A 1.5-kg ball is throw at 10 m/s. What is the balls momentum?
Answer : The momentum of ball is, 15 kg.m/s
Explanation :
Momentum : It is defined as the motion of a moving body. Or it is defined as the product of mass of velocity of an object.
Formula of momentum is:
where,
p = momentum = ?
m = mass = 1.5 kg
v = velocity = 10 m/s
Now put all the given values in the above formula, we get:
Therefore, the momentum of ball is 15 kg.m/s
A block of mass 3m is placed on a frictionless horizontal surface, and a second block of mass m is placed on top of the first block. The surfaces of the blocks are rough. A constant force of magnitude F is applied to the first block as shown in the figure. (a) Construct free-body diagrams for each block. (b) Identify the horizontal force that causes the block of mass m to accelerate. (c) Assume that the upper block does not slip on the lower block, and find the acceleration of each block in terms of m and F.
By Newton's second law, assuming F is horizontal,
• the net horizontal force on the larger block is
F - µmg = 3mA
where µmg is the magnitude of friction felt by the larger block due to rubbing with the smaller one, µ is the coefficient of static friction between the two blocks, and A is the block's acceleration;
• the net vertical force on the larger block is
4mg - 3mg - mg = 0
where 4mg is the mag. of the normal force of the surface pushing up on the combined mass of the two blocks, 3mg is the weight of the larger block, and mg is the weight of the smaller block;
• the net horizontal force on the smaller block is
µmg = ma
where µmg is again the friction between the two blocks, but notice that this points in the same direction as F. It is the only force acting on the smaller block in the horizontal direction, so (b) static friction is causing the smaller block to accelerate;
• the net vertical force on the smaller block is
mg - mg = 0
where mg is the magnitude of both the normal force of the larger block pushing up on the smaller one, and the weight of the smaller block.
(You should be able to draw your own FBD's based on the forces mentioned above.)
(c) Solve the equations above for A and a :
A = (F - µmg) / (3m)
a = µg
what's is the best definition of AVERAGE SPEED?
Answer:
The average speed is the distance travelled divided by the time taken: Average speed=Distance travelledTime taken.
A bar magnet is held in place while another bar magnet is placed near it. The second bar magnet spins around and
attaches to the first magnet on one end. Which statement is correct about the energy stored in the magnetic field?
(1 point)
O The increase in the energy stored in the system is proportional to the increase in kinetic energy.
O The decrease in the energy stored in the system is proportional to the decrease in kinetic energy.
O The increase in the energy stored in the system is proportional to the decrease in kinetic energy.
O The decrease in the energy stored in the system is proportional to the increase in kinetic energy.
Answer:
o
Explanation:
the increase energy stored in thw system is proportional to the decrease in kinetic energy
The increase in the energy stored in the system is proportional to the decrease in kinetic energy.
What is energy stored in the system ?"The energy stored in the system means the sum of energies of both magnets when second magnet stop spin and stick with first magnet. It is clear that the rotational kinetic energy of second magnet decrease and becomes part of the system. Hence the increase in the energy stored in the system is proportional to the decrease in kinetic energy."
What is kinetic energy ?"Kinetic energy is a form of energy that an object or a particle has by reason of its motion. If work, which transfers energy, is done on an object by applying a net force, the object speeds up and thereby gains kinetic energy."
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what is conductivity?
Answer:
Conductivity is the measure of the ease at which an electric charge or heat can pass through a material. A conductor is a material that gives very little resistance to the flow of an electric current or thermal energy.
Explanation:
brainliest plss
Calculate the force of gravity on the 1-kg mass if it were 3.2x10^6 m above Earth's surface that is, if it were one and a half
Earth radii from Earth's center).
Answer:
F= 4.3N
the question (for seo and search engine optimization to get this question to the top)
Calculate the force of gravity on the 1-kg mass if it were 3.2×106m above Earth's surface (that is, if it were one and a half Earth radii from Earth's center).
