A student dropped a textbook from the top floor of his dorm and it fell according to the formula s(t) = -16t2 + 8 underroot t, where t is the time in seconds and s(t) is the distance in feet from the top of the building. A) Write a formula for the average velocity of the ball for t near 4. B) Find the average velocity for the time interval beginning when t = 4 with duration 1 seconds, 0.5 seconds, and 0.05 seconds. C) What is your estimate for the instantaneous velocity of the ball at t = 4.

Answers

Answer 1

Answer:

Explanation:

s(t) = -16t2 + 8√t

A )

Average velocity

s(t) / t = (-16t2 + 8√t)/t

A(t)= -16t +  8 / √t

average velocity of the ball for t near 4.

A(t) =  -16t +  8 / √t

          Lt t⇒4

B )

Distance covered in 4 s

-16t2 + 8√t

= - 16 x 16 + 8 x 2

= - 240

Distance covered in 5 s

= - 16 x 25 + 8 √5

= -400 + 17.88

= -382.12

distance covered in duration from 4 to 5 sec

= -142.12

velocity = - 142.12 / 1 = - 142.12 m /s

Distance covered in 4.5 s

= -16 x 4.5² + 8√4.5

= -324 + 16.97

= -307

distance covered during 4 to 4.5

= 67

velocity during 4 to 4.5

= -67 / .5

- 134 m /s

distance covered in 4.05 s

-16 x 4.05² + 8√4.05

-262.44 + 16.1

-246.34

distance covered during 4 to 4.05

= -6.34

velocity during 4 to 4.05

= -6.34 / .05

- 126.8 m /s

C )

Instantaneous velocity at t = 4

= - 120 m /s

Answer 2

(A) As 't' approaches to 4s, the formula of average velocity is

[tex]v_{avg} _{|(t\rightarrow4)}=Lim_{|(t\rightarrow4)}[-16t+ \frac{8}{\sqrt{t}} ][/tex]

(B) The average velocity for the time interval starting at t = 4 with a duration of 1 second is [tex]142.11\,m/s[/tex].

The average velocity for the time interval starting at t = 4 with a duration of 0.5 seconds is [tex]-134.058\,m/s[/tex]

The average velocity for the time interval starting at t = 4 with a duration of 0.05 seconds is [tex]-126.8\,m/s[/tex].

(C) The instantaneous velocity of the ball at 4s is [tex]-126\,m/s[/tex].

The answers are explained as follows.

Given that the distance is a function of time.

[tex]s(t)=-16\,t^2\,+\,8\sqrt{t}[/tex]

(A) The average velocity can be given by,

[tex]v_{avg}=\frac{-16\,t^2\,+\,8\sqrt{t} }{t} =-16t+ \frac{8}{\sqrt{t}}[/tex]

As 't' approaches to 4s, the formula becomes;

[tex]v_{avg} _{|(t\rightarrow4)}=Lim_{|(t\rightarrow4)}[-16t+ \frac{8}{\sqrt{t}} ][/tex]

(B) We know that the average velocity or in this case speed is the total distance by the total time taken.

Distance covered in 4 s can be found by putting [tex]t=4s[/tex] in the distance formula.

[tex]s(4)=(-16\times16)+(8\times2)=-240\,m[/tex]

Distance covered in 5 s can also be found by the same method

[tex]s(5)=(-16\times25)+(8\times\sqrt{5} )=-382.11\,m[/tex]

Therefore, the distance covered in from 4 to 5 seconds is;

[tex]s(5) -s(4)=-382.11\,m-(-240\,m)=-142.11\,m[/tex]So, the average velocity here = [tex]\frac{-142.11\,m}{5\,s-4\,s}=-142.11\,m/s[/tex]

Distance covered in 4.5 s is given by,

[tex]s(4.5)=(-16\times4.5^2)+(8\times\sqrt{4.5} )=-307.029\,m[/tex]

Therefore, the distance covered in 4 to 4.5 seconds is;

