The cart is then pushed up the ramp, compressing the spring a distance A from equilibrium. When
released from rest, the cart oscillates up and down the ramp with a period of T₁. Assume that any friction
is negligible.
The spring is then replaced with a second spring that has a constant k2 = 2k₁, and the new period, T2, is
measured.
Determine the period of T2 in terms of T₁.

The Cart Is Then Pushed Up The Ramp, Compressing The Spring A Distance A From Equilibrium. Whenreleased

Answers

Answer 1

When the spring is replaced with a spring with double of initial spring constant k2 = 2k₁, the new period, T2, is [tex]\sqrt{\frac{1}{2} } \ T_1[/tex].

Period of the mass oscillation

The period of the oscillation of the mass or cart on the spring is given by the following formula;

[tex]T = 2\pi \sqrt{\frac{m}{k} } \\\\[/tex]

at a costant mass;

[tex]T_1\sqrt{k_1} = T_2\sqrt{k_2} \\\\T_2 = \frac{T_1\sqrt{k_1} }{\sqrt{k_2} }[/tex]

when spring constant is doubled, k2 = 2k1. the new period, T2 is determined as follows;

[tex]T_2 = \frac{T_1\sqrt{k_1} }{\sqrt{2k_1} } \\\\T_2 = \frac{T_1\sqrt{k_1} }{\sqrt{2} \times \sqrt{k_1} } \\\\T_2 = \frac{T_1}{\sqrt{2} }\\\\T_2 = \sqrt{\frac{1}{2} } \ T_1[/tex]

Thus, when the spring is replaced with a spring with double of initial spring constant k2 = 2k₁, the new period, T2, is [tex]\sqrt{\frac{1}{2} } \ T_1[/tex].

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Related Questions

Please help quickly!!!

State the basic rules to draw a vector quantity

Answers

Explanation:

i dont to i want to copy and paste on my printer

What best describes the speed of light waves in solids, liquids, and gases?
O The speed is fastest in solids.
O The speed is fastest in liquids.
O The speed is fastest in gases.
O The speed is the same in all matter.

Answers

Answer:

C

Explanation:

Generally, the speed of light slows down when passing through a medium that is not a vacuum. This is not always the case, but I will be ignoring the rare/exotic exceptions. Light has a harder time traveling through solids and liquids than it does with gases.

Answer:

its c

Explanation:

The fundamental frequency of a musical note is 330Hz. What is the frequency of the 3rd overtone?

Answers

The 3rd  overtone or the third harmonic given that the fundamental frequency is 330Hz is 990Hz

What is an Harmonic?

Hamonics defined as the number gotten by multiplying the nth overtone by the fundamental frequecency.

In summary, the expression for the nth Hamonic or overtone is given as

Fn = Fundamental Frequency*N

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HELP!! ASAP I DONT KNOW HOW TO THIS ​

Answers

Hope this helps! Please give Brainliest!

This is all about reflection. So my theory on this is that you have to look at the checklist:

L: Location

O Orientation

S: Size

T :

Answer the questions (by questions I mean the LOST questions, where they ask you to choose on of the options. For example, for 'T' you have to choose as to whether it is 'real or virtual' ) by using the diagram below:

You pull on a crate using a rope as in (Figure 1), except the rope is at an angle of 20.0 ∘ above the horizontal. The weight of the crate is 245 N , and the coefficient of kinetic friction between the crate and the floor is 0.270. What must be the tension in the rope to make the crate move at a constant velocity?
Express your answer with the appropriate units.

What is the normal force that the floor exerts on the crate?
Express your answer with the appropriate units.

Answers

Hi there!

For an object on an incline with friction being pulled, the following forces are present.

Force due to Gravity Force due to FrictionForce due to tension

The force due to friction opposes the force due to gravity which would cause the object to slide down. (The force due to friction acts up the incline). Additionally, the force due to the rope is also upward.

Let up the incline be positive, and down the incline be negative.

Doing a summation of forces:
[tex]\Sigma F = F_T + F_f - F_g[/tex]

For the crate to be moving at a constant velocity, there is NO net force acting on the crate, so:
[tex]0 = F_T + F_f - F_g[/tex]

Now, we can express each force as an equation.

Force due to tension:

Must be solved for.

