Find the angle(s) of rotation that will carry a 12 sided polygon onto itself.

1 answer:

6 0

There are 2 ways of looking at this problem:

1. Mathematical
2. Logical

Personally, I think #2 is the most efficient way of answering:

When you think about it, in order to complete a full rotation, an object must rotate 360°.

Therefore in order for a 12-sided polygon to rotate onto itself, the angle of rotation is 360°.

Hope this helps!

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mr sanchez owns a square field. the side lengths are 0.9 kilometers. there are 1980 prairie dog burrows in the field. what is th

nata0808 [166]

Density is the measurement of the amount of mass per unit of volume.
In this case we should calculate the density of prairie dog burrows on a square field. This is a surface charge density.It is defined as the total amount of units q per km^2.
to calculate the density of prairie dog burrows, we should divide the total number of prairie dog burrows in the field by the size of the field. Thus,

prairie dog burrows in square kilometers= number of dog burrows/ size of the field

size of the field=0.9*0.9=900*900=180000m^2
1980/180000 m^2= 0.011 dog burrows in square meter
11 dogs in square kilometer

5 0

2 years ago

the function v(t)=-9.8t+5 gives the instantaneous velocity of an object thrown upward with an initial velocity of 5 m/sec. at wh

olya-2409 [2.1K]

Answer:

0.5 s (using 1 significan figure since the initial velocity is given with 1 significant figure)

Explanation:

Let's see what each term in the function v (t) = - 9.8t + 5 means:

Term: - 9.8 t

The variable t is the time

The coffecient - 9.8 (which is negative) means that the velocity is reduced 9.8 m/s each second.

That means that the motion is uniformly decelerated with acceleration - 9.8 m/s².

Term + 5

The term + 5, means that the object was launched with an upward velocity of 5 m/s.

Hence the equation tells that after the object was launched upward it starts to lose speed and will reach a maximum height when the velocity is equal to zero, from which it starts falling.

So, you can calculate when the object reachs it maximum height and starts falling by making the velocity, v (t), equal to zero and solving for t. This is how you do it:

v (t) = 0
0 = - 9.8t + 5
9.8t = 5 remember that the units of 9.8 is m/s² and of 5 is m/s

t = 5 m/s / 9.8 m/s² = 0.51 s

So, the object starts fallin at 0.51 s. Since, the velocity is reported with 1 significant digit you answer should also show 1 significant digit, which means t = 0.5 s.

3 0

2 years ago

Find the differential equation of the family of tangent lines to the parabola y^2 = 2x

dusya [7]

$\bf 
y^2=2x\implies y=\sqrt{2x}\implies y=x^{\frac{1}{2}}
\\ \quad \\
\cfrac{dy}{dx}=\boxed{?}$