F= 4.3N
Answer:
Recuerda que la Ley de gravitación universal de Newton puede enunciarse así: “Toda partícula de
materia en el universo atrae a todas las demás partículas con una fuerza que es directamente
proporcional a las masas de las partículas e inversamente proporcional al cuadrado de la distancia que
las separa”. Ley que se puede expresar simbólicamente de la siguiente forma:
2
1 2
d
m m F ⋅ ∝
Podemos expresar la proporcionalidad de la ley de gravitación universal en forma de una ecuación
exacta introduciendo la constante de proporcionalidad G, llamada constante de gravitación universal:
2
1 2
d
m m F G ⋅ = ⋅ donde
2
What is the period of a wave that completes 3 waves in 2 seconds?
P = 3÷2
= 1.5
Explanation:
hope it helps
Pls help! Tysm!!! :D
Answer:
Slowing a bike by applying the brkaes is an xmaple of acceleration
Explanation:
A toy is undergoing SHM on the end of a horizontal spring with force constant 310 N/m . When the toy is 0.120 m from its equilibrium position, it is observed to have a speed of 3 m/s and a total energy of 3.6 J .
1.) Find the mass of the toy.
2.) Find the amplitude of the motion.
3.) Find the maximum speed obtained by the object during its motion.
Answer:
1) the mass of the toy is 0.304 kg
2) the amplitude of the motion is 0.1524 m
3) the maximum speed obtained by the object during its motion is 4.87 m/s
Explanation:
Given the data in the question;
force constant of spring k = 310 N/m
position of toy x = 0.120 m
speed v = 3 m/s
Total energy E = 3.6 J
let m represent mass of toy.
1.) Find the mass of the toy.
we know that; The total energy of the system equals the sum of kinetic energy of the toy and the potential energy of the spring;
E = [tex]\frac{1}{2}[/tex]kx² + [tex]\frac{1}{2}[/tex]mv²
we substitute
3.6 = ( [tex]\frac{1}{2}[/tex] × 310 × (0.120)² ) + ( [tex]\frac{1}{2}[/tex] × m × (3)² )
3.6 = 2.232 + 4.5m
3.6 - 2.232 = 4.5m
1.368 = 4.5m
m = 1.368 / 4.5
m = 0.304 kg
Therefore, the mass of the toy is 0.304 kg
2) Find the amplitude of the motion.
we know that;
E = [tex]\frac{1}{2}[/tex]kA²
where A is the amplitude of the motion,
we substitute
3.6 = [tex]\frac{1}{2}[/tex] × 310 × A²
3.6 = 155 × A²
A² = 3.6 / 155
A² = 0.0232258
A = √0.0232258
A = 0.1524 m
Therefore, the amplitude of the motion is 0.1524 m
3) Find the maximum speed obtained by the object during its motion;
we know that;
E = [tex]\frac{1}{2}[/tex]m[tex]v_{max[/tex]²
where [tex]v_{max[/tex] is the maximum speed
so we substitute
3.6 = [tex]\frac{1}{2}[/tex] × 0.304 × [tex]v_{max[/tex]²
3.6 = 0.152 × [tex]v_{max[/tex]²
[tex]v_{max[/tex]² = 3.6 / 0.152
[tex]v_{max[/tex]² = 23.6842
[tex]v_{max[/tex]² = √23.6842
[tex]v_{max[/tex]² = 4.8664 ≈ 4.87 m/s
Therefore, the maximum speed obtained by the object during its motion is 4.87 m/s
Violet light (410 nm) and red light
(685 nm) pass through a diffraction
grating with d = 3.33 x 10-6 m. What is
the angular separation between them
for m = 2?
Answer:10.03
Explanation:acellus
A uniform rod of length 50cm and mass 0.2kg is placed on a fulcrum at a distance of 40cm from the left end of the rod. At what distance from the left end of the rod should a 0.6kg mass be hung to balance the rod?
a.48 cm
b. 50 cm
c. 45 cm
d. the rod can not be balanced with this mass.
e.42 cm
show your work. NO LINKS.
Answer:
x = 45 cm
Explanation:
Given that,
The length of a rod, L = 50 cm
Mass, m₁ = 0.2 kg
It is at 40cm from the left end of the rod.
We need to find the distance from the left end of the rod should a 0.6kg mass be hung to balance the rod.
The centre of mass of the rod is at 25 cm.
Taking moments of both masses such that,
[tex]15\times 0.2=x\times 0.6\\\\x=\drac{3}{0.6}\\\\x=5\ cm[/tex]
The distance from the left end is 40+5 = 45 cm.
