Coffee or certain cola drinks can be used to test the effect of __________ on reaction time. What drug completes the sentence?

At time t0 = 0 the mass happens to be at y0 = 4.05 cm and moving upward at velocity v0 = +4.12 m/s. (Mind the units!) Calculate

Katen [24]

Answer:

A = 5.727 cm

Explanation:

at time t = 0s the displacement of mass is 4.05 cm and velocity 4.12 m/s

we know that velcoity for simple harmonic motion is given as

$v_o = \omega \sqrt {A^2 - Y_O^2}$

W KNOW THAT

$\omega = \frac{v_0}{Y_o}$

Therefore we get

$Y_O^2 = A^2 - Y_O^2$

$A =\sqrt 2 * Y_O$

$A =\sqrt 2 * 4.05\\$

A = 5.727 cm

4 0

3 years ago

The temperature at the surface of the Sun is approximately 5,300 K, and the temperature at the surface of the Earth is approxima

N76 [4]

Answer:

The entropy change of the Universe that occurs is 19.346 J/K

Explanation:

Given;

temperature of the sun, $T_s$ = 5,300 K

temperature of the Earth, $T_E$ = 293 K

radiation energy transferred by the sun to the earth, E = 6000 J

The sun loses Q of heat and therefore decreases its entropy by the amount

$\delta S_{sun} = \frac{-Q}{T_s}$

The earth gains Q of heat and therefore increases its entropy by the amount

$\delta S_{Earth} = \frac{-Q}{T_E}$

The total entropy change is:

$\delta S_{Earth} + \delta S_{sun} = \frac{Q}{T_E} -\frac{Q}{T_S} \\\\ = Q(\frac{1}{T_E} -\frac{1}{T_S} )\\\\= 6000(\frac{1}{293} -\frac{1}{5300} )\\\\=6000(0.0032243)\\\\= 19.346 \ J/K$

Therefore, the entropy change of the Universe that occurs is 19.346 J/K

4 0

3 years ago

In a 35 mm single lens reflex camera (SLR) the distance from the lens to the film is varied in order to focus on objects at vary

Evgesh-ka [11]

Answer:

range of movement is 1.49 mm

Explanation:

given data

focal length = 45 mm

distance = 1.4 m

distance from the lens = 35 mm

distance from infinity down = 1.4 m =

to find out

range of movement

solution

we will apply here lens equation that is

1/f = 1/p + 1/q

here f = 45 and p = infinity to 1400 mm

we find here image distance that is q

1/45 = 0 + 1/q ......1

q = 45 mm

and

1/45 = 1/1400 + 1/q ......2

q = 46.49

so range of movement

that is 46.49 - 45

range of movement is 1.49 mm

8 0

3 years ago

Find a unit vector in the direction in which f increases most rapidly at P and give the rate of chance of f in that direction; f

Burka [1]

Answer:

Check attachment for complete question

Question

Find a unit vector in the direction in which

f increases most rapidly at P and give the rate of change of f

in that direction; Find a unit vector in the direction in which f

decreases most rapidly at P and give the rate of change of f in

that direction.

f (x, y, z) = x²z e^y + xz²; P(1, ln 2, 2).

Explanation:

The function, z = f(x, y,z), increases most rapidly at (a, b,c) in the

direction of the gradient and decreases

most rapidly in the opposite direction

Given that

F=x²ze^y+xz² at P(1, In2, 2)

1. F increases most rapidly in the positive direction of ∇f

∇f= df/dx i + df/dy j +df/dz k

∇f=(2xze^y+z²)i + (x²ze^y) j + (x²e^y + 2xz)k

At the point P(1, In2, 2)

Then,

∇f= (2×1×2×e^In2+2²)i +(1²×2×e^In2)j +(1²e^In2+2×1×2)

∇f=12i + 4j + 6k

Then, unit vector

V= ∇f/|∇f|

Then, |∇f|= √ 12²+4²+6²

|∇f|= 14

Then,

Unit vector

V=(12i+4j+6k)/14

V=6/7 i + 2/7 j + 3/7 k

This is the increasing unit vector

The rate of change of f at point P is.

|∇f|= √ 12²+4²+6²

|∇f|= 14

2. F increases most rapidly in the positive direction of -∇f

∇f=- (df/dx i + df/dy j +df/dz k)

∇f=-(2xze^y+z²)i - (x²ze^y) j - (x²e^y + 2xz)k

At the point P(1, In2, 2)

Then,

∇f= -(2×1×2×e^In2+2²)i -(1²×2×e^In2)j -(1²e^In2+2×1×2)

∇f=-12i -4j - 6k

Then, unit vector

V= -∇f/|∇f|

Then, |∇f|= √ 12²+4²+6²

|∇f|= 14

Then,

Unit vector

V=-(12i+4j+6k)/14

V= - 6/7 i - 2/7 j - 3/7 k

This is the increasing unit vector

The rate of change of f at point P is.

|∇f|= √ 12²+4²+6²

|∇f|= 14

6 0

4 years ago

Read 2 more answers

a flashlight bulb with a potential difference of 6.0 v across it has a resistance of 8.0 how much current is the bulb filament

Andreas93 [3]

Answer:

Explanation:

Ohm's law states that the current (I) through a conductor between two points is directly proportional to the voltage (V) across the two points. The constant of proportionality is called the Resistance (R) of the conductor.

The formula can be expressed as:

V = I.R

The intensity of the current through a resistor can be calculated by solving the equation for I:

$\displaystyle I=\frac{V}{R}$

A flashlight bulb is an example of a resistor with the specific task to emit light when it's hot enough.

The potential difference (or voltage) is V=6 V and the resistance is R=8Ω, thus the current is:

$\displaystyle I=\frac{6~V}{8~\Omega}$

I = 0.75 Amp

3 0

3 years ago