Wortelformules herleiden
Herleid tot de gevraagde vorm.
3p
Herleid de formule \(y = \sqrt{39 x} + \sqrt{50 x}\) tot de vorm \(y = a \sqrt{x} \text{.}\)
Rond \(a\) af op twee decimalen.
○
(herleiden)
\(y = \sqrt{39 x} + \sqrt{50 x}\)
\(\text{} = \sqrt{39} ⋅ \sqrt{x} + \sqrt{50} ⋅ \sqrt{x}\)
1p
○
(wortels berekenen)
\(y = 6{,}244... ⋅ \sqrt{x} + 7{,}071... ⋅ \sqrt{x}\)
1p
○
\(y = -0{,}83 \sqrt{x}\)
1p
Herleid tot de gevraagde vorm.
3p
Maak \(x\) vrij bij de formule \(y = 6{,}6 \sqrt{{x \over 46}} \text{.}\)
Rond af op twee decimalen.
○
(balansmethode)
\(6{,}6 \sqrt{{x \over 46}} = y\)
\(\sqrt{{x \over 46}} = {1 \over 6{,}6} ⋅ y\)
\(\sqrt{{x \over 46}} = 0{,}151... ⋅ y\)
1p
○
(kwadrateren)
\({x \over 46} = (0{,}151... ⋅ y)^{2}\)
\({x \over 46} = (0{,}151...)^{2} ⋅ y^{2}\)
1p
○
(balansmethode)
\(x = 46 ⋅ (0{,}151...)^{2} ⋅ y^{2}\)
\(x = 1{,}06 ⋅ y^{2}\)
1p
Herleid tot de gevraagde vorm.
3p
Herleid de formule \(y = {x^{2} \over 362 ⋅ z}\) tot de vorm \(x = a ⋅ \sqrt{z ⋅ y} \text{.}\)
Rond \(a\) af op twee decimalen.
○
(kruislings vermenigvuldigen)
\({y \over 1} = {x^{2} \over 362 ⋅ z}\)
\(x^{2} = y ⋅ 362 ⋅ z\)
1p
○
(neem de wortel)
\(x = \sqrt{y ⋅ 362 ⋅ z}\)
1p
○
(herleid)
\(x = \sqrt{362} ⋅ \sqrt{z ⋅ y}\)
\(x = 19{,}03 ⋅ \sqrt{z ⋅ y}\)
1p