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3 years ago

Y = 1/2x + 3 on a graph

Mathematics

1 answer:

Misha Larkins [42]3 years ago

8 0

Answer:

Step-by-step explanation:

What is the question? If you want to know how to graph this equation, it's usually easiest to start with the intercepts, i.e., the points where the line crosses the axes.

y = ½x + 3 tells you that the line crosses the y-axis at (0,3), so plot that point.

Then let y = 0 and solve for x.

0 = ½x + 3

x = 6

The line crosses the x-axis at (6,0), so plot that point as well.

Then draw the line passing through those two points.

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Which of the diagrams below represents the contrapositive of the statement "If it is an elm, then it is a tree"?

Murrr4er [49]

Answer:

Right

Step-by-step explanation:

For a contrapositive, we switch the hypothesis and conclusion and then negate it.

Switch

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3 years ago

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3 years ago

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3 years ago

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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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3 years ago