Wortelformules herleiden
Herleid tot de gevraagde vorm.
3p
Herleid de formule \(y = \sqrt{45 x} - \sqrt{26 x}\) tot de vorm \(y = a \sqrt{x} \text{.}\)
Rond \(a\) af op twee decimalen.
○
(herleiden)
\(y = \sqrt{45 x} - \sqrt{26 x}\)
\(\text{} = \sqrt{45} ⋅ \sqrt{x} - \sqrt{26} ⋅ \sqrt{x}\)
1p
○
(wortels berekenen)
\(y = 6{,}708... ⋅ \sqrt{x} - 5{,}099... ⋅ \sqrt{x}\)
1p
○
\(y = 1{,}61 \sqrt{x}\)
1p
Herleid tot de gevraagde vorm.
3p
Maak \(x\) vrij bij de formule \(y = 2{,}7 \sqrt{{x \over 54}} \text{.}\)
Rond af op twee decimalen.
○
(balansmethode)
\(2{,}7 \sqrt{{x \over 54}} = y\)
\(\sqrt{{x \over 54}} = {1 \over 2{,}7} ⋅ y\)
\(\sqrt{{x \over 54}} = 0{,}370... ⋅ y\)
1p
○
(kwadrateren)
\({x \over 54} = (0{,}370... ⋅ y)^{2}\)
\({x \over 54} = (0{,}370...)^{2} ⋅ y^{2}\)
1p
○
(balansmethode)
\(x = 54 ⋅ (0{,}370...)^{2} ⋅ y^{2}\)
\(x = 7{,}41 ⋅ y^{2}\)
1p
Herleid tot de gevraagde vorm.
3p
Herleid de formule \(y = {x^{2} \over 840 ⋅ z}\) tot de vorm \(x = a ⋅ \sqrt{z ⋅ y} \text{.}\)
Rond \(a\) af op twee decimalen.
○
(kruislings vermenigvuldigen)
\({y \over 1} = {x^{2} \over 840 ⋅ z}\)
\(x^{2} = y ⋅ 840 ⋅ z\)
1p
○
(neem de wortel)
\(x = \sqrt{y ⋅ 840 ⋅ z}\)
1p
○
(herleid)
\(x = \sqrt{840} ⋅ \sqrt{z ⋅ y}\)
\(x = 28{,}98 ⋅ \sqrt{z ⋅ y}\)
1p