Is my answer correct?

A circular dartboard has a radius of 2 meters and a red circle in the center. Assume you hit the target at a random point. For w

Sati [7]

Answer:

1.549 m

Explanation:

Given:

The radius of the circular board, r = 2 m

The probability of hitting the red is given as 0.6

Now, this probability of hitting the red can be conclude as

0.6 = (Area of red)/ (Total area of the board)

Total area of the board = πr² = π × 2²

let the radius of the red area be R

thus, area of red circle, = πR²

on substituting the value of the area, we have

0.6 = (πR²)/ (π × 2²)

or

R² = 2.4

or

R = 1.549 m

Thus, the radius of the red circle is 1.549 m

3 0

2 years ago

a circular loop is hanging on the wall. it has a radius of 33.3 cm and is comprised of 12 coils. there is a magnetic field perpe

Vika [28.1K]

Answer:

I = 2.19A, anticlockwise direction.

Explanation:

Given r = 33cm = 0.33m, N = 12, ΔB = 7.5 - 1.5 = 6.0T, Δt = 3s, R = 3.75Ω

By Faraday's law of electromagnetic induction when there is a change in flux in a coil or loop, an emf is induced in the coil or loop which is proportional to the time rate of change of the magnetic flux through the loop.

The emf E is related to the flux by the formula

E = – NdФ/dt

Where N = number of turns in the coil, Ф = magnetic flux through the loop = BA, B = magnetic field strength, A = Area

In this problem the strength of the magnetic field changes. As a result the flux too changes and an emf is induced in the coil.

So

ΔФ = ΔB×A = ΔB×πr² = 6×π×0.33² = 2.05Wb

E = -NΔФ/Δt = 12×2.05/3 = 8.2V

I = E/R = 8.2/ 3.75 = 2.19A

The direction of the current can be found by pointing the thumb of your right hand in the direction of the magnetic field and curling the remaining fingers around this direction. The direction of the curl of these fingers give the direction of current which in this case is anticlockwise.

5 0

3 years ago

Unpolarizedlight of intensity I_0 is incident on three polarizingfilters. The axis of the first is vertical, that of the secondi

Marina86 [1]

To solve this problem it is necessary to apply the concepts related to the law of Malus which describe the intensity of light passing through a polarizer. Mathematically this law can be described as:

$I = I_0 cos^2\theta$

Where,

$I_0 =$ Indicates the intensity of the light before passing through the polarizer

I = Resulting intensity

$\theta$ = Indicates the angle between the axis of the analyzer and the polarization axis of the incident light

From the law of Malus when the light passes at a vertical angle through the first polarizer its intensity is reduced by half therefore

$I_1= \frac{I_0}{2}$

In the case of the second polarizer the angle is directly 60 degrees therefore

$I_2 = I_1 cos^2\theta$

$I_2 = (\frac{I_0}{2} ) cos^2(60)$

$I_2 = 0.125I_0$

In the case of the third polarizer, the angle is reflected on the perpendicular, therefore, its angle of index would be

$\theta_3 = 90-60 = 30$

Then,

$I_3 = I_2 cos^2\theta_3$

$I_3 = 0.125I_0 cos^2 (30)$

$I_3 = 0.09375I_0$

Then the intensity at the end of the polarized lenses will be equivalent to 0.09375 of the initial intensity.

5 0

2 years ago

michael kicks a ball at an angle if 36* horizontal. its initial velocity is 46 m/s. Find the maximum height it can reach, total

MAVERICK [17]

(a) At its maximum height, the ball's vertical velocity is 0. Recall that

${v_y}^2-{v_{0y}}^2=2a_y\Delta y$

Then at the maximum height $\Delta y=y_{\mathrm{max}}$ , we have

$-\left(\left(46\,\dfrac{\mathrm m}{\mathrm s}\right)\sin36^\circ\right)^2=2\left(-9.8\,\dfrac{\mathrm m}{\mathrm s^2}\right)y_{\mathrm{max}}$

$\implies y_{\mathrm{max}}=37\,\mathrm m$

(b) The time the ball spends in the air is twice the time it takes for the ball to reach its maximum height. The ball's vertical velocity is

$v_y=v_{0y}+a_yt$

and at its maximum height, $v_y=0$ so that

$0=\left(46\,\dfrac{\mathrm m}{\mathrm s}\right)\sin36^\circ+\left(-9.8\,\dfrac{\mathrm m}{\mathrm s}\right)t$

$\implies t=2.8\,\mathrm s$

which would mean the ball spends a total of about 5.6 seconds in the air.

(c) The ball's horizontal position in the air is given by

$x=v_{0x}t$

so that after 5.6 seconds, it will have traversed a displacement of

$x=\left(46\,\dfrac{\mathrm m}{\mathrm s}\right)\cos36^\circ(5.6\,\mathrm s)$

$\implies x=180\,\mathrm m$

3 0

2 years ago

Scientists _____. Select all that apply.

Annette [7]

The true answer is the choice A
Scientists can predict volcanic eruptions as long as adequate resources are available.Volcanic eruptions are one of the earthly activities which can be predicted by means of adequate resources (warming of the earth's crust, appearance of volcanic lava etc...). By contrast, earthquakes is a dangerous natural disaster that scientists cannot be predicted or mastering the time where it occurs.

5 0

3 years ago