Question 8 a-e plz

Question 8 A-e Plz

Answers

Answer 1

Answer:

(a) t = 0 s

(b) t = 0 s, 30 s, 55 s

(c) t = 40 s to t = 60 s

(d) t = 10 s to t = 15 s

(e) a = 6 m/s^2

Explanation:

(a) The car is at starting position at t = 0 s and v = 0 m/s.

(b) The velocity of car is zero when the time is t = 0 s, 30 s and 55 s.

(c) from t = 40 s to 60 s the car is moving in the negative direction.

(d) The fastest speed is 60m/s from t = 10 s to t = 15 s.

(e) The slope of the velocity time graph gives acceleration.

a = (60 - 0) / (10 - 0) = 6 m/s^2


Related Questions

Question 3 of 10
Which statement describes the law of conservation of energy?
A. Air resistance has no effect on the energy of a system.
B. Energy cannot be created or destroyed.
C. The total energy in a system can only increase.
D. Energy cannot change forms.
هما
SUBMIT

Answers

Answer:

B . energy cannot be created or destroyed

recognizing forms of energy

Answers

Answer:

hi the question isn't obvious and need a photo I guess

The question is missing

Why is the force of attraction between the Earth and ourselves so huge compared to the attraction between two apples?

Answers

Answer:

Answer in explanation

Explanation:

The force of attraction between two bodies is governed by Newton's Law of Gravitation:

[tex]F = \frac{Gm_1m_2}{r^2}[/tex]

where,

G = Universal Gravitational Constant

m₁ = mass of the first body

m₂ = mass of the second body

r = distance between the two bodies

F = Force

Hence, it is clear from the formula that the magnitude of the force is directly proportional to the product of the masses of the objects. So in the case of the earth and ourselves, the mass of the earth is very large in order of 10²⁴ kg. Due to this huge mass, the attraction between the earth and ourselves is so huge as compared to the attraction between two apples. Because the masses of the apple are very small in grams.

What word chemical equation describes this chemical reaction?

Answer : sodium + chlorine → sodium chloride

Answers

Sodium + chlorine = sodium chloride

What is (a) the x component and (b) the y component of the net electric field at the square's center

Answers

Answer:

What is (a) the x component and (b) the y component of the net electric field at the square's center

A ​12.5-m fire truck ladder is leaning against a wall. Find the distance d the ladder goes up the wall​ (above the fire​ truck) if the ladder makes an angle of with the horizontal

Answers

Complete Question

A 12.5-m fire truck ladder is leaning against a wall. Find the distance d the ladder goes up the wall​ (above the fire​ truck) if the ladder makes an angle of  

40° 16' with the horizontal.

Answer:

 [tex]d=8.01m[/tex]

Explanation:

From the question we are told that:

Length of ladder [tex]l=12.5m[/tex]

Angle [tex]\theta=40° 16'=20.26 \textdegree[/tex]

Generally the Trigonometric equation for distance d it goes up the wall is mathematically given by

 [tex]d=l sin \theta[/tex]

 [tex]d=12.5 sin 40.26[/tex]

 [tex]d=8.01m[/tex]

A particle of mass 1.2 mg is projected vertically upward from the ground with a velocity of 1.62 x 10 cm/h. Use the above information to answer the following four questions: 7. The kinetic energy of the particle at time t = 0 s is A. 1.215 x 10-3 J B. 2.430 J C. 1215 J D. 9.72 x 106 J E. OJ (2)​

Answers

Answer:

K = 0 J

Explanation:

Given that,

The mass of the particle, m = 1.2 mg

The speed of the particle, [tex]v=1.62\times 10\ cm/h[/tex]

We need to find the kinetic energy of the particle at time t = 0 s.

At t = 0 s, the particle is at rest, v = 0

So,

[tex]K=\dfrac{1}{2}mv^2[/tex]

If v = 0,

[tex]K=0\ J[/tex]

So, the kinetic energy of the particle at time t = 0 s is 0 J.

Part AFind the x- and y-components of the vector d⃗ = (4.0 km , 29 ∘ left of +y-axis).Express your answer using two significant figures. Enter the x and y components of the vector separated by a comma.d⃗ = km Part BFind the x- and y-components of the vector v⃗ = (2.0 cm/s , −x-direction).Express your answer using two significant figures. Enter the x and y components of the vector separated by a comma.v⃗ = cm/s Part CFind the x- and y-components of the vector a⃗ = (13 m/s2 , 36 ∘ left of −y-axis).Express your answer using two significant figures. Enter the x and y components of the vector separated by a comma.a⃗ x = m/s2

Answers

Solution :

Part A .