[tex]s(4.5)-s(4)=-307.029\,m-(-240\,m)=67.029\,m[/tex]

So, the average velocity here = [tex]\frac{-67.029\,m}{4.5\,s-4\,s}=-134.058\,m/s[/tex]

Distance covered in 4.05 s is given by,

[tex]s(4.05)=(-16\times4.05^2)+(8\times\sqrt{4.05} )=-246.34\,m[/tex]

Therefore, the distance covered in 4 to 4.05 seconds is;

[tex]s(4.05)-s(4)=-246.34\,m-(-240\,m)=-6.34\,m[/tex]

So, the average velocity here = [tex]\frac{-6.34\,m}{4.05\,s-4\,s}=-126.8\,m/s[/tex]

(C) The instantaneous velocity of the ball can be found by differentiating the function [tex]s(t)[/tex].

[tex]v(t)=\frac{ds(t)}{dt} =\frac{d}{dt}(-16\,t^2\,+\,8\sqrt{t})=-32t+\frac{4}{\sqrt{t} }[/tex]For the instantaneous velocity of the ball at 4s, substitute [tex]t=4\,s[/tex] in the above equation.

[tex]v(t)=(-32\times4)+\frac{4}{2}=-126\,m/s[/tex]

Learn more about finding the velocity at a given time here:

https://brainly.com/question/17174392?referrer=searchResults


Related Questions

which is an accurate description of what occurs when a log burns

Answers

Answer:

charcoal

Explanation:

Answer:

charcoal

Explanation:

Mark as Brainliest

A model rocket accelerates upward from the ground with a constant acceleration, reaching a height of 50 m in 8 s.What is the speed (in m/s) at a height of 50 m?A: 1.07×101 B: 1.25×101 C: 1.46×101 D: 1.71×101 E: 2.00×101

Answers

Answer:

The  value is  [tex]v =  12.5 \  m/s[/tex]

Explanation:

From the question we are told that

    The  height is  [tex]h  =  50 \  m[/tex]

    The  time taken is  [tex]t =  8 \ s [/tex]

   

From the equation of motion we have  that

 [tex]s =  ut + \frac{1}{2}  * a * t^2[/tex]

Here u = 0  because the rocket started at rest

  [tex]50 =  0 + \frac{1}{2} * a  * 8^2[/tex]

=>   [tex]a =  \frac{100}{64}[/tex]

=>    [tex]a =  1.5625 \ m/s^2[/tex]

Also from the kinematic equation we have that

    [tex]v  =  u + at[/tex]

=>  [tex]v =  0 +  (8  *  1.5625)[/tex]

=>   [tex]v =  12.5 \  m/s[/tex]

       

If you want to replicate another scientist's experiment, which sections of their laboratory report will provide you with the most valuable information?

Answers

If research results can be replicated, it means they are more likely to be correct. Replication is important in science so scientists can “check their work.” The result of an investigation is not likely to be well accepted unless the investigation is repeated many times and the same result is always obtained.

A sound wave is observed to travel through a liquid with a speed of 1400 m/s. The specific gravity of the liquid is 1.8.
Determine the bulk modulus for this fluid.

Answers

Answer:

21

Explanation:

I think its 21 because its 21

What two processes are involved in the formation of Earth’s magnetic field?

Answers

Answer:

i. Geodynamo

ii. Gravitational energy conversion

Explanation:

The outer core of the Earth is believed to be in molten form, consisting of mainly iron and nickel. The reaction (mixture) between these components or elements generates conventional currents which is maintained by the gravitational energy produced in the process. Thus, magnetic fields are generated continuously due to the continuous flow of electric current during the processes.

Two vectors of magnitudes |A| = 8 units and |B| = 5 units make an angle that can vary from 0° to 180°. The magnitude of the resultant vector A + B CANNOT have the value of:

Answers

The question is missing the alternatives. Here is the complete question.

