Which statement best describes what happens when more waves pass a certain point per second?

Carbon-14 is used to determine the time an organism was living. The amount of carbon-14 an organism has is constant with the atm

lutik1710 [3]

Answer:

The age of the organism is approximately 11460 years.

Explanation:

The amount of carbon-14 decays exponentially in time and is defined by the following equation:

$\frac{n(t)}{n_{o}} = e^{-\frac{t}{\tau} }$ (1)

Where:

$n_{o}$ - Initial amount of carbon-14.

$n(t)$ - Current amount of carbon-14.

$t$ - Time, measured in years.

$\tau$ - Time constant, measured in years.

Then, we clear the time within the formula:

$t = -\tau \cdot \ln \frac{n(t)}{n_{o}}$ (2)

In addition, time constant can be calculated by means of half-life of carbon-14 ( $t_{1/2}$ ), measured in years:

$\tau = \frac{t_{1/2}}{\ln 2}$

If we know that $\frac{n(t)}{n_{o}} = 0.25$ and $t_{1/2} = 5730\,yr$ , then the age of the organism is:

$\tau = \frac{5730\,yr}{\ln 2}$

$\tau \approx 8266.643\,yr$

$t = -(8266.643\,yr)\cdot \ln 0.25$

$t \approx 11460.001\,yr$

The age of the organism is approximately 11460 years.

8 0

3 years ago

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Suppose you want to design an air bag system that can protect the driver at a speed 100 km/h (60 mph) if the car hits a brick wa

34kurt

When solving question that contains equations and the use mathematical computations, It is always ideal to list the parameters given.

Now, given that:

the speed of the car which is the initial velocity (u) = 100 km/h before it hits the wall.
after hitting the wall, the final velocity will be (v) = 0 km/h

Assumptions:

Suppose we make an assumption that the distance travelled during the collision of the car with the brick wall (S) = 1 m
That the car's acceleration is also constant.

∴

For a motion under constant acceleration, we can apply the kinematic equation:

$\mathsf{v^2 = u^2 + 2as}$

where;

v = final velocity

u = initial velocity

a = acceleration

s = distance

From the above equation, making acceleration (a) the subject of the formula:

$\mathsf{v^2 - u^2 =2as }$

$\mathsf{a = \dfrac{v^2 - u^2 }{2s}}$

The initial velocity (u) is given in km/h, and we need to convert it to m/s as it has an effect on the unit of the acceleration.

since 1 km/h = 0.2778 m/s

100 km/h = 27.78 m/s

$\mathsf{a = \dfrac{(0)^2 - (27.78)^2 }{2(1)}}$

$\mathsf{a = \dfrac{- 771.7284 }{2}}$

a = - 385.86 m/s²

Similarly, from the kinematic equation of motion, the formula showing the relation between time, acceleration and velocity is;

v = u + at

where;

v = 0

-u = at

$\mathsf{t = \dfrac{-u}{a}}$

$\mathsf{t = \dfrac{-27.78}{-385.86}}$

t = 0.07 seconds

An airbag is designed in such a way as to prevent the driver from hitting on the steering wheel or other hard substance that could damage the part of the body. The use of the seat belt is to keep the driver in shape and in a balanced position against the expansion that occurred by the airbag during the collision on the brick wall.

Thus, we can conclude that the airbag must be inflated at 0.07 seconds faster before the collision to effectively protect the driver.

Learn more about the kinematic equation here:

brainly.com/question/11298125?referrer=searchResults

3 0

3 years ago

Rita jeptoo of kenya was the first female finisher in the 110th boston marathon. she ran the first 10.0 km in a time of 0.5689 h

stira [4]

Part a

Answer: 17.58 km/h

$Average speed=\frac{Total\hspace{1mm}Distance}{Total\hspace{1mm}Time}$