Force due to gravity:

On an incline, this is equivalent to the SINE component of its weight.  (Force of gravity is STILL THE WEIGHT, but on an incline, it contains a horizontal component that contributes to the net force)

This is expressed as:
[tex]F_g = Mgsin\theta[/tex]

Force due to friction:

Equivalent to the normal force and coefficient of friction. The normal force is the VERTICAL component of the object's weight, so:

[tex]N = Mgcos\theta[/tex]

[tex]F_f = \mu Mgcos\theta[/tex]

Now, plug these expressions into the above equation.

[tex]0 = F_T + \mu Mgcos\theta - Mgsin\theta\\\\Mgsin\theta - \mu Mgcos\theta = F_T[/tex]

Mg = 245 N (weight). Plug in all values:
[tex]245sin(20) - 0.270(245)cos(20) = F_T\\\\F_T = \boxed{21.634 N}[/tex]

The normal force is equivalent to the vertical component (PERPENDICULAR TO THE INCLINE) of the weight (cosine), so:

[tex]N = Mgcos\theta\\\\N = 245cos(20) = \boxed{230.225 N}[/tex]

To find the tension in the rope needed to make the crate move at a constant velocity, we need to consider the forces acting on the crate.

1. Tension in the rope (T): This force is applied upwards at an angle of 20 degrees above the horizontal.

2. Weight of the crate (W): This force acts downward vertically and is equal to 245 N.

3. Normal force (N): This force is exerted by the floor on the crate and acts perpendicular to the surface of the floor.

4. Kinetic friction force (f_k): This force opposes the motion of the crate and acts parallel to the surface of the floor. The magnitude of kinetic friction is given by: f_k = μ_k * N, where μ_k is the coefficient of kinetic friction (0.270 in this case).

Since the crate is moving at a constant velocity, the net force on the crate must be zero. In other words, the forces pulling the crate forward (T and the horizontal component of the weight) must balance the forces opposing its motion (kinetic friction). The vertical forces (the vertical component of the weight and the normal force) must also balance.

Let's proceed with the calculations:

Horizontal Forces:

T * cos(20°) - f_k = 0

T * sin(20°) + N - W = 0

We can now solve for T and N:

From the horizontal forces equation:

T * cos(20°) = f_k

vertical force:

T = f_k / cos(20°)

T = (0.270 * N) / cos(20°)

From the vertical forces equation:

T * sin(20°) + N = W

T * sin(20°) + N = 245 N

Now, substitute the expression for T from the horizontal forces equation:

(0.270 * N) / cos(20°) * sin(20°) + N = 245 N

Now, solve for N:

N * (0.270 * tan(20°) + 1) = 245 N

N = 245 N / (0.270 * tan(20°) + 1)

Now, plug in the values and calculate N:

N = 245 N / (0.270 * tan(20°) + 1)

N ≈ 208.75 N

Now, we can calculate the tension in the rope (T):

T = (0.270 * N) / cos(20°)

T ≈ (0.270 * 208.75 N) / cos(20°)

T ≈ 67.24 N

So, the tension in the rope needed to make the crate move at a constant velocity is approximately 67.24 N, and the normal force exerted by the floor on the crate is approximately 208.75 N.

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The time period of 2 pendulums are 1.22 s and 0.54 s. Calculate the ratio of their lengths.

Answers

[tex]~~~~~\dfrac{T_1}{T_2}= \dfrac{1.22}{0.54}\\\\\\\implies \dfrac{2\pi \sqrt{\dfrac{L_1}{g}}}{2\pi \sqrt\dfrac{L_2}g}}= 2.259\\\\\\\implies \dfrac{\sqrt{L_1}}{\sqrt g} \times \dfrac{\sqrt g}{\sqrt{L_2}} = 2.259\\\\\\\implies \sqrt{\dfrac{L_1}{L_2}} = 2.259\\\\\\\implies \dfrac{L_1}{L_2} = 5.104\\\\\\\implies L_1:L_2 = 5.104[/tex]

A new band sensation is playing a concert and recording it for a live album to be released this summer. The band asks the sound mixer if he can autotune
the singer who has a habit of singing slightly lower than the note.
What would the mixer need to do to the sound wave? How would it affect the characteristics of the wave?

Answers

The sound mixer will need to increase the amplitude of the sound wave produced by the singer which will increase the loudness of the sound.