Given : The [tex]x[/tex] and [tex]y[/tex] components of the vector, d = [tex]\text{4 km 29}[/tex] degree left of [tex]y[/tex]-axis.

So the [tex]x[/tex] component is = -4 x sin (29°) = -1.939 km

           [tex]y[/tex] component is = 4 x cos (29°) = 3.498 km

Part B

Given : The [tex]x[/tex] and [tex]y[/tex] components of the vector, [tex]\text{v = 2 cm/s}[/tex] , [tex]\text{-x direction}[/tex]

So the [tex]x[/tex] component is = -2 cm/s

           [tex]y[/tex] component is = 0

Part C

Given : The [tex]x[/tex] and [tex]y[/tex] components of the vector, [tex]\text{a = 13 m/s, 36 degree}[/tex] left of [tex]y[/tex]-axis.

So the [tex]x[/tex] component is = -13 x sin (36°) = -7.6412 [tex]m/S^2[/tex]

           [tex]y[/tex] component is = -13 x cos (36°) = -10.517 [tex]m/S^2[/tex]

The x- and y-components of the vectors  is mathematically given as as follows for each Part respectively

x= -1.939 km, y= 3.498 km

x= -2 cm/s, 0

y=, x= -7.6412m/s^2, -10.517m/s^2

What are the x- and y-components of the vectors?

Question Parameters:

Generally, we follow a basic principle where

x component= Fsin\theta

y component= Fcos\theta

Therefore

For A

x component is

x= -4 x sin (29°)

x= -1.939 km

 y component is

y= 4 x cos (29°)

y= 3.498 km

For B

x component is

x= -2 cm/s            

y component is

y= 0

For C

x component is

x= -13 x sin (36°)

x= -7.6412m/s^2      

y component is

y= -13 x cos (36°)

y= -10.517m/s^2  

Read more about Cartession co ordinate

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A uniform 1500-kg beam, 20.0 m long, supports a 15,000-kg printing press
5.0 m from the right support column (Figure slide 8). Calculate the force
on each of the vertical support columns.

Answers

Answer:

[tex]\mathbf{F_1=4.41*10^4\ N}[/tex]

[tex]\mathbf{F_2 = 1.176*10^5 \ N}[/tex]

Explanation:

The missing image of the figure slide is attached in below.

However, from the model, it is obvious that it is in equilibrium.

As a result, the relation of the force and the torque is said to be zero.

i.e.

[tex]\sum F = 0[/tex] and [tex]\sum \tau = 0[/tex]

From the image, expressing the forces through the y-axis, we have:

[tex]F_1+F_2 = W_B + W_P \\ \\ \implies 9.8(1500+15000) \\ \\ \implies \mathtt{1.617\times 10^5 \ N}[/tex]

Also, let the force [tex]F_1[/tex] be the pivot and computing the torque to determine [tex]F_2[/tex]:

Then:

[tex]F_1(0)+F_2(20.0) = 10.0W_B + 15.0W_P[/tex]

[tex]F_2 = \dfrac{((10*1500)+(15*15000))*9.8}{20.0}[/tex]

[tex]F_2 = 117600 \ N[/tex]

[tex]\mathbf{F_2 = 1.176*10^5 \ N}[/tex]

For the force equation:

[tex]F_1+F_2=1.617*10^5 \ N;[/tex]

where:

[tex]F_2 = 1.176*10^5 \ N[/tex]

Then:

[tex]F_1+1.176*10^5 \ N=1.617*10^5 \ N[/tex]

[tex]F_1=1.617*10^5 \ N-1.176*10^5 \ N[/tex]

[tex]F_1=44100\ N[/tex]

[tex]\mathbf{F_1=4.41*10^4\ N}[/tex]

12) If, after viewing a specimen at low power, you switch to high-dry power and, after using fine focus, cannot find the specimen, what things could you do to help yourself (before calling me over to assist you?)

Answers

Answer:

See the answer below

Explanation:

After seeing an object on a slide at the low-power objective of the microscope and it disappears on changing to high power, the following can be done to resolve the problem

1. Drop a few drops of immersion oil on the slide and view again under high the power objective.

2. If the object is still not visible after the action above, return the microscope to the low-power objective and make sure the object is refocused and centered. Then carefully change back to the high power objective and use the fine adjustment to bring it into focus.