Two vectors of magnitude |A| = 8units and |B| = 5units make an angle that can vary from 0° to 180°. The magnitude of the resultant vector A+B CANNOT have the value of:

A. 2 units

B. 5 units

C. 8 units

D. 12 units

Answer: A. 2 units

Explanation: Vector is an entity that has characteristics as magnitude and direction. Resultant vector is the "sum" of 2 or more vectors.

In this question, the vectors have magnitude and angle varies from 0° to 180°.

When angle between vectors A and B is 0°, they are parallel and pointing to the same direction, so:

[tex]V_{R} = |A| + |B|[/tex]

[tex]V_{R}=8+5[/tex]

[tex]V_{R}[/tex] = 13

When the angle is 180°, it means vectors are in opposing directions, so:

[tex]V_{R} = |A| - |B|[/tex]

[tex]V_{R} = 8-5[/tex]

[tex]V_{R}[/tex] = 3

From the calculations, we can conclude the magnitude of resultant vector varies between 3 and 13.

The least value is 3, so it cannot have a value of 2 units.

Maddie Cat can ride her tricycle at an amazing speed of 3.75 meters per second.
How far can she go in 5.0 seconds?

Answers

Distance = (speed) x (time)

Distance = (3.75 m/s) x (5.0 s)

Distance = 18.75 meters

Answer: 3.75 x 5.0= 18.75 meters

Explanation:

A flag pole is attached to the side of a building 5.00 ft off the ground and it hangs down 30 degrees from the vertical. If the pole is 6.00 ft in length, how high in feet is the top of the pole at its highest point (sticking out from building)? (Hint: draw a picture) E​

Answers

Answer:

   h ’= 0.6963 m

this is the height of the part of the post it supports.

Explanation:

For this exercise we can use the trigonometric relationships

Let's start by finding the vertical component of the height of the pole

             cos 30 = x / L

             x = L cos 30

             x = 6 cps 30

             x = 5.196 m

with this length, the post has the same height as the building, so there are

               Aₓ = L -x

               Δx = 6 -5.196

               Δx = 0.804 ft

the height of this section is

               cos 30 = h ’/ Dx

               h ’= 0.804 cos30

               h ’= 0.6963 m

this is the height of the part of the post it supports.

Tony completed a 720 km journey with an average speed of 90 km/h for the first 285 km he travelled at an average speed of 95 Km/h what was the average speed for the remaining journey

Answers

Answer:

[tex]Speed = 87 km/h[/tex]

Explanation:

Given

Total Distance = 720km

Average Speed = 90km/h

Average Speed (285km) = 95km/h

Required

Determine the average speed for the rest of the journey

First we need to determine the time taken to complete the journey using

[tex]Speed = \frac{Distance}{Time}[/tex]

[tex]90 = \frac{720}{Time_1}[/tex]

Make Time the subject of formula

[tex]Time_1 = \frac{720}{90}[/tex]

[tex]Time_1 = 8 hour[/tex]

Next, we determine the time taken to complete 285km of the journey using

[tex]Speed = \frac{Distance}{Time}[/tex]

[tex]95 = \frac{285}{Time_2}[/tex]

Make Time the subject of formula

[tex]Time_2 = \frac{285}{95}[/tex]

[tex]Time_2 = 3 hours[/tex]

The difference between these calculated times is the time taken to complete the rest of the journey

[tex]Time = Time_1 - Time_2[/tex]

[tex]Time = 8\ hour - 3\ hour[/tex]

[tex]Time = 5\ hour[/tex]

Also, we need to calculate the distance of the rest of the journey

[tex]Distance = 720\ km - 285\ km[/tex]

[tex]Distance = 435\ km[/tex]

The average speed can then be calculated;

[tex]Speed = \frac{Distance}{Time}[/tex]

[tex]Speed = \frac{435}{5}[/tex]

[tex]Speed = 87 km/h[/tex]

Hence, the average speed of the rest of the journey is 87km/h

If a gannet hits the water at 32 m/s, what height did it dive from? Assume that the gannet was motionless before starting its dive.

