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german
3 years ago
11

Choose the correct description of the graph of the compound inequality: (5 points)

Mathematics
1 answer:
skad [1K]3 years ago
4 0

Answer:

D

Step-by-step explanation:

Firstly,  

≤  or  ≥  means closed circle, and

<   or >  means open circle

Now, let's solve the compound inequality:

x - 1 ≤ 7

x ≤ 8

and

2x ≥ 22

x ≥ 11

This solution means "everything left of 8 (inclusive and closed circle)" and "everything right of 11 (inclusive and closed circle)"

Looking at the choices, D is right.

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Implicit differentiation of 1/x +1/y=5 y(4)= 4/19<br> y'(4)=?
Aneli [31]
\frac{1}{x} +\frac{1}{y} = 5\\\\x^{-1}+y^{-1}=5\\

Above, I changed the fraction form of x and y into exponential form so it is easier to see the differentiation. Now, we can differentiate:

-1x^{-2}+-1y^{-2}\frac{dy}{dx}=5\\\\\frac{-1}{x^2}-\frac{1}{y^2}\frac{dy}{dx}=5\\\\-\frac{1}{y^2}\frac{dy}{dx}=5+\frac{1}{x^2}\\\\\frac{dy}{dx}=-5y^2-\frac{y^2}{x^2}

Now that we have dy/dx, we can plug in the x, which is 4, and the y, which is 4/19. We know these values of x and y because your question stated y(4) = 4/19.

\frac{dy}{dx}=-5(\frac{4}{19})^2-\frac{(\frac{4}{19})^2}{(4)^2}\\\\\frac{dy}{dx}=-5(\frac{16}{361})-\frac{(\frac{16}{361})}{16}\\\\\frac{dy}{dx}=\frac{-80}{361}-\frac{1}{361}\\\\\frac{dy}{dx}=\frac{-81}{361}
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The answer to 1. Is c

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