3 years ago

Which ratio forms a proportion with 25/35 . A. 3/5 B. 15/21 C.24/34 D. 5/11

Mathematics

1 answer:

lesya [120]3 years ago

3 0

B. Because 25 times 3/5 equals 15 and 35 times 3/5 equals 21.

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Solve this GCSE question

Alona [7]

Answer:

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2 years ago

Read 2 more answers

Rationalize the numerator or denominator, and simplify:

allochka39001 [22]

$\dfrac{\sqrt[3]{x+h}-\sqrt[3]x}h\times\dfrac{\sqrt[3]{(x+h)^2}+\sqrt[3]{x(x+h)}+\sqrt[3]{x^2}}{\sqrt[3]{(x+h)^2}+\sqrt[3]{x(x+h)}+\sqrt[3]{x^2}}=\dfrac{(\sqrt[3]{x+h})^3-(\sqrt[3]x)^3}\cdots$
$=\dfrac{x+h-x}\cdots=\dfrac h\cdots$

The $h$ s then cancel, leaving you with the $\cdots=\sqrt[3]{(x+h)^2}+\sqrt[3]{x(x+h)}+\sqrt[3]{x^2}$ term.

If it's not clear what I did above, consider the substitution $a=\sqrt[3]{x+h}$ and $b=\sqrt[3]x$ . Then

$a^3-b^3=(a-b)(a^2+ab+b^2)$
$\implies\dfrac{a-b}h=\dfrac{a-b}h\times\dfrac{a^2+ab+b^2}{a^2+ab+b^2}=\dfrac{a^3-b^3}{h(a^2+ab+b^2)}$