Answers

Answer:

The value  is  [tex]h =  52.2 \  m[/tex]

Explanation:

From the question we are told that

 The  velocity  at which he hit the water  is  [tex]v  =  32 \  m/s[/tex]

   

Generally from kinematic equation

     [tex]v^2 =  u^2  + 2gh[/tex]

Here the initial velocity u = 0 m/   given that the gannet started the jump from rest.

  =>   [tex]32^2  =  0^2  +  2*(9.8)h[/tex]

 =>     [tex]h =  52.2 \  m[/tex]

The fastest land animal is the cheetah. A cheetah can run 100 meter dash in 5.95 seconds, calculate the cheetahs average speed in meters per second

Answers

Answer:

16.80672269 m/s

Explanation:

100 divide by 5.95 seconds

Answer:

16.8m/s

Explanation:

S=D/T

=

[tex] \frac{100}{5.95} [/tex]

=16.80672269

=16.8

a 20 ft shipping container on a cargo ship has a mass of 24000 kg and a volume of 33.2m3. what is the density of the shipping container

Answers

Answer:

722.89

Explanation:

mass=24000kg

volume=33•2

density=?

now,

density=mass/volume

=24000/33•2

=722•89

density=722•89 kg/m^3

What net force is needed to accelerate a 1.25 kg book 5.00 m/s2?

Answers

Answer:

F = 6.25 N

Explanation:

Given that,

Mass of the book is 1.25 kg

Acceleration of the book is 5 m/s²

We need to find the net force needed to accelerate the book. Net force is given by :

F = ma

[tex]F=1.25\times 5\\\\F=6.25\ N[/tex]

So, 6.25 N of force is acting on the book.

Light of wavelength 600 nm illuminates a diffraction grating. The second order maximum is at an angle of 65 degrees. a) List your known variables. b) What is the spacing between slits in this grating? c) How many lines per millimeter does this grating have?

Answers

Answer:

A. Known variables include

Wavelength = 600nm

Theta= 65°

m= 2

B.

d= m x wavelength / sin theta

= 2 * 600*10^-9 /sin 65°

= 1.3*10^-6m

C.

N = 1/d

So N = 1/1.3*10^-6m

=76.9 lines per micro meter

How does society shape reality?

Answers

Society shapes us through our gender, it dictates what jobs would be suitable for us, what we should wear, how we should look, who we are to socialise with and what is acceptable or not.

which sentences describes an object that has kinetic energy

Answers

Anything associated with the movement of objects has kinetic energy.
Examples are river flowing, moving cars, wind mills, or even just simple walking and running

Answer:

A boat sails across the Ocean

Explanation:

Out of all the options on Edmentum none of them where moving so it would only make sense that this is the only one with kinetic energy.

What are some superheroes that resemble neurotransmitter functions. Dopamine: Acetylcholine: Endorphins: GABA: Glutamates: Norepinephrine: Serotonin:

Answers

Answer:

Serotonin

___________

Regular exercise is positively related to wellnes t or f

Answers

The answer is true. Because if you exercise regularly your body will be in better shape than if you didn’t exercise! Hope this helps

Which is one physical property that all stars have? pick one They are made of gases. They shine very brightly. They have a triangle shape. They contain iron in their cores.

Answers

Answer: They are made of gases

The physical property that all stars have will be they are made of gases. option 1 is correct.

What is a star?

A star is a heavenly body made up of a brilliant spheroid of plasma held together by gravity. The Sun is the closest star to Earth.

Many additional stars may be seen with the normal eye at night, but due to their great distance from Earth, they appear as stationary points of light in the sky.

The physical property that all stars have will be they are made of gases.

Hence option 1 is correct.

