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Blababa [14]
3 years ago
10

Which angle of rotation is determined by the matrix below?{1/2 -sqrt3/2 sqrt3/2 1/2] 30° 60° 120° 300°

Mathematics
1 answer:
strojnjashka [21]3 years ago
3 0

Answer:

  60°

Step-by-step explanation:

You have the rotation matrix ...

  \left[\begin{array}{cc}\cos{\theta}&-\sin{\theta}\\\sin{\theta}&\cos{\theta}\end{array}\right]=\left[\begin{array}{cc}\dfrac{1}{2}&-\dfrac{\sqrt{3}}{2}\\\dfrac{\sqrt{3}}{2}&\dfrac{1}{2}\end{array}\right]

This tells you the angle of rotation is ...

  \tan{\theta}=\dfrac{\sin{\theta}}{\cos{\theta}}=\dfrac{\left(\dfrac{\sqrt{3}}{2}\right)}{\left(\dfrac{1}{2}\right)}=\sqrt{3}\\\\\theta=\arctan{\sqrt{3}}=60^{\circ}

The angle of rotation is 60°.

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So,

If this was mental math, I would round 1.87 to the nearest pound and 2.46 to the nearest half pound, making the following addition problem:
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So I would say about 4.5 pounds of meat.

But if you're rounding to the nearest pound for both, then you have this equation:
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Answer:

The area of the patio without the tub is 53.44 ft²

Step-by-step explanation:

In order to calculate the area of the patio that is not covered by the hot tub we need to calculate the total area of the patio and subtract it by the area of the tub. Since the patio is rectangular it's area is given by "area = length*width" and the area of the tub is given by "area = pi*r²".

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To compare the area we need to convert the areas to the same unit, to do that we will convert the area of the tub from in² to ft², in order to do that we need to divide the value by 144. We have:

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We then multiply the possible choices together to get 990*990=980100 possible ways to hand out the six medals

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