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TiliK225 [7]
3 years ago
10

Spinning a loop of wire between the poles of a magnet will induce an electric current. Which of the following conditions will mi

nimize the induced current? 1. The plane of the loop is perpendicular to the magnetic field 2. The plane of the loop is halfway between parallel and perpendicular 3. The plane of the loop is parallel to the magnetic field 4. The magnetic flux through the wire is minimized
Mathematics
1 answer:
Rina8888 [55]3 years ago
6 0
By definition, electromagnetic induction is the term that is generally used to describe the method of generating a potential difference across a conductor through a changing magnetic field. In addition, the induce current would be minimised if the loop is placed parallel to the magnetic field itself. Therefore, C. 
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A cone-shaped paper drinking cup is to be made to hold 27 cm of water. Find the height h and radius r of the cup that will use t
andreyandreev [35.5K]

Answer:

  • r = 2.632 cm
  • h = 3.722 cm

Step-by-step explanation:

The formula for the volume of a cone of radius r and height h is ...

  V = (1/3)πr²h

Then r² can be found in terms of h and V as ...

  r² = 3V/(πh)

The lateral surface area of the cone is ...

  A = (1/2)(2πr)√(r² +h²) = πr√(r² +h²)

The square of the area is ...

  T = A² = π²r²(r² +h²)

Substituting for r² using the expression above, we have ...

  T = π²(3V/(πh))((3V/(πh) +h²) = 9V²/h² +3πVh

We want to find the minimum, which we can do by setting the derivative to zero.

  dT/dh = -18V²/h³ +3πV

This will be zero when ...

  3πV = 18V²/h³

  h³ = 6V/π . . . . . multiply by h³/(3πV)

For V = 27 cm³, the value of h that minimizes paper area is ...

  h = 3∛(6/π) ≈ 3.7221029

The corresponding value of r is ...

  r = √(3V/(πh)) = 9/√(π·h) ≈ 2.6319242

The optimal radius is 2.632 cm; the optimal height is 3.722 cm.

_____

The second derivative test applied to T finds that T is always concave upward, so the value we found is a minimum.

__

Interestingly, the ratio of h to r is √2.

8 0
3 years ago
Find $y$ if the point $(-6,y)$ is on the line that passes through $(-1,7)$ and $(3,-2)$.
vichka [17]

Answer:

  y = 18.25

Step-by-step explanation:

The 2-point form of the equation of a line can be used to write the equation of the line through the given points.

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  y = (-2 -7)/(3 -(-1))(x -(-1)) +7

  y = -9/4(x +1) +7

For x = -6 this evaluates to ...

  y = -9/4(-6 +1) +7 = (9/4)(5) +7 = 45/4 +7

  y = 18 1/4

6 0
3 years ago
Micheal used addition to find 9x100 and he said the product was 90. What did he do wrong?
Vlada [557]

Answer:

He did 9 times 10 instead of 9 times 100.

8 0
2 years ago
State the domain of the rational function. f(x) = seventeen divided by quantity five minus x
alexandr1967 [171]

If we are going to write the equation in its mathematical form, we will see that it becomes,

<span>                                        f(x) = 17/(x – 5)</span>

The domain of the function is the number of x that would allow us to solve the equation and get a real value for f(x). In this equation, x can take any real numbers so long as it is not 5. This is because 5 – 5 in the denominator will lead to 0 which in turn makes the equation indefinite.

<span> </span>

4 0
3 years ago
Help me please Thanks
Klio2033 [76]
The answer is 1;3 because if you simplified 2;6 you get 1;3 so the answer to that is
a: 1;3
4 0
3 years ago
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