To learn more about the stars refer to the link;

https://brainly.com/question/24493066

A silver block of silver block of density 10.5 g/cm3 has a volume of 30 cm3. Which of the following is the correct mass of the block ​

Answers

Answer :

➝ Density of block = 10.5 g/cm³

➝ Volume of block = 30 cm³

We have to find mass of block[tex].[/tex]

➠ Density is defined as mass of substance per unit volume[tex].[/tex]

[tex]\dag\:\boxed{\bf{Density=\dfrac{Mass}{Volume}}}[/tex]

[tex]:\implies\sf\:Mass=Density\times Volume[/tex]

[tex]:\implies\sf\:Mass=10.5\times 30[/tex]

[tex]:\implies\boxed{\boxed{\bf{\red{Mass=315\:g}}}}[/tex]

Starting from rest, a panther accelerates at 3 m/s/s for 10 seconds. What is the final velocity of the panther

Answers

Answer:

Final velocity = 30 m/s

Explanation:

We are given;

Initial velocity; u = 0 m/s

Acceleration; a = 3 m/s²

Time; t = 10 seconds

From Newton's first law of motion, the final velocity is given by the formula;

v = u + at

Plugging in the relevant values gives;

v = 0 + (3 × 10)

v = 30 m/s

Which is true for a car moving around a circular track with constant speed? 1. It has zero acceleration2. it has an acceleration directed toward the center of its path3. it has an acceleration directed away fromt he center of its path4. it has an acceleration with a direction that cannot be determined from the information given5. it has an acceleration component in the direction of its velocity.

Answers

Answer:

2. it has an acceleration directed toward the center of its path

Explanation:

For a car moving with constant velocity around a circular track, there is a a change in the direction of the velocity at every point on the path taken by the car around the track. This change in direction generates an acceleration on the car which will be directed towards the center of the track. This is why the inertia force on a person inside the car when it is driven around a circular track is usually away from the center of the track, since the inertia force acts in an opposite direction to the acceleration on a body.

Which of the following is the best way to make a conclusion? A. The experiment must be manipulated until the results show what you want B. Estimate results to where they should be C. Choosing the results you like best D. Comparing data from the experiment to

Answers

Answer:

D

Explanation:

You should compare your results and data with your original hypothesis.  It is okay to have a hypothesis that was shown to be false.  That's science. Things do not always work out.  You can always discuss what you could have done differently and things that went wrong.  There is no right answer in science!

If you do not have enough time to complete a full workout, you should:
A. Cut the cool-down portion short.
B. Skip the warm-up and cool-down portions altogether.
C. Cut the warm-up portion short.
D. Cut the exercise portion short.

Answers

Answer:

the answer to this question would be cut the exercise portion down (D)

this is because warm ups and cooling down during exercise are more important than the exercise itself

Explanation:

the four strings of a bass guitar are 0.865 m long and are tuned to the notes g (98 hz), d (73.4 hz), a (55 hz), and e (41.2 hz). in one bass guitar, the g and d strings have a linear mass density of 4.8 g/m, and the a and e strings have a linear mass density of 29.8 g/m.what is the total force exerted by the strings on the neck?​

Answers

Answer: Total force = 636,554.55N

Explanation: To determine tension of strings, wave speed on a string is necessary. Speed is found by:

v = f.λ

f is frequency

λ is wavelength

For the strings, wavelength equals to:

[tex]\lambda = 2L[/tex]

L is the length of the bass guitar string

Then, wave speed:

[tex]v=f.2L[/tex]

Tension on a string is

[tex]v=\sqrt{\frac{F_{T}}{\mu} }[/tex]

[tex]v^{2}=\frac{{F_{T}} }{\mu}[/tex]

[tex]F_{T} = v^{2}\mu[/tex]

[tex]F_{T} = (2f\lambda)^{2}\mu[/tex]

[tex]F_{T} = 4(f\lambda)^{2}\mu[/tex]

μ is linear mass density

For g string:

[tex]F_{T} = 4(98.0.865)^{2}.4.8[/tex]

[tex]F_{T}[/tex] = 137970.3N

For d string:

[tex]F_{T} = 4(73.4.0.865)^{2}.4.8[/tex]

[tex]F_{T}=[/tex] 77397.25N

For a string:

[tex]F_{T} = 4(55.0.865)^{2}.29.8[/tex]

[tex]F_{T}=[/tex] 269795N

For e string:

[tex]F_{T} = 4(41.2.0.865)^{2}.29.8[/tex]

[tex]F_{T}=[/tex] 151392N

Total force = 137,970.3 + 77,397.25 + 269,795 + 151,392

Total force = 636,554.55N

Total force exerted on the neck by the strings is 636,554.55N.

