3 years ago

2 ratios equivalent to 36:15

Mathematics

1 answer:

Snowcat [4.5K]3 years ago

3 0

Answer:

24:10, 60:25

Step-by-step explanation:

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4x2 +9y2 = 72

Kamila [148]

Answer:

<h2> $\bold{\left(\dfrac{3}{13}\ ,\ \dfrac{4\sqrt{13}}{13}\right)\qquad\vee\qquad \left(\dfrac{3}{13}\ ,\ -\dfrac{4\sqrt{13}}{13}\right)}$ </h2>

Step-by-step explanation:

x - y² = -1 ⇒ - y² = - x - 1 ⇒ y² = x + 1 {x≥-1}

4x² + 9y² = 72

4x² + 9(x + 1)² = 72

4x² + 9(x² + 2x + 1) = 72

4x² + 9x² + 18x + 9 - 72 = 0

13x² + 18x - 63 = 0 ⇒ a = 13, b = 18, c = -63

$x=\dfrac{-18\pm\sqrt{18^2-4\cdot13\cdot(-63)}}{2\cdot13}=\dfrac{-18\pm\sqrt{324+252}}{26}=\dfrac{-18\pm\sqrt{576}}{26}\\\\x=\dfrac{-18+24}{26}=\dfrac3{13}\qquad\vee\qquad x=\dfrac{-18-24}{26}=-\dfrac{21}{13}\\\\ y^2= x + 1\quad\iff\quad x\ge-1\\\\y^2=\dfrac3{13}+1\\\\ y^2=\dfrac{16}{13}\\\\y=\dfrac{4}{\sqrt{13}}=\dfrac{4\sqrt{13}}{13}\qquad\vee\qquad y=-\dfrac{4\sqrt{13}}{13}$