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jeka94
2 years ago
5

I really need help on these two. Its fine if you dont get both of them. i will give you 25 points

Mathematics
1 answer:
masya89 [10]2 years ago
3 0

<u><em>Answer:</em></u>

He read 1/3 of the book on the second day

He didn't finish the book in two days.

<u><em>Step-by-step explanation:</em></u>

Lets find 3/5 of 5/9

If we said, find 3/5 of x, the answer would be 3/5x.

3/5*x = 3/5x

In the same way, \frac{3}{5} *\frac{5}{9} = \frac{15}{45} = \frac{1}{3}

He read 1/3 of the book on the second day

Does 5/9 + 1/3 equal to 1?

1/3 = 3/9

5/9 + 3/9 = 8/9

He didn't finish the book in two days.

Hope this helps :)

Have a nice day!

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Answer:

5/6

Step-by-step explanation:

2 1/2 -> 5/2

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0.83333333333 as a simplied fraction is 5/6

4 0
2 years ago
1) Let f(x)=6x+6/x. Find the open intervals on which f is increasing (decreasing). Then determine the x-coordinates of all relat
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Answer:

1) increasing on (-∞,-1] ∪ [1,∞), decreasing on [-1,0) ∪ (0,1]

x = -1 is local maximum, x = 1 is local minimum

2) increasing on [1,∞), decreasing on (-∞,0) ∪ (0,1]

x = 1 is absolute minimum

3) increasing on (-∞,0] ∪ [8,∞), decreasing on [0,4) ∪ (4,8]

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4) increasing on [2,∞), decreasing on (-∞,2]

x = 2 is absolute minimum

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x = 0 is local minimum, x = 4/9 is absolute maximum

Step-by-step explanation:

To find minima and maxima the of the function, we must take the derivative and equalize it to zero to find the roots.

1) f(x) = 6x + 6/x

f\prime(x) = 6 - 6/x^2 = 0 and x \neq 0

So, the roots are x = -1 and x = 1

The function is increasing on the interval (-∞,-1] ∪ [1,∞)

The function is decreasing on the interval [-1,0) ∪ (0,1]

x = -1 is local maximum, x = 1 is local minimum.

2) f(x)=6-4/x+2/x^2

f\prime(x)=4/x^2-4/x^3=0 and x \neq 0

So the root is x = 1

The function is increasing on the interval [1,∞)

The function is decreasing on the interval (-∞,0) ∪ (0,1]

x = 1 is absolute minimum.

3) f(x) = 8x^2/(x-4)

f\prime(x) = (8x^2-64x)/(x-4)^2=0 and x \neq 4

So the roots are x = 0 and x = 8

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The function is decreasing on the interval [0,4) ∪ (4,8]

x = 0 is local maximum, x = 8 is local minimum.

4) f(x)=6(x-2)^{2/3} +4=0

f\prime(x) = 4/(x-2)^{1/3} has no solution and x = 2 is crtitical point.

The function is increasing on the interval [2,∞)

The function is decreasing on the interval (-∞,2]

x = 2 is absolute minimum.

5) f(x)=8\sqrt x - 6x for x>0

f\prime(x) = (4/\sqrt x)-6 = 0

So the root is x = 4/9

The function is increasing on the interval (0,4/9]

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