This question involves the concepts of the tension force in strings, linear mass density, and frequency.

The total force exerted by strings on the guitar is "359.4 N".

The tension force exerted by each string is given as:

[tex]F_T=v^2\mu[/tex]

where,

F_T = tension force = ?

v = speed = (frequency)(wavelength) = fλ

μ = linear mass density

Therefore,

[tex]F_T=f^2\lambda^2\mu[/tex]

but for strings in this case:

[tex]\lambda = 2(Length of string) = 2(0.865\ m)=1.73\ m[/tex]

Therefore,

[tex]F_T=f^2(1.3\ m)^2\mu[/tex]

For string g:

[tex]F_{Tg}=(98\ Hz)^2(1.3\ m)^2(4.8\ x\ 10^{-3}\ kg/m)\\F_{Tg}=77.9\ N[/tex]

For string d:

[tex]F_{Td}=(73.4\ Hz)^2(1.3\ m)^2(4.8\ x\ 10^{-3}\ kg/m)\\F_{Td}=43.7\ N[/tex]

For string a:

[tex]F_{Ta}=(55\ Hz)^2(1.3\ m)^2(29.8\ x\ 10^{-3}\ kg/m)\\F_{Ta}=152.3\ N[/tex]

For string e:

[tex]F_{Te}=(41.2\ Hz)^2(1.3\ m)^2(29.8\ x\ 10^{-3}\ kg/m)\\F_{Te}=85.5\ N[/tex]

So, the total force will be the sum of all tension forces:

[tex]F=F_{Tg}+F_{Td}+F_{Ta}+F_{Te}[/tex]

F = 77.9 N + 43.7 N + 152.3 N + 85.5 N

F = 359.4 N

Learn more about Tension Force here:

https://brainly.com/question/3445152?referrer=searchResults

a) An electric circuit is rates, 240V, 13Ω calculate the amount of current that can be used by this appliance.​

Answers

Answer:

18.4615385 amps

Explanation:

The voltage V in volts (V) is equal to the current I in amps (A) times the resistance R in ohms (Ω):

who is known as father of science?​

Answers

GalileoGalilei is known as the father of science

Calculate the displacement traveled (in m) from start to finish.

Answers

Answer:

nnkn

Explanation:

nkn

Answer 10000 m
Explanation:
Displacement means the shortest distance.
So, from point a to b the total displacementis 10 km and converting into metres its 10000 metre

How does the Coriolis effect impact ocean currents in the Northern and Southern Hemispheres?

Answers

The Coriolis effect describes the pattern of deflection taken by objects not firmly connected to the ground as they travel long distances around the Earth.The key to the Coriolis effect lies in Earth’s rotation. Specifically, Earth rotates faster at the Equator than it does at the poles. Earth is wider at the Equator, sThe Coriolis effect bends the direction of surface currents to the right in the Northern Hemisphere and left in the Southern Hemisphere.

Let’s pretend you’re standing at the Equator and you want to throw a ball to your friend in the middle of North America. If you throw the ball in a straight line, it will appear to land to the right of your friend because he’s moving slower and has not caught up.

 

Now let’s pretend you’re standing at the North Pole. When you throw the ball to your friend, it will again to appear to land to the right of him. But this time, it’s because he’s moving faster than you are and has moved ahead of the ball.

Everywhere you play global-scale "catch" in the Northern Hemisphere, the ball will deflect to the right.

A child on a bridge throws a rock straight down to the water below. The point where the child released the rock is 74 m above the water and it took 2.7 s for the rock to reach the water. Determine the rock's velocity (magnitude & direction) at the moment the child released it. Also determine the rock's velocity (magnitude & direction) at the moment it reached the water. Ignore air drag.