Amplitude of sound wave

The amplitude of a sound wave is the maximum vertical displacement of the sound wave.

The sound mixer will need to increase the amplitude of the sound wave produced by the singer.

The increase in the amplitude of the sound wave produced by the lower tune singer will result in increased loudness of the sound.

Thus, the sound mixer will need to increase the amplitude of the sound wave produced by the singer which will increase the loudness of the sound.

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Holding a pen crosswise in your mouth is likely to improve your mood, a result predicted by

Answers

Answer:

the facial-feedback hypothesis

Explanation:

When ocean temperature rises,
a. excess gas is released into the atmosphere.
b. the ocean absorbs and holds carbon dioxide.
c. carbon dioxide is equalized between the ocean and atmosphere. d. no change takes place.

Answers

Answer:

see below

Explanation:

Kind of like when yo open a warm soda .....excess gas is released

When you think about and describe the characteristics of a giraffe, what type of model are you using?

Answers

Answer:

The giraffe is the tallest of all mammals. It reaches an overall height of 18 ft (5.5 m) or more. The legs and neck are extremely long. The giraffe has a short body, a tufted tail, a short mane, and short skin-covered horns

What emits infrared radiation?
Question 5 options:


Humans


Non-living objects


Anything that contains atoms

Answers

Answer:

anything that contains atoms is the correct answer of given statement

Then, complete the riddle below by finding the matching number and writing the letter.
Newton's Second Law
44k el effe &
forces cause an object to accelerate.
3
10
Acceleration depends on I & I and M a ½ ½.
11 12
13
14 15
16
17
18
19
As the force increases, the
accelera
i on
20
21
29
30 31
increases, too.
Why did the artist paint on cement blocks instead of paper?
"
11
He wanted to create

Answers

Answer:

I have no clue I'm just trying to get points

Explanation:

:) sorry

what is electronic logic​

Answers

Answer:

Digital logic is the basis of computing and many other electronic devices as well as control systems found in this continually advancing digital world.

(too short, sorry)


The position x of a particle moving along x axis varies with time t as x = Asin(wt) , where A and w are constants . The acceleration of the particle varies with its position as

[tex] \small \red{ \rm Nonsense = Report} \checkmark[/tex]

Answers

Let's see

[tex]\\ \rm\Rrightarrow x=Asin(\omega t)\dots(1)[/tex]

Now we know the formula of acceleration

[tex]\\ \rm\Rrightarrow \alpha=-A\omega^2sin(\omega t)[/tex]

[tex]\\ \rm\Rrightarrow \alpha=-Asin(\omega t)\times \omega^2[/tex]

From eq(1)

[tex]\\ \rm\Rrightarrow \alpha=-x\omega^2[/tex]

Or

[tex]\\ \rm\Rrightarrow \alpha=-\omega^2x[/tex]

Given that the position x of a particle along X-axis varies with time t by the equation:

[tex]{:\implies \quad \sf x=A\sin (\omega t)}[/tex]

As it defines the position, so x is just displacement here, and we need to find the acceleration first for telling with what if varies, so by definition, the second differential coefficient of displacement is acceleration, so differentiating both sides w.r.t.x of the above equation in accordance with chain rule we have:

[tex]{:\implies \quad \sf \dfrac{dx}{dt}=A\cos (\omega t)\cdot \omega \cdot \dfrac{dt}{dt}}[/tex]

[tex]{:\implies \quad \sf \dfrac{dx}{dt}=A\omega \cos (\omega t)}[/tex]

Differentiating both sides w.r.t.x by chain rule again to get the 2nd order derivative

[tex]{:\implies \quad \sf \dfrac{d^{2}x}{dt^{2}}=-A\omega \sin (\omega t)\cdot \omega \dfrac{dt}{dt}}[/tex]

[tex]{:\implies \quad \sf \dfrac{d^{2}x}{dt^{2}}=-A\omega^{2}\sin (\omega t)}[/tex]

Re-write as :

[tex]{:\implies \quad \sf \dfrac{d^{2}x}{dt^{2}}=-\omega^{2}\{A\sin (\omega t)\}}[/tex]

Can be further written as

[tex]{:\implies \quad \sf \dfrac{d^{2}x}{dt^{2}}=-x\omega^{2}}[/tex]

This is the Required answer

If they ask you the differential equation for the acceleration of a wave (as the given equation was general equation of a wave), you can simply write:

[tex]{:\implies \quad \sf \dfrac{d^{2}x}{dt^{2}}+x\omega^{2}=0}[/tex]

Edwin Hubble discovered that:

Galaxies were moving away from us

Some stars got brighter and dimmer in patterns.

