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3 years ago

7

A machinist can produce 114 parts in 6 minutes. At this rate, how many parts can be produced in 15 minutes?

2 answers:

Reil [10]3 years ago

6 0

Answer: 285 parts

Step-by-step explanation:

114 parts per 6 minutes

114*2 = 228

114/2=57

15 minutes =285

KonstantinChe [14]3 years ago

4 0

285

just figure out how many is made then multiple that by 15

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Intersection point of Y=logx and y=1/2log(x+1)

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Answer:

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The Problem:

What is the intersection point of $y=\log(x)$ and $y=\frac{1}{2}\log(x+1)$ ?

Step-by-step explanation:

To find the intersection of $y=\log(x)$ and $y=\frac{1}{2}\log(x+1)$ , we will need to find when they have a common point; when their $x$ and $y$ are the same.

Let's start with setting the $y$ 's equal to find those $x$ 's for which the $y$ 's are the same.

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$x^2=x+1$

This is a quadratic equation.

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Comparing this to $ax^2+bx+c=0$ we see the following:

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$x=\frac{1 \pm \sqrt{(-1)^2-4(1)(-1)}}{2(1)}$

$x=\frac{1 \pm \sqrt{1+4}}{2}$

$x=\frac{1 \pm \sqrt{5}}{2}$

So we have the solutions to the quadratic equation are:

$x=\frac{1+\sqrt{5}}{2}$ or $x=\frac{1-\sqrt{5}}{2}$ .

The second solution definitely gives at least one of the logarithm equation problems.

Example: $\log(x)$ has problems when $x \le 0$ and so the second solution is a problem.

So the $x$ where the equations intersect is at $x=\frac{1+\sqrt{5}}{2}$ .

Let's find the $y$ -coordinate.

You may use either equation.

I choose $y=\log(x)$ .

$y=\log(\frac{1+\sqrt{5}}{2})$

The intersection is $(\frac{1+\sqrt{5}}{2},\log(\frac{1+\sqrt{5}}{2})$ .

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