Hence, at a distance of 45 cm from the left end it will balance the rod.
Tritium and helium-3 have the same number of nucleons, but tritium has one proton and two neutrons whereas helium-3 has two protons and one neutron. Without doing a calculation, decide which nucleus has a greater binding energy. Explain. (Select all that apply.)
a. This happens in part because the tritium nucleus has greater Coulombic repulsion.
b. This happens in part because the helium-3 nucleus has greater Coulombic repulsion between nucleons.
c. This happens in part because the tritium nucleus has an extra neutron enhancing the nuclear forces.
d. Helium-3 is more stable.
e. This happens in part because the helium-3 nucleus has fewer neutrons.
f. Tritium is more stable.
Answer:
Tritium is more stable.
This happens in part because the tritium nucleus has an extra neutron enhancing the nuclear forces.
Explanation:
The binding energy is the energy that holds nucleons together in the nucleus. It depends on the number of nucleons present in the nucleus. The greater the number of nucleons, the greater the binding energy.
Also, the more the number of neutrons in a nucleus, the greater the nuclear forces. Helium-3 has only one neutron while tritium has two neutrons. The extra neutron in tritium enhances the nuclear forces hence tritium has a greater binding energy than Helium-3
Tritium is more stable.this happens in part because the tritium nucleus has an extra neutron enhancing the nuclear forces.
What is binding energy?
The binding energy is the energy that holds nucleons together in the nucleus. It depends on the number of nucleons present in the nucleus.
The greater the number of nucleons, the greater the binding energy.Also, the more the number of neutrons in a nucleus, the greater the nuclear forces.
Helium-3 has only one neutron while tritium has two neutrons. The extra neutron in tritium enhances the nuclear forces hence tritium has greater binding energy than Helium-3
Thus tritium is more stable.this happens in part because the tritium nucleus has an extra neutron enhancing the nuclear forces.
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An ideal parallel plate capacitor is charged by connecting it to a battery. The battery is then removed so that charges may no longer enter onto or exit from the plates of the capacitor. There is nothing between the capacitor plates. As the plates are moved closer together, the magnitude of the electric field between them:_________
a. decreases
b. increases
c. remains the same
Answer:
c. remains the same
Explanation:
The capacitance of a capacitor is can be represented as;
C = Q/V
There will be no charge flow from the battery to the capacitor or vice versa if the battery is disconnected.
Due to energy conservation, the energy contained and stored in a capacitor will continue to retain and be the same, since an increase in capacitance reduces the voltage, resulting in the same final energy stored.
You have a 6.00 V power supply, and
a 30.0 ohm and a 75.0 ohm resistor.
Find the current flowing out of the
battery if the resistors are connected
in parallel.
Answer: 0.28 A
Explanation:
Answer:
.28
Explanation:
Acellus
If you build a circuit with 3 D batteries, what is the voltage of the circuit?
A) 3 volts
B) 4.5 volts
C) 3 Amps
D) 4.5 Ohms
Answer:
a
Explanation:
Answer:
d
Explanation:
3. A dog walks 12 meters to the east and then 16 meters back to the west.
For this motion, what is the distance moved?
What is the magnitude and direction of the displacemeni?
Answer:
[tex]distance = 16 + 12 \\ = 28 \: meters \\ \\ displacement = {}^{ + } 12 + {}^{ - } 16 \\ = - 4 \: meters \\ magnitude = > |s| = 4 \: meters[/tex]
A microbe is ejected from its home planet by a violent event such as a volcanic eruption or a meteorite impact. The subsequent fate of the microbe depends on the balance of the two main forces that act on it, namely, the gravitational attraction of the star around which the planet orbits and radiation pressure due to the luminosity of the star.
Required:
Model the microbe as a dark sphere of radius a at a distance r from the star. Assume that the total power radiated by the star P = 1.0 x 1031 J/s (greater than that of the sun by a factor of 30,000). Derive an expression for the radiation force on the microbe. Give your answer in terms of p, r,c and a.
