅ y)^{2}\)
\({x \over 38} = (0{,}263...)^{2} ⋅ y^{2}\)
1p
○
(balansmethode)
\(x = 38 ⋅ (0{,}263...)^{2} ⋅ y^{2}\)
\(x = 2{,}63 ⋅ y^{2}\)
1p
Herleid tot de gevraagde vorm.
3p
Herleid de formule \(y = {x^{2} \over 185 ⋅ z}\) tot de vorm \(x = a ⋅ \sqrt{z ⋅ y} \text{.}\)
Rond \(a\) af op twee decimalen.
○
(kruislings vermenigvuldigen)
\({y \over 1} = {x^{2} \over 185 ⋅ z}\)
\(x^{2} = y ⋅ 185 ⋅ z\)
1p
○
(neem de wortel)
\(x = \sqrt{y ⋅ 185 ⋅ z}\)
1p
○
(herleid)
\(x = \sqrt{185} ⋅ \sqrt{z ⋅ y}\)
\(x = 13{,}60 ⋅ \sqrt{z ⋅ y}\)
1p