.

Mathematics

1 answer:

Damm [24]3 years ago

8 0

Step-by-step explanation:

It cannot be (4, -3) as there would be 2 outputs (3 and -3) for the input 4, therefore it becomes a one-to-many relationship and not a function.

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What number is it if you subtract 2 from a number and the new number and its absolute value are not equal?

ZanzabumX [31]

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3 years ago

You are designing a rectangular garden. the garden will be enclosed by fencing on three sides and by a house on the fourth side.

RUDIKE [14]

Suppose the dimensions of the rectangle is x by y and let the side enclosed by a house be one of the sides measuring x, then the sides that is to be enclosed are two sides measuring y and one side measuring x.

Thus, the length of fencing needed is given by

P = x + 2y

The area of the rectangle is given by xy,

i.e.

$xy = 288 \\ \\ \\ \\ \Rightarrow y= \frac{288}{x}$

Substituting for y into the equation for the length of fencing needed, we have

$P=x+2\left( \frac{288}{x} \right)=x+ \frac{576}{x}$

For the amount of fencing to be minimum, then

$\frac{dP}{dx} =0 \\ \\ \Rightarrow1- \frac{576}{x^2} =0 \\ \\ \Rightarrow \frac{576}{x^2} =1 \\ \\ \Rightarrow x^2=576 \\ \\ \Rightarrow x=\sqrt{576}=24$

Now, recall that

$y= \frac{288}{x} = \frac{288}{24} =12$

Thus, the length of fencing needed is given by

P = x + 2y = 24 + 2(12) = 24 + 24 = 48.

Therefore, 48 feets of fencing is needed to enclose the garden.

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3 years ago

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Maurinko [17]

Answer:

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Step-by-step explanation:

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The equinox which occurs around September happens in the Northern Hemisphere and is also known as the Fall or Autumnal equinox. Whereas, the equinox which occurs at the Southern Hemisphere is also known as the Spring or Vernal equinox. During an equinox, the tilt of the earth is perpendicular to the sun.

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