Triangulation was not a reliable method for measuring distances

All of the above.​

Answers

Answer:

galaxies were moving away from us

Explanation:

i got 100% on my quiz

A small block sits at one end of a flat board that is 2.50 m long. The coefficients of friction between the block and the board are μs = 0.450 and μk = 0.400. The end of the board where the block sits is slowly raised until the angle the board makes with the horizontal is α0, and then the block starts to slide down the board.

Answers

Hi there!

In order for a block to begin sliding, the force due to STATIC friction must be overcome.

In this instance, the following forces are acting on the block ALONG the axis of the incline.

Force due to gravity (Fg)Force due to STATIC friction (Fs)

Force due to gravity:

On an incline, the component of the force due to gravity contributing to the object's downward movement is equivalent to the horizontal (sine) component.

[tex]F_g = Mgsin\theta[/tex]

Force due to static friction:
The force due to friction is equivalent to the normal force multiplied by the coefficient of friction.

The normal force is the cosine component (perpendicular to the incline), so:
[tex]N = Mgcos\theta\\\\F_s = \mu_sMgcos\theta[/tex]

To find the minimum angle for the block to begin sliding, we can set the two forces equal to 0. They work in opposite directions (let down the incline be negative and up the incline be positive).

[tex]\Sigma F = F_s - F_g\\\\0 = F_s - F_g\\\\0 = \mu_sMgcos\theta - Mgsin\theta\\\\Mgsin\theta = \mu_sMgcos\theta[/tex]

Cancel out 'Mg' and rearrange to solve for theta.

[tex]sin\theta = \mu_scos\theta\\\\tan\theta = \mu_s\\\\\theta = tan^{-1}(\mu_s) = tan^{-1}(.45) = \boxed{24.228^o}[/tex]

What are the similarities of life science and applied science?

Answers

Answer~

Both life science and physical science helps to understand the natural habitat of the earth. Life science deals with the living thing; thus, it is a study of the organic world. On the other hand, physical science deals with nonliving things; thus, it is a study of the inorganic world.

Explanation:

The cone and the cylinder below have equal surface area.
2r
OA. True
B. False

Answers

1 Find the surface area of the cylinder
we know that
the surface area of a cylinder is equal to




Substitute


2 Find the surface area of the cone
we know that
the surface area of a cone is equal to



3 Compare the surface area of the cylinder with the surface area of the cone

therefore
the answer is
False

B. False, the surface area of the cone and the cylinder is not the same.

What is the Surface area?

The area or region that an object’s surface occupies is known as its surface area. Volume, on the other hand, refers to how much room an object has. Geometry has numerous shapes and dimensions, including spheres, cubes, cuboids, cones, cylinders, etc. Each form has its own volume and surface area.

If the slant height of the cone is 2r, then we can use the Pythagorean theorem to find the radius of the cone:

l² = (2r)² - r²

l² = 3r²

l = r√3

Using this value for the radius of the cone, the formula for its surface area becomes:

A(cone) = πrl + πr²

A(cone) = π(r)(r√3) + πr²

A(cone) = πr²(1 + √3)

For the cylinder, we can use the given height and radius to find its surface area:

A(cylinder) = 2πrl + 2πr²

A(cylinder) = 2π(r)(r) + 2π(r²)

A(cylinder) = 2πr²(1 + r)

Comparing the two surface area formulas, we can see that they are not equal in general, since each figure's coefficient in front of the second term (πr²) is different.

Therefore, we cannot conclude that the two figures have the same surface area based on the information.

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what is the mathematical equation for resistivity​

Answers

Answer:

See below

Explanation:

rho = R A/l     R = resistance   A = cross sectional area l = length

A sound wave is produced when a medium begins to

Answers

Answer:

when a medium begins to vibrate

An airplane of mass 270,000 kg that is sitting on a runway has its center of gravity located at 10.0 m in front of the main landing wheels as shown. Find the magnitude of the force exerted by the runway on the nose wheel located 25.0 m from the main landing wheels.

