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2 years ago

Lim (h->0) (sqrt(25+h)-5)/h.

1 answer:

5 0

$\lim_{h \to 0} \frac{ \sqrt{25+h} -5}{h}= \frac{0}{0}$
We have to multiply numerator and denominator by: √(25-h)+ 5:
$\lim_{h \to 0} \frac{ \sqrt{25+h}-5}{h}* \frac{ \sqrt{25+h} +5}{ \sqrt{25+h}+5} = \\ \lim_{h \to 0} \frac{25+h-25}{h( \sqrt{25+h}+5) } = \\ \lim_{h \to 0} \frac{1}{ \sqrt{25+h} +5} = \\ = \frac{1}{5+5}=$ = 1/10 = 0.1

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3 years ago

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Svetlanka [38]

40 cm.

let the length of the first part be 3x, second part be 4x, third part be 5x.

where x is a positive length in cm.

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so that the ratio of lengths of the 3 parts be 3:4:5.

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2 years ago

Which of the following is a like radical to mc001-1.jpg?

mixer [17]

You haven't provided the expression or the choices, therefore, I cannot provide an exact answer.
However, I'll try to help you understand the concept so that you can solve the question you have

Like radicals are characterized by the following:
1- They both have the same root number (square root, cubic root , ...etc)
2- They both have the same radicand (meaning that the expression under the root is the same in both radicals)

Examples of like radicals:
3 $\sqrt{xyz}$ and 7 $\sqrt{xyz}$
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Check the choices you have. The one that satisfies the above two conditions would be your correct choice

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Step-by-step explanation:

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k0ka [10]

<h3>The equation is:</h3><h3> $x^2 - 7x + 12 = 0$ </h3><h3>The number is 3 or 4</h3><h3><em><u>Solution:</u></em></h3>

Given that,

7 added to the square of a number is equal to 7 times the number, minus 5

Let "x" be the unknown number

From given,

7 added to square of x = 7 times the x minus, 5

$7 + x^2 = 7x - 5$

Solve the above equation

$x^2 -7x +7+5 = 0\\\\x^2 - 7x + 12 = 0$

Split the middle term

$x^2 -3x - 4x + 12 = 0\\\\Group\ the\ expressions\\\\(x^2-3x) -(4x - 12) = 0\\\\Take\ the\ common\ factor\ out\\\\x(x -3) -4(x -3) = 0\\\\(x-3)(x-4) = 0$

We have two solutions

x - 3 = 0

x = 3

And

x - 4 = 0

x = 4

Thus number is 3 or 4

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2 years ago