A) 750 m
First of all, let's find the wavelength of the microwave. We have
is the frequency
is the speed of light
So the wavelength of the beam is

Now we can use the formula of the single-slit diffraction to find the radius of aperture of the beam:

where
m = 1 since we are interested only in the central fringe
D = 30 km = 30,000 m
a = 2.0 m is the aperture of the antenna (which corresponds to the width of the slit)
Substituting, we find

and so, the diameter is

B) 0.23 W/m^2
First we calculate the area of the surface of the microwave at a distance of 30 km. Since the diameter of the circle is 750 m, the radius is

So the area is

And since the power is

The average intensity is

There are three forces acting on the book.
1. Force due to gravity
2. Force exerted downward by the hamster
3. Normal Force in reaction to the downward forces
Since the book is not moving, the net force is zero. The summation of all forces must be zero. Then we could find the normal force which is unknown (denoted as x).
∑F = -(4 kg)(9.81 m/s2) - 3 N + x =0
∑F = -39.24 N - 3N + x =0
x = 42 N
Therefore, the normal force is 42 N.
We can calculate the acceleration of Cole due to friction using Newton's second law of motion:

where

is the frictional force (with a negative sign, since the force acts against the direction of motion) and m=100 kg is the mass of Cole and the sled. By rearranging the equation, we find

Now we can use the following formula to calculate the distance covered by Cole and the sled before stopping:

where

is the final speed of the sled

is the initial speed

is the distance covered
By rearranging the equation, we find d:
Answer:
- < 25 m/s
- triangle inequality
- between north and east
- 45° < angle < 60°
Explanation:
(a) Just as one-dimensional numbers add on a number line by putting them end-to-end, so two-dimensional numbers add on a coordinate plane the same way.
Here, we choose to let the positive y-axis represent North, and the positive x-axis, East. This is the way a map is conventionally oriented. The velocity of the plane is represented by a vector pointing north (up). Its length represents the magnitude of the velocity. Likewise, the wind is represented by a vector of length 15 pointing east (right). The sum of these is the hypotenuse of the triangle they form.
The magnitude of the sum can be found here using the Pythagorean theorem, but for the purpose of this question, you're not asked to find that.
Instead, you're asked to estimate whether it is more or less than 25 (m/s).
Your knowledge of the triangle inequality will tell you that the hypotenuse (resultant) must be shorter than the sum of the lengths of the sides of the triangle, hence must be less than 10+15 = 25.
__
(b) The triangle inequality says the resultant is less than the sum of the other two sides of the triangle.
__
(c) Since the wind is blowing the plane toward the east, but the plane is traveling toward the north, the resulting direction is somewhere between north and east.
__
(d) "Somewhere between north and east" can be expressed as the inequality ...
0° < angle < 90°
Answer:
Tissues that are damaged or injured.
Explanation:
Dystrophic calcification involves the deposition of calcium in soft tissues despite no disturbance in the calcium metabolism, and this is often seen at damaged tissues.
Examples of areas in the body where dystrophic calcification can occur include atherosclerotic plaques and damaged heart valves.