2 years ago

Line M contains points (4,3) and (1,2). Write a possible equation of line K that is

1 answer:

6 0

I believe the answer is y = -3x + 15
This is what I got from calculating it but I haven’t done this type of equation in a while

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Which statement correctly describes the translations used to graph the following exponential function?

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2 years ago

Find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) dx x(l

Pepsi [2]

I'm assuming the integral is

$\displaystyle \int \frac{dx}{x (\ln(x^2))^5}$

We have

$\ln(x^2) = 2 \ln|x| \implies (\ln(x^2))^5 = 32 (\ln|x|)^5$

Then substituting $y=\ln|x|$ and $dy=\frac{dx}x$ , the integral transforms and reduces to

$\displaystyle \int \frac{dx}{x(\ln(x^2))^5} = \frac1{32} \int \frac{dy}{y^5} \\\\ ~~~~~~~~ = \frac1{32} \left(-\frac1{4y^4}\right) + C \\\\ ~~~~~~~~ = -\frac1{128(\ln|x|)^4} + C$

which we can rewrite as

$128 (\ln|x|)^4 = 8\cdot2^4(\ln|x|)^4 = 8 (2\ln|x|)^4 = 8 (\ln(x^2))^4$

and so

$\displaystyle \int \frac{dx}{x (\ln(x^2))^5} = \boxed{-\frac1{8(\ln(x^2))^4} + C}$

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1 year ago

How do you Simplify :(2p^-3)^5

iragen [17]

Answer:

The final simplification is (32p^-15).

Step-by-step explanation:

Given:

(2p^-3)^5 we have to simplify.

Property to be used:(Power rule)

Power rule states that: $(a^x)^y=a^x^y$ ...the exponents were multiplied.

Using power rule.

We have,

⇒ $(2p^-3)^5$

⇒ $(2^5)(p^-3^*5)$ ...taking exponents individually.

⇒ $32(p^-^1^5)$ ... $2^5=2*2*2*2*2=32$

⇒ $32p^-^1^5$

So our final values are 32p^-15

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