Answers

For an airplane of mass 270,000 kg , the magnitude of the force exerted is mathematically given as

N2=1584431.13N

N1=1061568.87N

What is the magnitude of the force exerted by the runway on the nose wheel located 25.0 m from the main landing wheels.?

Generally, the equation for the Force balance is mathematically given as

N1+N2=270000*g

Therefore

N2*10=N1*15

N1=10N2/15

N1=0.67N2

Hence

0.67N2+N2=270000*g

N2=1584431.13N

N1=1061568.87N

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What is the angular acceleration experienced by a uniform solid disc of mass 5-kg and radius 20 cm when a net
torque of 50 N.m is applied? Assume the disc spins about its center.

Answers

Answer:

7.07 radians per second

What best describes the relationship between sleep and memory? The quantity of sleep impacts memory, while the quality of sleep does not. The quantity of sleep does not impact memory, while the quality of sleep does. The quantity and quality of sleep have no impact on memory. The quantity and quality of sleep both impact memory.

Answers

Answer:
The quantity and quality of sleep both impact memory.

Explanation:

Research has shown that memories of certain procedures, like playing a melody on a piano, can actually improve while you sleep. Memories seem to become more stable in the brain during the deep stages of sleep. This can be affected by how good your sleep is and how much you sleep. Too much rest can make a being lazy, whereas not enough sleep can make you fatigued and reduce productivity.

Hope this helps!
Please give Brainliest!

Answer:

The quantity and quality of sleep both impact memory.

Explanation:

North of Carthage is this, it is a shallow evaporate lake:
A. Rub al-Khali
B. Sebkhet Arina
C. Sebkhet Qaddafi

Answers

Sebkhet Arina

Explanation:

sorry if it's wrong need more information

a sound has a wavelength of 0.52028. If the speed is 343.00m/s, what is the musical note?

Answers

f = (343m/s) / 0.77955m = 439.997 0r 440 Hz Pitch is an A. 2. A note has a wavelength of 0.52028 m. If the speed of sound is 343.00

A piece of fine fiber with a diameter of =6.5 m is used to prop apart the edges of two perfectly flat 3.3-cm-long pieces of glass (see diagram). When the setup is illuminated from above with light of wavelength =590 nm , an interference pattern of alternating bright and dark bands will be seen in the reflected light. If the setup is viewed from high above, how many dark bands will be seen?

Answers

We need frequency:-

[tex]\\ \rm\Rrightarrow \nu=\dfrac{c}{\lambda}[/tex]

[tex]\\ \rm\Rrightarrow \nu=\dfrac{3\times 10^8m/s}{590\times 10^{-9}m}[/tex]

[tex]\\ \rm\Rrightarrow \nu=0.0051\times 10^{17}Hz[/tex]

[tex]\\ \rm\Rrightarrow \nu=5.1\times 10^{14}Hz[/tex]

Can anyone help me on this? It’s a water cycle.

Answers

Answer:

The water cycle shows the continuous movement of water within the Earth and atmosphere. It is a complex system that includes many different processes. Liquid water evaporates into water vapor, condenses to form clouds, and precipitates back to earth in the form of rain and snow.

Explanation:

A sample of ore containing radioactive strontium 38Sr90 has an activity of 8.2 × 105 Bq. The atomic mass of strontium is 89.908 u, and its half-life is 28.8 yr (1 yr = 3.156 × 107 s). How many grams of strontium are in the sample?

Answers

From the activity values and the decay constant, the mass of of Strontium in the sample is:

[tex]1.62 × 10^{-7}g[/tex]

What is the decay constant of an element?

The decay constant of an element is the probability of decay of a nucleus per unit time.

{λ = ln 2 / t1/2 

where;

t1/2 is the half-life of the isotope.

The half-life is converted to seconds since the decay constant is asked in per seconds.

[tex]28.8 years = 28.8 × 3.156 × 10^{7} = 908928000 s \\ [/tex]

Hence;

[tex]λ = \frac{ln2}{90892800s} = 7.626 s^{-1}[/tex]

                                       

The activity of the element, A, the decay constant, λ and the number of nuclei, N are related as follows:

A = (–) λN

[tex]N = \frac{8.25 ×10^{5}}{7.626×10^{-10}} = 1.082 × 10^{15} [/tex]              

Molar mass of Strontium-90 is 90 g.