Three 30 g metal balls, one of aluminum, copper and lead, are placed in a large beaker of hot water for a few minutes. [The specific heats of aluminum, copper, and lead are 903, 385, and 130 J / (kg ° C), respectively].
to. Which of the balls, if any, will reach the highest temperature? Explain.
b. Which of the balls, if any, will have the most heat energy? Explain.

Answers

Answer:

The answer is below

Explanation:

Specific heat capacity is an intensive property of a material. The specific heat of a material is the amount of energy required to raise the temperature of one unit mass m of material by one unit of temperature.

a) Temperature is inversely proportional to specific heat capacity. If the same amount of heat is applied to all three balls, the ball that will reach the highest temperature is the ball with the least specific heat capacity.

Hence lead will have the highest temperature since it has the least specific heat capacity.

b) The quantity of heat is directly proportional to the specific heat capacity. Hence if all balls experience the same temperature change, the ball that have the most energy will be that with the highest specific heat capacity.

Hence aluminum will have the most heat since it has the highest specific heat capacity.

Every object around you is attracted to you. In fact, every object in the galaxy is attracted to every other object in the galaxy.

a. True
b. False

Answers

Answer:

True

Explanation:

With the gravitational pull that our planets have, we are able to remain in orbit. This demonstrates how every object in the galaxy is attracted to every other object. Every object in the universe that has mass exerts a gravitational pull on every other mass. We as humans do it too, but since our force isn't strong, we don't have much of an effect. I hope this helped and please don't hesitate to reach out with more questions!

The velocity-time graph of a body is given. What quantities are represented by (a) slope of the graph and (b) area under the graph?​

Answers

Answer:

a) acceleration

b) displacement

Explanation:

The velocity-time graph is a graph of velocity versus time. The velocity (m/s) would be on the Y-axis while time (s) would be on the X-axis.

a) The slope of a graph is given by: change in Y-axis/change in X-axis = ΔY/ΔX

In a velocity-time graph, ΔY = change in velocity and ΔX = change in time.

Hence, the slope of a velocity-time graph becomes: change in velocity/change in time.

Also, acceleration = change in velocity/change in time.

Hence, the slope of a velocity-time graph = acceleration.

b) Assuming that the area under a velocity-time graph is a rectangle, the area is given as:

Area of a rectangle = length x breadth

                                  = velocity x time (m/s x s)

Also, displacement = velocity x time (m)

Hence, the area under a velocity-time graph of a body would give the displacement of the body.

how much amount of heat energy is required to convert 5 kg of ice at - 5° c into 100°c steam?​

Answers

Assuming no heat lost to the surrounding,

-5⁰C ice → 0⁰C ice

Specific heat capacity of ice = 2.0 x 10³ J/kg/⁰C

Q = mc∆θ

Q = 5(2.0 x 10³) x (0-(-5))

Q = 50000J

0⁰C ice → 0⁰C water

Specific latent heat of fusion of ice = 3.34 x 10⁵J/kg

Q = mLf

Q = 5(3.34 x 10⁵)

Q = 1670000J

0⁰C water → 100⁰C water

Specific heat capacity of water = 4.2 x 10³ J/kg/⁰C

Q = mc∆θ

Q = 5(4.2 x 10³) x (100-0)

Q = 2100000J

100⁰C water → 100⁰C steam

Specific latent heat of vaporization of water = 2.26 x 10⁶ J/kg

Q = mLv

Q = 5(2.26 x 10⁶)

Q = 11300000J

Total amount of heat required

= 50000 + 1670000 + 2100000 + 11300000

= 15120000J

Explain what a circuit breaker is and how it helps protect your house?

Answers

Explanation:

A circuit breaker is an electrical switch designed to protect an electrical circuit from damage caused by overcurrent/overload or short circuit. Its basic function is to interrupt current flow after protective relays detect a fault.

Circuit breakers have been designed to detect when there is a fault in the electricity, so it will “trip” and shut down electrical flow. ... This detection is key to preventing surges of electricity that travel to appliances or other outlets, which can cause them to break down

As you move farther away from a source emitting a pure tone, the ___________ of the sound you hear decreases.

