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Mathematics

1 answer:

Naya [18.7K]3 years ago

3 0

Answer:

The answer is d=37 in

Step-by-step explanation:

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3 years ago

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If a /b = p /q, then (a + b )/b = _______.

USPshnik [31]

$\dfrac ab=\dfrac pq\implies b=\dfrac{aq}p$

Substituting into the second expression,

$\dfrac{a+b}b=\dfrac{a+\dfrac{aq}p}{\dfrac{aq}p}=\dfrac{ap+aq}{aq}=\dfrac{p+q}q$

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4 years ago

6(840.25)+15(1,374.05)+9(1.222.43)/30

kifflom [539]

Answer:

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4 0

3 years ago

10. Determine the open interval(s) on which the function f(x) = 12x - x^3 is increasing.

Gre4nikov [31]

Answer:

$\large\boxed{x\in(-2,\ 2)}$

Step-by-step explanation:

$f(x)=12x-x^3$

Calculate the derivative of the function:

$f'(x)=\left(12x-x^3\right)'=(12x)'-\left(x^3\right)'=12-3x^2$

Calculate the zeros of the derivative:

$f'(x)=0\Rightarrow12-3x^2=0\qquad\text{add}\ 3x^2\ \text{to both sides}\\\\3x^2=12\qquad\text{divide both sides by 3}\\\\x^2=4\to x=\pm\sqrt4\\\\x=\pm2$

Let's check the derivative sign:

$f'(x)>0\iff12-3x^2>0\qquad\text{use the distributive property}\\\\-3(x^2-4)>0\\\\-3(x^2-2^2)>0\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\-3(x-2)(x+2)>0\\^{\qquad x=2\qquad x=-2$