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 ![12-2x](https://tex.z-dn.net/?f=12-2x)
Dimension of new box is ![(12-2x)\times (12-2x)\times x](https://tex.z-dn.net/?f=%2812-2x%29%5Ctimes%20%2812-2x%29%5Ctimes%20x)
Volume ![V=(12-2x)\times (12-2x)\times x](https://tex.z-dn.net/?f=V%3D%2812-2x%29%5Ctimes%20%2812-2x%29%5Ctimes%20x)
![V=\left ( 12-2x\right )^2\cdot x](https://tex.z-dn.net/?f=V%3D%5Cleft%20%28%2012-2x%5Cright%20%29%5E2%5Ccdot%20x)
For maximum volume differentiate with respect to x we get
![\Rightarrow\frac{\mathrm{d} V}{\mathrm{d} x}=2\times \left ( 12-2x\right )\times \left ( -2\right )\cdot x+\left ( 12-2x\right )^2=0](https://tex.z-dn.net/?f=%5CRightarrow%5Cfrac%7B%5Cmathrm%7Bd%7D%20V%7D%7B%5Cmathrm%7Bd%7D%20x%7D%3D2%5Ctimes%20%5Cleft%20%28%2012-2x%5Cright%20%29%5Ctimes%20%5Cleft%20%28%20-2%5Cright%20%29%5Ccdot%20x%2B%5Cleft%20%28%2012-2x%5Cright%20%29%5E2%3D0)
we get x=6 and 4 but at x=6 volume becomes zero therefore x=4 is valid
![V=\left ( 12-2\cdot 4\right )^2\cdot 4](https://tex.z-dn.net/?f=V%3D%5Cleft%20%28%2012-2%5Ccdot%204%5Cright%20%29%5E2%5Ccdot%204)
![V=4^3](https://tex.z-dn.net/?f=V%3D4%5E3)
![V=64\ in.^3](https://tex.z-dn.net/?f=V%3D64%5C%20in.%5E3)
Answer:
8.57 Hz
Explanation:
From the question given above, the following data were obtained:
Wavelength (λ) = 3.5 m
Velocity (v) = 30 m/s
Frequency (f) =?
The velocity, wavelength and frequency of a wave are related according to the equation:
Velocity = wavelength × frequency
v = λ × f
With the above formula, we can simply obtain the frequency of the wave as follow:
Wavelength (λ) = 3.5 m
Velocity (v) = 30 m/s
Frequency (f) =?
v = λ × f
30 = 3.5 × f
Divide both side by 3.5
f = 30 / 3.5
f = 8.57 Hz
Thus, the frequency of the wave is 8.57 Hz
T<span>he correct unit for electrical power is "watt".
</span>
That<span>’s actually the unit that measures the rate per time that electric energy is transferred.</span>
<span>
</span>
<span>Have a nice day! :)</span>
Answer:
Option (A) , (b) and (d) are correct option
Explanation:
According to Coulomb's law electric force between two charges is given by
![F=\frac{1}{4\pi \epsilon _0}\frac{q_1q_2}{r^2}](https://tex.z-dn.net/?f=F%3D%5Cfrac%7B1%7D%7B4%5Cpi%20%5Cepsilon%20_0%7D%5Cfrac%7Bq_1q_2%7D%7Br%5E2%7D)
From the relation we can say that force is directly proportional to magnitude of charges and inversely proportional to distance between them '
So if we increase the distance then force will decrease
Increase if any of the charge get larger
If force is attractive then both the charge will be of different sign and is force is repulsive then both the charges of same sign
From above conclusion we can say that (a), (b) and (d) are correct option
Answer:
4.7 s
Explanation:
The complete question is presented in the attached image to this solution.
v(t) = 61 - 61e⁻⁰•²⁶ᵗ
At what time will v(t) = 43 m/s?
We just substitute 43 m/s into the equation for the velocity of the diver and solve for t.
43 = 61 - 61e⁻⁰•²⁶ᵗ
- 61e⁻⁰•²⁶ᵗ = 43 - 61 = -18
e⁻⁰•²⁶ᵗ = (18/61) = 0.2951
In e⁻⁰•²⁶ᵗ = In 0.2951 = -1.2205
-0.26t = -1.2205
t = (1.2205/0.26) = 4.694 s = 4.7 s to the nearest tenth.
Hope this Helps!!!