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2 years ago

To which set of numbers does the number -12 belong?

1 answer:

3 0

That belongs to the integers set, also rational and real number set

integers are like -4,-3,-2,-1,0,1,2,3,4 etc
rational numbers are number that can be written in form a/b where a and b are integers and b≠0
real numbes include rational numbers

so integers, rational number and real numbers

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Differentiating a Logarithmic Function in Exercise, find the derivative of the function. See Examples 1, 2, 3, and 4.

Leni [432]

Answer: $\dfrac{2x^2-1}{x(x^2-1)}$

Step-by-step explanation:

The given function : $y=\ln(x(x^2 - 1)^{\frac{1}{2}})$

$\Rightarrow\ y=\ln x+\ln (x^2-1)^{\frac{1}{2}}$ [ $\because \ln(ab)=\ln a +\ln b$ ]

$\Rightarrow y=\ln x+\dfrac{1}{2}\ln (x^2-1)}$ [ $\because \ln(a)^n=n\ln a$ ]

Now , Differentiate both sides with respect to x , we will get

$\dfrac{dy}{dx}=\dfrac{1}{x}+\dfrac{1}{2}(\dfrac{1}{x^2-1})\dfrac{d}{dx}(x^2-1)$ (By Chain rule)

[Note : $\dfrac{d}{dx}(\ln x)=\dfrac{1}{x}$ ]

$\dfrac{1}{x}+\dfrac{1}{2}(\dfrac{1}{x^2-1})(2x-0)$

[ $\because \dfrac{d}{dx}(x^n)=nx^{n-1}$ ]

$=\dfrac{1}{x}+\dfrac{1}{2}(\dfrac{1}{x^2-1})(2x) = \dfrac{1}{x}+\dfrac{x}{x^2-1}\\\\\\=\dfrac{(x^2-1)+(x^2)}{x(x^2-1)}\\\\\\=\dfrac{2x^2-1}{x(x^2-1)}$

Hence, the derivative of the given function is $\dfrac{2x^2-1}{x(x^2-1)}$ .

8 0

3 years ago

A tuxedo rental service charges a $150 flat fee for a suit plus $50 per additional day. Write and solve an equation to determine

V125BC [204]

Answer:

150+50*4=350

Step-by-step explanation:

hope it helped sorry if it's not what you wanted.

4 0

2 years ago

Read 2 more answers

You withdrew $47.25 from your

sladkih [1.3K]

Answer:

47.25 + 23.75 = 71

Step-by-step explanation:

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3 years ago

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Which statement is true using Cavalieri’s principles ?

Kay [80]

Answer:

One of the benefits of Cavalieri's principle is that it allows us to determine the volume of an oblique prism (or oblique cylinder). When dealing with two prisms (or two cylinders), if the base areas are equal and the heights are equal, then the volume is V = Bh regardless of the overall shape.

( i cant see the answers well so estimate to the one that applies)

5 0

2 years ago

How to solve this problem 7/20 =

wlad13 [49]

7/20=2.857142857142857 divide 20 by 7

4 0

2 years ago