Answers

Answer:

frequency

Explanation:

The phenomenon of apparent change in frequency due to the relation motion between the source and the observer is called Doppler's effect.

So, when we move farther, the frequency of sound decreases. The formula of the Doppler's effect is  

[tex]f' = \frac{v + v_o}{v+ v_s} f[/tex]

where, v is the velocity of sound, vs is the velocity of source and vo is the velocity of observer, f is the true frequency. f' is the apparent frequency.

A block of mass M is connected by a string and pulley to a hanging mass m. The coefficient of kinetic friction between block M and the table is 0.2, and also, M = 20 kg, m = 10 kg. How far will block m drop in the first seconds after the system is released?
How long will block M move during above time?
At the time, calculate the velocity of block M
Find out the deceleration of the block M, if the connected string is
removal by cutting after the first second. Then, calculate the time
taken to contact block M and pulley.

Answers

Answer:

a)  y = 0.98 t², t=1s y= 0.98 m,  

b) he two blocks must move the same distance

c) v = 1.96 m / s,  d)  a = -1.96 m / s², e)  x = 0.98 m

Explanation:

For this exercise we can use Newton's second law

Big Block

Y axis

             N-W = 0

             N = M g

X axis

             T- fr = Ma

the friction force has the expression

             fr = μ N

             fr = μ Mg

small block

             w- T = m a

             

we write the system of equations

             T - fr = M a

             mg - T = m a

we add and resolved

             mg-  μ Mg = (M + m) a

             a = [tex]g \ \frac{m - \mu M}{m+M}[/tex]

             a = [tex]9.8 \ \frac{10- 0.2 \ 20}{ 10 \ +\ 20}[/tex]

             a = 9.8 (6/30)

             a = 1.96 m / s²

a) now we can use the kinematic relations

             y = v₀ t + ½ a t²

the blocks come out of rest so their initial velocity is zero

             y = ½ a t²

             y = ½ 1.96 t²

             y = 0.98 t²

for t = 1s y = 0.98 m

       t = 2s y = 1.96 m

b) Time is a scale that is the same for the entire system, the question should be oriented to how far the big block will move.

As the curda is in tension the two blocks must move the same distance

c) the velocity of the block M

           v = vo + a t

           v = 0 + 1.96 t

for t = 1 s v = 1.96 m / s

       t = 2 s v = 3.92 m / s

d) the deceleration if the chain is cut

when removing the chain the tension becomes zero

           -fr = M a

          - μ M g = M a

          a = - μ g

          a = - 0.2 9.8

          a = -1.96 m / s²

e) the distance to stop the block is

         v² = vo² - 2 a x

        0 = vo² - 2a x

        x = vo² / 2a

        x = 1.96² / 2 1.96

        x = 0.98 m

the time to travel this distance is

        v = vo - a t

        t = vo / a

        t = 1.96 /1.96

        t = 1 s

A tire is filled with air at 22oC to a gauge pressure of 240 kPa. After driving for some time, if the temperature of air inside the tire is 45oC, what fraction of the original volume of air must be removed to maintain the pressure at 240 kPa?

Answers

Answer:

7.8% of the original volume.

Explanation:

From the given information:

Temperature [tex]T_1[/tex] = 22° C = 273 + 22 = 295° C

Pressure [tex]P_1[/tex] = 240 kPa

Temperature [tex]T_2[/tex] = 45° C

At initial temperature and pressure:

Using the ideal gas equation:

[tex]P_1V_1 =nRT_1[/tex]

making V_1 (initial volume) the subject:

[tex]V_1 = \dfrac{nRT_1}{P_1}[/tex]

[tex]V_1 = \dfrac{nR*295}{240}[/tex]

Provided the pressure maintained its rate at 240 kPa, when the temperature reached 45° C, then:

the final volume [tex]V_2[/tex] can be computed as:

[tex]V_2 = \dfrac{nR*318}{240}[/tex]

Now, the change in the volume ΔV =  V₂ - V₁

[tex]\Delta V = \dfrac{nR*318}{240}- \dfrac{nR*295}{240}[/tex]

[tex]\Delta V = \dfrac{23nR}{240}[/tex]

The required fraction of the volume of air to keep up the pressure at (240) kPa can be computed as:

[tex]= \dfrac{\dfrac{23nR}{240}}{ \dfrac{295nR}{240}}[/tex]

[tex]= {\dfrac{23nR}{240}} \times { \dfrac{240}{295nR}}[/tex]

[tex]= 0.078[/tex]

= 7.8% of the original volume.

