3 years ago

Write as a polynomial: y^2(y+5)(y–3)

1 answer:

3 0

You mean expand

so first do the parnethesees bits becasue the rest can be done later

(y+5)(y-3)
foil aka distribute
y^2+5y-3y-15
y^2+2y-15

now remember tha tis all multilied by y^2
y^2(y^2+2y-15)
y^4+2y^3-15y^2

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Given that triangle ABC is right angle triangle. CD is altitude such that AD=BC

ABC is a right angle triangle so apply Pythogorean theorem

$AC^{2} + BC^{2} = AB^{2}$

$AC^{2} + AD^{2} = AB^{2}$ (Given that AD = BC)

$AC^{2} + AD^{2} = 3^{2}$ (Given that AB=3)

$AC^{2} + AD^{2} = 9$ ...(i)

ADC is a right angle triangle so apply Pythogorean theorem

$AD^{2} + CD^{2} = AC^{2}$

$AD^{2}+(\sqrt{2})^2= AC^{2}$

$AD^{2}+2= AC^{2}$

$AD^{2}=AC^{2} -2$ ...(ii)

Plug value (ii) into (i)

$AC^{2} + AC^{2}-2 = 9$

$2AC^{2} -2=9$

$2AC^{2} =11$

$AC^{2} =\frac{11}{2}$

$AC=\sqrt{\frac{11}{2} }$

Hence final answer is $AC=\sqrt{\frac{11}{2} }$

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