When two bodies are charged, the total charge before and after charging remains the same because of:

The sound intensity of a certain type of food processor in normally distributed with standard deviation of 2.9 decibels. If the

Maru [420]

Answer: $(48.41,\ 52.19)$

Explanation:

The confidence interval for population mean is given by :-

$\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}$

Given : Sample size : $n=9$

Sample mean : $\ovreline{x}=50.3\text{ decibels}$

Standard deviation : $\sigma=2.9\text{ decibels }$

Significance level : $\alpha=1-0.95=0.05$

Critical value : $z_{\alpha/2}=z_{0.025}=1.96$

Now, the 95% confidence interval estimate of the (true, unknown) mean sound intensity of all food processors of this type :-

$50.3\pm (1.96)\dfrac{2.9}{\sqrt{9}}\\\\\approx50.3\pm1.89\\\\=(50.3-1.89,\ 50.3+1.89)=(48.41,\ 52.19)$

6 0

3 years ago

The earth exerts a force of 1.00 newtons on an object in free fall. what is the objects mass?

ICE Princess25 [194]

On or near the surface of the Earth, 1 newton is the weight of about 102 grams of mass.

Note that the gravitational force between the object and the Earth is always the
same. It doesn't matter whether the object is falling, flying, floating, fluttering,
rising, sinking, rolling, sliding, or just laying there. It doesn't change.

3 0

3 years ago

PLEASE HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP

frozen [14]

A. Since it does not say the ball is moving your answer is A.

4 0

3 years ago

At one instant a bicyclist is 21.0 m due east of a park's flagpole, going due south with a speed of 13.0 m/s. Then 21.0 s later,

andre [41]

Answer:

Part a)

$d = 21\sqrt2 = 29.7 m$

Part b)

Direction is 45 degree North of West

Part c)

$v_{avg} = 1.41 m/s$

Part d)

direction of velocity will be 45 Degree North of West

Part e)

$a = 0.875 m/s^2$

Part f)

$\theta = 45 degree$ North of East

Explanation:

Initial position of the cyclist is given as

$r_1 = 21.0 m$ due East

final position of the cyclist after t = 21.0 s

$r_2 = 21.0 m$ due North

Part a)

for displacement we can find the change in the position of the cyclist

so we have

$d = r_2 - r_1$

$d = 21\hat j - 21\hat i$

so magnitude of the displacement is given as

$d = 21\sqrt2 = 29.7 m$

Part b)

direction of the displacement is given as

$\theta = tan^{-1}\frac{y}{x}$

$\theta = tan^{-1}\frac{21}{-21}$

so it is 45 degree North of West

Part c)

For average velocity we know that it is defined as the ratio of displacement and time

so here the magnitude of average velocity is defined as

$v_{avg} = \frac{\Delta x}{t}$

$v_{avg} = \frac{29.7}{21}$

$v_{avg} = 1.41 m/s$

Part d)

As we know that average velocity direction is always same as that of average displacement direction

so here direction of displacement will be 45 Degree North of West

Part e)

Here we also know that initial velocity of the cyclist is 13 m/s due South while after t = 21 s its velocity is 13 m/s due East

So we have

change in velocity of the cyclist is given as

$\Delta v = v_f - v_i$

$\Delta v = 13\hat i - (-13\hat j)$

now average acceleration is given as

$a = \frac{\Delta v}{\Delta t}$

$a = \frac{13\hat i + 13\hat j}{21}$

so the magnitude of acceleration is given as

$a = \frac{13\sqrt2}{21} = 0.875 m/s^2$

Part f)

direction of acceleration is given as

$\theta = tan^{-1}\frac{y}{x}$

$\theta = tan^{-1}\frac{13}{13}$

$\theta = 45 degree$ North of East

4 0

3 years ago

A 0.15-kg apple falls off a tree branch that is 2.8 m above the thick grass. The apple sinks 0.066 m into the grass while stoppi

Soloha48 [4]

Answer:

F = 62.4 N

Explanation:

We must solve this problem in two parts, the first with energy to find the speed with which it reaches the grass and with impulse to determine the strength in the grass

Let's look for the speed of arrival to the grass, write the energy in two points

Initial

Em₀ = U = m g h

Point 2, just by touching the grass

Em₂ = K = ½ m v²

Em₀ = Em₂

m g h = ½ m v²

v = √ 2gh

v = √( 2 9.8 2.8)

v = 7.4 m/s

Let's calculate the momentum until it stops

I = F t = m vf -m v₀

I = 0-0.15 (-7.4)

I = 1.11 N s

We must find the time during which the apple stops, let's use kinematics to find the average acceleration

$v_{f}$ = v = 7.4 m/s

$v_{f}$ ² = v₀² + 2 a y

0 = v₀² + 2 a y

a = v₀² / 2y

a = 7.4²/2 0.066

a = 414.85 m / s²

Now let's look for the time to stop with this acceleration

$v_{f}$ = v₀ + at

0 = v₀ + at

t = v₀ / a

t = 7.4 / 414.85

t = 0.0178 s

Let's calculate with the momentum

I = F t

F = I / t

F = 1.11 / 0.0178

F = 62.4 N

8 0

3 years ago