The Lamborghini Huracan has an initial acceleration of 0.85g. Its mass, with a driver, is 1510 kg. If an 80 kg passenger rode along, what would the car's acceleration be?​

Answers

Answer:

7.9 [tex]\frac{m}{s^{2} }[/tex]

Explanation:

Take the fact that mass is inversely proportional to accelertation:

m ∝ a

Therefore m = a, but because we are finding the change in acceleration, we would set our problem up to look more like this:

[tex]\frac{m_{1} }{m_{2} } = \frac{a_{2} }{a_{1} } \\[/tex]

Using algebra, we can rearrange our equation to find the final acceleration, [tex]a_{2}[/tex]:

[tex]a_{2} = \frac{a_{1}*m_{1} }{m_{2} } \\[/tex]

Before plugging everything in, since you are being asked to find acceleration, you will want to convert 0.85g to m/s^2. To do this, multiply by g, which is equal to 9.8 m/s^2:

0.85g * 9.8 [tex]\frac{m }{s^{2} }[/tex] = 8.33 [tex]\frac{m }{s^{2} }[/tex]

Plug everything in:

7.9 [tex]\frac{m }{s^{2} }[/tex] = [tex]\frac{ 8.33\frac{m}{s^{2} }*1510kg }{1590kg}[/tex]

(1590kg the initial weight plus the weight of the added passenger)

A TV satellite dish is designed to receive radio waves of wavelength
0.0644 meters. What is the frequency of the waves it receives? _______GHz

Give your answer in gigahertz (GHz). 1 GHz = 10^9 Hz.

Give your answer to the nearest tenth of a GHz (one place after the decimal). Just enter the number; do NOT use scientific notation.

Answers

Answer:

4.7 GHz

Explanation:

Applying,

v = λf................. Equation 1

Where v = velocity of the radio wave, λ = wavelength, f = frequency

make f the subject of the equation

f = v/λ.............. Equation 2

Note: A radio wave is an electromagnetic wave, as such it moves with a velocity of 3.00 x 10⁸ m/s

From the question,

Given: λ = 0.0644 meters

Constant: v = 3.00 x 10⁸ m/s

Substitute these values into equation 2

f = (3.00 x 10⁸)/0.0644

f = 4.66×10⁹ Hz

f = 4.7 GHz

write down the following units in the ascending of their value A) mm nm cm um B) 1m 1cm 1km 1mm. convert the following units into SI without changing their values? A)3500g B)2.5km C)2h​

Answers

Answer:

A) nm, um, mm, cm

B) 1mm, 1cm, 1m, 1km

A) 3500g, B) 2500m, C) 7200 seconds

When a rigid body rotates about a fixed axis, all the points in the body have the same Group of answer choices linear displacement. angular acceleration. centripetal acceleration. tangential speed. tangential acceleration.

Answers

Answer:

angular acceleration.

Explanation:

Newton's law of universal gravitation states that the force of attraction (gravity) acting between the Earth and all physical objects is directly proportional to the Earth's mass, directly proportional to the physical object's mass and inversely proportional to the square of the distance separating the Earth's center and that physical object.

Generally, when a rigid body is made to rotate about a fixed axis, all the points in the body would typically have the same angular acceleration, angular displacement, and angular speed.

An unwary football player collides with a padded goalpost while running at a velocity of 7.50 m/s and comes to a full stop after compressing the padding and his body 0.350 m. (a) What is his deceleration

Answers

Answer:

a= -80.357 m/s

Explanation:

use the formula

vf^2=vi^2+2a(xf-xi)

Plug in givens

0=(7.50)^2+2a(0.350m)

solve for acceleration

a= -80.357 m/s

suppose the tank is open to the atmosphere instead of being closed. how does the pressure vary along

Answers

Answer:

Pressure is more in the open container than the closed one.

Explanation:

The pressure due to the fluid at a depth is given by

Pressure = depth x density of fluid x gravity

So, when the container is open, the atmospheric pressure is also add  up but when  the container is closed only the pressure due to the fluid is there.

So, when the container is open, the pressure is atmospheric pressure + pressure due to the fluid.

hen the container is closed only the pressure due to the fluid is there.