Answers

The rock's altitude y at time t, thrown with initial velocity v, is given by

[tex]y=74\,\mathrm m+vt-\dfrac12gt^2[/tex]

where [tex]g=9.80\frac{\rm m}{\mathrm s^2}[/tex] is the acceleration due to gravity.

After t = 2.7 s, the rock reaches the water (0 altitude), so

[tex]0=74\,\mathrm m+v(2.7\,\mathrm s)-\dfrac12g(2.7\,\mathrm s)^2[/tex]

[tex]\implies v=-\dfrac{74\,\mathrm m-\frac g2(2.7\,\mathrm s)^2}{2.7\,\mathrm s}\approx-14.177\dfrac{\rm m}{\rm s}[/tex]

so the rock was thrown with a velocity with magnitude 14 m/s and downward direction.

Its velocity at time t is [tex]v-gt[/tex] (with no horizontal component), so that at the moment it hits the water, its velocity is

[tex]v-g(2.7\,\mathrm s)\approx-40.637\dfrac{\rm m}{\rm s}[/tex]

That is, its final velocity has an approximate magnitude of 41 m/s, also directed downward.

Other Questions
I just need the answer Kane is training for a marathon. He starts by running 3 miles during every train session. Each week plans to increase the distance of his run by 1/4 mile. What could be called ironically paradoxical about what happens to the king in this story? A) He has over 200 wives, but no son. Eliminate B) He conquers countries, kills the old people, and enslaves the young. C) He marries Adiaha as a political gestures, and then winds up forgetting who she is. D) He is a powerful ruler, but winds up getting manipulated by both his head wife and "the spider." 1.Give short introduction to body care? The primary orchestral instrumental pallets consist if Which of the following was a chief reason that the American colonists chose to forma confederacy?a) It offered a strong central government structure.b) The constitution did not protect individual rights.c) It would free the British from supporting the colonies.d) It would be easier to gain aid and recognition from foreign nations. Evaluate the following expression.-8 - 10 x ( - 7 ) How does a system of checks and balances protect against abuse of power? Point K is on line segment JL. Given KL = 7 and JL = 11, determine the length JK. Answer: JK= For the past 10 years, Tony was an agent for Its a Wonderful Life Insurance Company. While his career started out strong, Tony got involved in some transactions involving cash that violated his companys ethical policies, and they terminated him as an agent last month, but did not notify Tonys clients of his termination, and have not yet collected company forms and logos from Tony. Last week, Christopher, a long-time client of Tonys, purchased a new Its a Wonderful Life life insurance policy from Tony to cover the costs of his newborn childs college education. The policy binder indicated that the insurance was in force as soon as Christopher signed the application and paid the premium (since Christopher was a long-time customer of Tony and the Insurance Company). Which of the following statements is correct? A. The life insurance policy is not in force because Tony was no longer an agent of Its a Wonderful Life Insurance Company.B. The policy is in effect because Tony had the apparent authority to issue the policy.C. The policy is in effect because Tony had the implied authority to issue the policy.D. The policy is in effect because Tony had the express authority to issue the policy. write a fraction and a percent for the shaded portion of each one. Which types of government allow voters to elect representatives? Select two options.fascist governmentsdirect democraciesabsolute monarchiesm constitutional monarchiesrepresentative democracies What is the hydrogen ion concentration of a solution with pH 5.60? Why do you think the War of 1812 has been referred to as America's Forgotten War"? Why should it bestudied and remembered today? Categorize each property as either physical or chemical. Physical Properties Chemical Properties melting pointcolordensityflammabilitycorrosivenesselectricalreactivity with acidshardness An unknown element X has the following isotopes: X (80.5% abundant) and X (19.5% abundant). What is the average atomic mass in amu of X? find the missing side that's indicated. Round your answers to the nearest tenth. hello please help, thank you Perform the indicated operation and simplify the result.b^2 - 3b - 10 B-2 -(B - 2)^2 B-5 There are 30 students in a class of 18 of them own at least one pet what fraction of the class own pets? Give your answer in its simplest form