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2 years ago

What is the discriminant of 9x^2+=10x

Mathematics

1 answer:

prisoha [69]2 years ago

4 0

9x^2-10x=0
D= b^2-4ac
b=-10
a=9
c=0
D=(-10)^2-4*9*0=10^2-0=100

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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

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

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

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

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3 years ago

Find an equation of the line with the given slope and y-intercept.

vlabodo [156]

Answer:

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Step-by-step explanation:

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2 years ago

How do I solve this?

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Answer:

x ≈ -4.419

Step-by-step explanation:

Separate the constants from the exponentials and write the two exponentials as one. (This puts x in one place.) Then use logarithms.

0 = 2^(x-1) -3^(x+1)

3^(x+1) = 2^(x-1) . . . . . add 3^(x+1)

3×3^x = (1/2)2^x . . . . .factor out the constants

(3/2)^x = (1/2)/3 . . . . . divide by 3×2^x

Take the log:

x·log(3/2) = log(1/6)

x = log(1/6)/log(3/2) . . . . . divide by the coefficient of x

x ≈ -4.419

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A graphing calculator is another tool that can be used to solve this. I find it the quickest and easiest.

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<em>Comment on alternate solution</em>

Once you get the exponential terms on opposite sides of the equal sign, you can take logs at that point, if you like. Then solve the resulting linear equation for x.

(x+1)log(3) = (x-1)log(2)

x=(log(2)+log(3))/(log(2)-log(3))