One hazard of space travel is the debris left by previous missions. There are several thousand objects orbiting Earth that are large enough to be detected by radar, but there are far greater numbers of very small objects, such as flakes of paint. Calculate the force exerted by a 0.100-mg chip of paint that strikes a spacecraft window at a relative speed of 4.00×10^3 m/s, given the collision lasts 6.00×10^8s.

Answers

Answer:

F = 6666.7 N

Explanation:

Given that,

Mass of a chip, m = 0.1 mg

Initial speed, u = 0

Final speed,[tex]v=4\times 10^{3}\ m/s[/tex]

Time of collision,[tex]t=6\times 10^{-8}\ s[/tex]

We know that,

Force, F = ma

Put all the values,

[tex]F=\dfrac{m(v-u)}{t}\\\\F=\dfrac{0.1\times 10^{-6}\times (4\times 10^3-0)}{6\times 10^{-8}}\\\\F=6666.7\ N[/tex]

So, the required force is 6666.7 N.

There are two beakers of water on the table. We can compare the average kinetic energy of the water molecules in the two beakers by measuring their

A temperatures.

B volumes.

C densities.

D masses.

Answers

Answer: masses

Explanation:

Trust me




A student claimed that thermometers are useless because a
thermometer always registers its own temperature. How would you
respond?
[

Answers

the thermometer is the temperature that is around it so its registering the temperature its supposed to

A hot air balloon is a sphere of volume 2210 m3. The density of the hot air inside is 1.13 kg/m3, while the air outside has a density of 1.29 kg/m3. The balloon itself has a mass of 240 kg. What is the TOTAL NET force acting on the balloon?
[?]N

Answers

The total net force acting on the balloon will be 24498 Newtons

Given that

Volume of the balloon = 2210 cubic meter

Density of the air inside the balloon = 1.13  kg/m3

What will be the net force exerted on the balloon ?

Here force on the balloon will be equal to the weight of the air displaced by balloon

[tex]F= mass of air displaced\times gravity[/tex]

[tex]F= Density \times volume \times gravity[/tex]

[tex]F=1.13 \times 2210 \times 9.81[/tex]

[tex]F=24498 N[/tex]

The total net force acting on the balloon will be 24498 Newtons

To know more about buoyancy force follow

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An inductor of inductance 0.02H and capacitor of capatance 2uF are connected in series to an a.c. source of frequency 200 Hz- Calculate the Impedance in the circuit . TC​

Answers

Explanation:

Given:

L = 0.02 H

C = [tex]2\:\mu \text{F}[/tex]

f = 200 Hz

The general form of the impedance Z is given by

[tex]Z = \sqrt{R^2 + (X_L - X_C)^2}[/tex]

Since this is a purely inductive/capacitive circuit, R = 0 so Z reduces to

[tex]Z = \sqrt{(X_L - X_C)^2} = \sqrt{\left(\omega L - \dfrac{1}{\omega C} \right)^2}[/tex]

[tex]\:\:\:\:\:\:\:= \sqrt{\left(2 \pi L - \dfrac{1}{2 \pi f C} \right)^2}[/tex]

[tex]\:\:\:\:\:\:\:= \sqrt{\left[2 \pi (200\:\text{Hz})(0.02\:\text{H}) - \dfrac{1}{2 \pi (200\:\text{Hz})(2×10^{-6}\:\text{F})} \right]^2}[/tex]

[tex]\:\:\:\:\:\:\:= \sqrt{(25.13\:\text{ohms} - 397.89\:\text{ohms})^2}[/tex]

[tex]\:\:\:\:\:\:\:=372.66\:\text{ohms}[/tex]

PLEASE HELP ME WITH THIS ONE QUESTION
The half-life of Barium-139 is 4.96 x 10^3 seconds. A sample contains 3.21 x 10^17 nuclei. How much of the sample is left after 1.98 x 10^4 seconds?

Answers

[tex]A=2.01×10^{16}\:\text{nuclei}[/tex]

Explanation:

Given:

[tex]\lambda = 4.96×10^3 s[/tex]

[tex]A_0 = 3.21x10^{17}[/tex] nuclei

t = 1.98×10^4 s

[tex]A=A_02^{-\frac{t}{\lambda}}[/tex]

[tex]A=(3.21×10^{17}\:\text{nuclei}) \left(2^{-\frac{1.98×10^4}{4.96×10^3}} \right)[/tex]

[tex]\:\:\:\:\:\:\:=2.01×10^{16}\:\text{nuclei}[/tex]

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