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3 years ago

Is 6.565656... a rational number?

Mathematics

1 answer:

Eduardwww [97]3 years ago

4 0

Yes it’s a rational number

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Derivative of these questions<br>

shtirl [24]

Answer: $\bold{y'=\dfrac{1}{2(a-b)^2}\bigg(\dfrac{1}{\sqrt{x+a}}+\dfrac{1}{\sqrt{x+b}}\bigg)}$

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

$y=\dfrac{1}{\sqrt{x+a}-\sqrt{x+b}}\\\\\\\text{Rationalize the denominator:}\\y=\dfrac{1}{\sqrt{x+a}-\sqrt{x+b}}\bigg(\dfrac{\sqrt{x+a}+\sqrt{x+b}}{\sqrt{x+a}+\sqrt{x+b}}\bigg)\\\\\\y=\dfrac{\sqrt{x+a}+\sqrt{x+b}}{x+a-x-b}\\\\\\y=\dfrac{\sqrt{x+a}+\sqrt{x+b}}{a-b}\\\\\\\text{Apply the derivative (derivative of the numerator (top) divided by the}\\\text{denominator (bottom) squared).}$

$\text{Derivative of }\sqrt{x+a}\quad \rightarrow \quad (x+a)^{\frac{1}{2}}\quad = \quad \dfrac{1}{2}(x + a)^{-\frac{1}{2}}\\\\\text{Derivative of }\sqrt{x+b}\quad \rightarrow \quad (x+b)^{\frac{1}{2}}\quad = \quad \dfrac{1}{2}(x + b)^{-\frac{1}{2}}\\\\\\\text{Derivative of}\ \dfrac{\sqrt{x+a}+\sqrt{x+b}}{a-b}:\\\\= \dfrac{\dfrac{1}{2}(x + a)^{-\frac{1}{2}}+\dfrac{1}{2}(x + b)^{-\frac{1}{2}}}{(a-b)^2}$

$\text{Factor out }\dfrac{1}{2}\ \text{from the numerator:}\\\\\dfrac{(x+a)^{-\frac{1}{2}}+(x+b)^{-\frac{1}{2}}}{2(a-b)^2}\\\\\\\text{Move the terms with negative exponents to the denominator:}\\\\=\dfrac{1}{2(a-b)^2}\bigg(\dfrac{1}{\sqrt{x+a}}+\dfrac{1}{\sqrt{x+b}}\bigg)$

3 0

4 years ago

Can someone please help me with this question??

steposvetlana [31]

Answer:

450

Step-by-step explanation:

3*150 because the 150is your main number or otherwise known as "b" and then 3 is the multiplier so 3 * 150

6 0

3 years ago

At a computer chip factory,a machine temporarily malfunctioned and damaged 2700 chips. Normally, 150 chips are damaged, and 400

cestrela7 [59]

78 takes to the malfunction.

7 0

4 years ago

20% of what number is 75?

nataly862011 [7]

Answer:

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Omar the tent maker wishes to support a 13.4-ft tent wall by attaching 25-ft cable to the top of it, and then anchoring the cabl

KATRIN_1 [288]

Answer:

21.11 ft

Step-by-step explanation:

This question would be solved using Pythagoras theorem

The Pythagoras theorem : a² + b² = c²

where a = length

b = base

c = hypotenuse

13.4² + b² = 25²

179.56 + b² = 625

b² = 625 - 179.56

b = 445.44

find the square root of 445.44

b = 21.11 ft

3 0

3 years ago