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3 years ago

I need help with number 1-4 I don’t understand..

Mathematics

1 answer:

Karo-lina-s [1.5K]3 years ago

8 0

Answer:

109°, obtuse
131°, obtuse
53°, acute
124°, obtuse

Step-by-step explanation:

You are exected to know the relationships of angles created where a transversal crosses parallel lines.

Corresponding angles are equal (congruent).
Adjacent angles are supplementary, as are any linear pair.
Opposite interior (or exterior) angles are equal (congruent).

The appearance of the diagram often gives you a clue.

You also expected to know the name (or category) of angles less than, equal to, or greater than 90°. Respectively, these are acute, right, and obtuse angles.

1. Adjacent angles are supplementary. The supplement of the given angle is 109°, so x will be obtuse.

2. Opposite exterior angles are equal, so y will be 131°. It is obtuse.

3. Opposite interior angles are equal, so w will be 53°. It is acute.

4. Corresponding angles are equal, so x will be 124°. It is obtuse.

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First find the critical points of f :

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Next check for critical points along the boundary, which can be found by converting to polar coordinates:

$f(x,y)=f(10\cos t,10\sin t)=g(t)=295-40\cos t-100\cos^2t$

Find the critical points of g :

$\dfrac{\mathrm dg}{\mathrm dt}=40\sin t+200\sin t\cos t=40\sin t(1+5\cos t)=0$

$\implies\sin t=0\text{ OR }1+5\cos t=0$

$\implies t=n\pi\text{ OR }t=\cos^{-1}\left(-\dfrac15\right)+2n\pi\text{ OR }t=-\cos^{-1}\left(-\dfrac15\right)+2n\pi$

where n is any integer. We get 4 critical points in the interval [0, 2π) at

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$t=\pi\implies f(-10,0)=235$

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Dennis_Churaev [7]

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3 years ago

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Nat2105 [25]

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