1 mole of Strontium-90 contains 6.02×10^23 nuclei.

The mass, m of Strontium in the sample is calculated:

[tex]m = 1.082 × 10^{15} × \frac{90 g}{6.02 × 10^{23}} = 1.62 × 10^{-7}g \\ [/tex]

Therefore, the mass of of Strontium in the sample is:

[tex]1.62 × 10^{-7} \: g[/tex]

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A car moving south speeds up from 10 m/s to 40 m/s in 15 seconds. What is the car’s acceleration?

Answers

Answer:

According to the question,

Initial velocity of car (at t=0) = 10 m/s

Final velocity of car (after 15 sec) = 40m/s

Time taken = 15 sec.

Now use, first equation of motion viz.

Explanation:

v = u + at.

40 = 10 + a *15

30 = a*15

a = 30/15

a = 2 m/sec square.

If you double the mass, what happen to the acceleration?

Answers

Answer: The math behind this is quite simple. If you double the force, you double the acceleration, but if you double the mass, you cut the acceleration in half.

Explanation:

Other Questions
Asians who immigrated to the united states after marrying american service personnel primarily came from china. korea. japan. india. This excerpt suggests that poetry is ____ to other art forms. inferior , superior , equal , similar HELP! WILL GIVE BRAINLYToday, the sum of Harper's age and Cadence's age is 61. 8 years ago Cadence was 4 times older than Harper. Part A: Enter Harper's age today. Part B: Enter Cadence's age today. 8. Which two-dimensional figure is formed when a right rectangular pyramidis sliced by a plane through the pyramid's vertex and perpendicular to thepyramid's base?A. a squareB. a triangleC. a trapezoidD. a parallelogram Which of the following best describes the impact of Creative Commons?Creative Commons gives creators of digital content the ability to indicate how their works can be legally used and distributed, enabling broad access to digital information.Creative Commons gives Internet users the right to legally use and distribute any previously copyrighted work, enabling broad access to digital information.Create Commons provides lossless transmission of messages, enabling reliable distribution of digital information.Creative Commons provides private transmission of messages, enabling secure distribution of digital information. What effect did the Peloponnesian War have on the city-states?It brought the city-states together into a newly formed empire.It left the city-states mostly the same as they were before the war.It weakened the city-states through the loss of life and the ruining of land.It expanded the city-states to cover more territory around the Aegean Sea. Two of the angles in a triangle measure 17 and 153 What is the measure of the third angle? A ray of light hits a mirror at 27 degrees from the normal. What is the angle between the reflected ray and the normal? Which line most accurately represents the line of best fit for the scatter plot?(I think its D, correct me if im wrong) Line ALine BLine CLine D Why the Jews flee Europe When Coca-Cola creates a website within its website called MyCoke where consumers can create a profile, and exchange thoughts, ideas, and more among themselves, it has developed what is called a __________. It is indirectly referenced from required. Class files. The War in Korea The outline to the right shows Korea. Follow the directions to complete the map. 8 Points 1. Label the line that represents the 38th parallel. 2. Label North Korea and South Korea. 3. The Sea of Japan lies east of Korea, and the Yellow Sea lies to the west. Label these two bodies of water. 4. Locate and label Seoul, which lies south of the 38th parallel on a river that flows northwest into the sea. 5. Label the Peoples Republic of China, which lies to the north of Korea. Label the Yalu River, which forms part of the border with the Peoples Republic of China. 6. Label Pusan, which lies on the southeast tip of Korea. 7. Label Inchon, which lies southwest of Seoul on a tiny inlet on the coast. 8. Label Pyongyang, at the end of a deep bay on the western coast of North Korea Which goods or services account for more than one third of Brazil's exports? Hardwood lumber mineral resources agriculture resources service sector jobs What is the surface area of this right prism?48 in84 in96 in120 in Jim is 8 ft 9 in tall. Jane is 23.5 in tall. How many times taller than Jane is Jim? __What is the length of HI to the nearest hundredth?1.32 km16.33 km38.02 km Show division using an area model. Can you show 24 4 with one rectangle? why is it important to protect people whose rights have been violated ? Find center and radius of this circle:[tex](x-9)^2+(y+4)^2=25[/tex]