Herleid tot de gevraagde vorm.
3p
Herleid de formule \(y = \sqrt{46 x} - \sqrt{33 x}\) tot de vorm \(y = a \sqrt{x} \text{.}\)
Rond \(a\) af op twee decimalen.
○
(herleiden)
\(y = \sqrt{46 x} - \sqrt{33 x}\)
\(\text{} = \sqrt{46} ⋅ \sqrt{x} - \sqrt{33} ⋅ \sqrt{x}\)
1p
○
(wortels berekenen)
\(y = 6{,}782... ⋅ \sqrt{x} - 5{,}744... ⋅ \sqrt{x}\)
1p
○
\(y = 1{,}04 \sqrt{x}\)
1p
Herleid tot de gevraagde vorm.
3p
Maak \(x\) vrij bij de formule \(y = 8{,}8 \sqrt{{x \over 79}} \text{.}\)
Rond af op twee decimalen.
○
(balansmethode)
\(8{,}8 \sqrt{{x \over 79}} = y\)
\(\sqrt{{x \over 79}} = {1 \over 8{,}8} ⋅ y\)
\(\sqrt{{x \over 79}} = 0{,}113... ⋅ y\)
1p
○
(kwadrateren)
\({x \over 79} = (0{,}113... ⋅ y)^{2}\)
\({x \over 79} = (0{,}113...)^{2} ⋅ y^{2}\)
1p
○
(balansmethode)
\(x = 79 ⋅ (0{,}113...)^{2} ⋅ y^{2}\)
\(x = 1{,}02 ⋅ y^{2}\)
1p
Herleid tot de gevraagde vorm.
3p
Herleid de formule \(y = {x^{2} \over 841 ⋅ z}\) tot de vorm \(x = a ⋅ \sqrt{z ⋅ y} \text{.}\)
Rond \(a\) af op twee decimalen.
○
(kruislings vermenigvuldigen)
\({y \over 1} = {x^{2} \over 841 ⋅ z}\)
\(x^{2} = y ⋅ 841 ⋅ z\)
1p
○
(neem de wortel)
\(x = \sqrt{y ⋅ 841 ⋅ z}\)
1p
○
(herleid)
\(x = \sqrt{841} ⋅ \sqrt{z ⋅ y}\)
\(x = 29{,}00 ⋅ \sqrt{z ⋅ y}\)
1p