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3 years ago

If two angles are both vertical and supplementary, then the angles are

Mathematics

2 answers:

docker41 [41]3 years ago

6 0

Ur answer would be RIGHT angle!!!

Hope its right!

7nadin3 [17]3 years ago

4 0

we know that

Supplementary angles are those angles whose sum is equal to $180$ degrees and vertical angles are angles that are congruent.

Let

x--------> the first angle

y--------> the second angle

$x=y$ --------> equation $1$

$x+y=180$ --------> equation $2$

Substitute equation $1$ in equation $2$

$x+[x]=180$

$2x=180$

$x=90$

$y=90$

therefore

<u>the answer is</u>

the angles are right angles

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Answer:

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<u>Maximization With Derivatives</u>

Given a function of one variable A(x), we can find the maximum or minimum value of A by using the derivatives criterion. If A'(x)=0, then A has a probable maximum or minimum value.

We need to find a function for the area of the pasture. Let's assume the dimensions of the pasture are x and y, and one divider goes parallel to the sides named y, and two dividers go parallel to x.

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$\displaystyle x=\frac{\frac{1}{2}-3y}{4}$

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Substituting x

$\displaystyle A=\frac{\frac{1}{2}-3y}{4}.y$

$\displaystyle A=\frac{\frac{1}{2}y-3y^2}{4}$

Differentiating with respect to y

$\displaystyle A'=\frac{\frac{1}{2}-6y}{4}$

Equate to 0

$\displaystyle \frac{\frac{1}{2}-6y}{4}=0$

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$\displaystyle y=\frac{1}{12}$

And also

$\displaystyle x=\frac{\frac{1}{2}-3\cdot \frac{1}{12}}{4}=\frac{1}{16}$

Compute the second derivative

$\displaystyle A''=-\frac{3}{2}.$

Since it's always negative, the point is a maximum

Thus, the maximum area is

$\displaystyle A=\frac{1}{12}\cdot \frac{1}{16}=\frac{1}{192}$

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