Answer:
I am 98% sure that the answers are B and A
Explanation:
Answer:
Double the current
Explanation:
The energy delivered by the heater is related to the current by the following relation:
E= ![I^{2}R t](https://tex.z-dn.net/?f=I%5E%7B2%7DR%20t)
let R * t = k ( ∴ R and t both are constant)
so E= k ![I^{2}](https://tex.z-dn.net/?f=I%5E%7B2%7D)
Now let:
E2= k I₂^2
E2= 4E
⇒ k I₂^2= 4* k ![I^{2}](https://tex.z-dn.net/?f=I%5E%7B2%7D)
Cancel same terms on both sides.
I₂^2= 4* ![I^{2}](https://tex.z-dn.net/?f=I%5E%7B2%7D)
taking square-root on both sides.
√I₂^2 = √4* I^2
⇒I₂= 2I
If we double the current the energy delivered each minute be 4E.
Answer:
They will both bounce back at the same speed they had before the collision
Explanation:
Assuming an elastic collision, kinetic energy will be conserved. Therefore, the billiard balls will have the same speed after the collision as before the collision.
Answer:
The maximum volume is 1417.87 ![inch^3](https://tex.z-dn.net/?f=inch%5E3)
Explanation:
<u>Optimization Using Derivatives</u>
We have a 24x30 inch piece of metal and we need to make a rectangular box by cutting a square from each corner of the piece and bending up the sides. The width of the piece is 24 inches and its length is 30 inches
When we cut a square of each corner of side x, the base of the box (after bending up the sides) will be (24-2x) and (30-2x), width and length respectively. The volume of the box is
![V=(24-2x)(30-2x)x](https://tex.z-dn.net/?f=V%3D%2824-2x%29%2830-2x%29x)
Operating
![V=4x^3-108x^2+720x](https://tex.z-dn.net/?f=V%3D4x%5E3-108x%5E2%2B720x)
To find the maximum value of V, we compute the first derivative and equate it to zero
![V'=12x^2-216x+720=0](https://tex.z-dn.net/?f=V%27%3D12x%5E2-216x%2B720%3D0)
Simplifying by 12
![x^2-18x+60=0](https://tex.z-dn.net/?f=x%5E2-18x%2B60%3D0)
Completing squares
![x^2-18x+81-81+60=0](https://tex.z-dn.net/?f=x%5E2-18x%2B81-81%2B60%3D0)
![(x-9)^2=21](https://tex.z-dn.net/?f=%28x-9%29%5E2%3D21)
We have two values for x
![x=9+\sqrt{21}=13.58\ inch](https://tex.z-dn.net/?f=x%3D9%2B%5Csqrt%7B21%7D%3D13.58%5C%20inch)
![x=9-\sqrt{21}=4.42\ inch](https://tex.z-dn.net/?f=x%3D9-%5Csqrt%7B21%7D%3D4.42%5C%20inch)
The first value is not feasible because it will produce a negative width (24-2(13.58))=-6.16
We'll keep only the solution
![x=4.42\ inch](https://tex.z-dn.net/?f=x%3D4.42%5C%20inch)
The width is
![w=(24-2(4.42))=15.16\ inch](https://tex.z-dn.net/?f=w%3D%2824-2%284.42%29%29%3D15.16%5C%20inch)
The length is
![l=(30-2(4.42))=21.16\ inch](https://tex.z-dn.net/?f=l%3D%2830-2%284.42%29%29%3D21.16%5C%20inch)
And the height
![x=4.42\ inch](https://tex.z-dn.net/?f=x%3D4.42%5C%20inch)
The maximum volume is
![V=(15.16)(21.16)(4.42)=1417.87\ inch^3](https://tex.z-dn.net/?f=V%3D%2815.16%29%2821.16%29%284.42%29%3D1417.87%5C%20inch%5E3)
Answer:
Explanation:
In physics, work can be described as force multiplied by the displacement of the object (distance caused by the force acted on the object).
Work is a form of energy, therefore, it is measured in joules.
If Alex pushed on an object with 10N of force, and the object moved 2 meters, the work of Alex will be equal to:
W = Ft
W = 10N * 2m
W = 20 Joules
But, if we have John, that pushed on an object with 2N of force, but, since the object was way smaller, therefore it had way less inertia, the object moved a distance equal to 10 meters. Let's also calculate his work.
W = Ft
W = 2N * 10m
W = 20 Joules
And we got the same result.
Work can also be used to calculate power.
Power is equal to P = Work / time
It can also be written as P = delta Work / delta time
Power is measured in joules per second.
With power you can make the difference between someone that got a 2 kg object up in 2 second, and someone that got a 2 kg object up in 5 second.
The more powerful one would be the one who managed to make the same work in less time.
Hope it Helped!