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FromTheMoon [43]
3 years ago
11

Precalc.

Mathematics
1 answer:
viktelen [127]3 years ago
6 0
Domain: x>0.

(\log_2x)^2+7\log_2x+12=0

Substitute t=\log_2x\in\mathbb{R}. We have:

 t^2+7t+12=0\\\\a=1\qquad b=7\qquad c=12\\\\\\\Delta=b^2-4ac=7^2-4\cdot1\cdot12=49-48=1\\\\\sqrt{\Delta}=\sqrt{1}=1\\\\\\
t_1=\dfrac{-b-\sqrt{\Delta}}{2a}=\dfrac{-7-1}{2}=\dfrac{-8}{2}=-4\\\\\\
t_2=\dfrac{-b+\sqrt{\Delta}}{2a}=\dfrac{-7+1}{2}=\dfrac{-6}{2}=-3

For t₁ there will be:

\log_2x=t_1\\\\\log_2x=-4\\\\2^{-4}=x\\\\x=\dfrac{1}{2^4}\\\\\\x=\dfrac{1}{16}=0,0625\\\\\\\boxed{x\approx0,063}

and for t₂:

\log_2x=t_2\\\\\log_2x=-3\\\\2^{-3}=x\\\\x=\dfrac{1}{2^3}\\\\\\x=\dfrac{1}{8}\\\\\\\boxed{x=0,125}

Answer d)


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Answer:

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but im guessing that you were trying to say (0,5) in which case its

7.07106781187

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Step-by-step explanation:

First, add together the prices of all the clothes:

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Then, subtract this from 75:

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5 0
3 years ago
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A solid metal prism has a rectangle base with sides of 4 inches and a height of 4inches a hole in the shape of a cylinder with a
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Answer:

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Step-by-step explanation:

Here is the complete question.

A solid metal prism has a rectangle base with sides of 4 inches and 6 inches and a height of 4 inches . A hole in the shape of a cylinder with a radius of 1 inch is drilled trough the entire length of the rectangular prism. What is the approximate volume of the remaining solid in cubic inches.

Solution

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The volume of the remaining solid = volume of solid prism - volume of cylindrical hole = (96 - 18.85) cubic inches = 77.15 cubic inches ≅ 77 cubic inches

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