Answer:
Explanation:
Given a square Piece whose side is 12 inches
Now square pieces are cut from each corner to make it a open box
Suppose x is the length of square piece at each corner
then
base square has a length of
Dimension of new box is
Volume
For maximum volume differentiate with respect to x we get
we get x=6 and 4 but at x=6 volume becomes zero therefore x=4 is valid
Answer:
The function has a maximum in
The maximum is:
Explanation:
Find the first derivative of the function for the inflection point, then equal to zero and solve for x
Now find the second derivative of the function and evaluate at x = 3.
If the function has a maximum
If the function has a minimum
Note that:
the function has a maximum in
The maximum is:
Answer:
X-rays travel through space faster than radio waves.
Explanation:
Electromagnetic waves consist of oscillations of the electric and the magnetic field in a plane perpendicular to the direction of motion the wave.
All electromagnetic waves travel in a vacuum always at the same speed, the speed of light, whose value is:
Electromagnetic waves are classified into 7 different types, according to their wavelength/frequency. From shortest to longest wavelength (and so, from highest to lowest frequency), we have:
Gamma rays
X rays
Ultraviolet
Visible light
Infrared radiation
Microwaves
Radio waves
Now we can analyze the 4 statements:
X-rays and radio waves are both forms of light, or electromagnetic radiation --> TRUE. They are both types of electromagnetic waves.
X-rays have higher frequency than radio waves. --> TRUE, as we can see from the table above.
X-rays have shorter wavelengths than radio waves. --> TRUE, as we can see from the table above.
X-rays travel through space faster than radio waves. --> FALSE: all electromagnetic waves travel in space at the same speed, the speed of light.