Answer:
[tex]F = P_r (\frac{a}{4r})^2[/tex]
Explanation:
The radiation pressure for a total absorption of the incident light is
P = S / c
Where S is the pointing vector, which is defined as the energy flux per unit area
S = I = P_r / A
where P_r powre irradiate by star, A is the area over which the energy emitted by the star is distributed, which is the surface of a sphere
A = 4π r²
substituting
S =[tex]\frac{P_r}{4 \pi r^2 }[/tex]
Pressure is defined by
P = F / A₂
Where A₂ is the area over which the force is applied, in this case the area of the microbe
A₂ = π a²
P = F / π a²
we substitute
[tex]\frac{F}{\pi a^2} = \frac{P_r}{ 4 \pi r^2}[/tex]
[tex]F = P_r (\frac{a}{4r})^2[/tex]
PLEASE HELP ME ASAP!!!!
Calculate the energy, wavelength, and frequency of the emitted photon when an electron moves from an energy level of -3.40 eV to -13.60 eV.
Answer:
(a) The energy of the photon is 1.632 x [tex]10^{-8}[/tex] J.
(b) The wavelength of the photon is 1.2 x [tex]10^{-17}[/tex] m.
(c) The frequency of the photon is 2.47 x [tex]10^{25}[/tex] Hz.
Explanation:
Let;
[tex]E_{1}[/tex] = -13.60 ev
[tex]E_{2}[/tex] = -3.40 ev
(a) Energy of the emitted photon can be determined as;
[tex]E_{2}[/tex] - [tex]E_{1}[/tex] = -3.40 - (-13.60)
= -3.40 + 13.60
= 10.20 eV
= 10.20(1.6 x [tex]10^{-9}[/tex])
[tex]E_{2}[/tex] - [tex]E_{1}[/tex] = 1.632 x [tex]10^{-8}[/tex] Joules
The energy of the emitted photon is 10.20 eV (or 1.632 x [tex]10^{-8}[/tex] Joules).
(b) The wavelength, λ, can be determined as;
E = (hc)/ λ
where: E is the energy of the photon, h is the Planck's constant (6.6 x [tex]10^{-34}[/tex] Js), c is the speed of light (3 x [tex]10^{8}[/tex] m/s) and λ is the wavelength.
10.20(1.6 x [tex]10^{-9}[/tex]) = (6.6 x [tex]10^{-34}[/tex] * 3 x [tex]10^{8}[/tex])/ λ
λ = [tex]\frac{1.98*10^{-25} }{1.632*10^{-8} }[/tex]
= 1.213 x [tex]10^{-17}[/tex]
Wavelength of the photon is 1.2 x [tex]10^{-17}[/tex] m.
(c) The frequency can be determined by;
E = hf
where f is the frequency of the photon.
1.632 x [tex]10^{-8}[/tex] = 6.6 x [tex]10^{-34}[/tex] x f
f = [tex]\frac{1.632*10^{-8} }{6.6*10^{-34} }[/tex]
= 2.47 x [tex]10^{25}[/tex] Hz
Frequency of the emitted photon is 2.47 x [tex]10^{25}[/tex] Hz.
A person pulls a box across the floor with a rope. The rope makes an angle of 40 degrees tot he horizontal, and a total of 125 newtons of force is applied. How much work is done if the box is pulled for 25 meters?
Answer:
The angle formed of the rope with the surface = 40°
Force applied = 125Newtons
The displacement covered by the box =25metres
W= FDcos theta
[125×40×cos(40°) ] Joules
= [ (3125×0.76604444311)]Joules
= 2393.88888472 joules(ans)
Hope it helps
By how many times would the gravitational force between two objects decrease if the distance between the two objects was tripled?
Answer:
If the separation distance between any two objects is tripled (increased by a factor of 3), then the force of gravitational attraction is decreased by a factor of 9 (3 raised to the second power).
What is hydrometer? Describe its use and any one type of hydrometer.
Answer:
An instrument for measuring the density of liquids.
Explanation:
A hydrometer is an instrument used to determine specific gravity. It operates based on the Archimedes principle that a solid body displaces its own weight within a liquid in which it floats. Hydrometers can be divided into two general classes: liquids heavier than water and liquids lighter than water.
Thermohydrometers is one type of hydrometer.
An organ pipe is 116 cm long. Determine the fundamental and first three audible overtones if the pipe is (a) closed at one end, and (b) open at both ends.
Answer:
(a) when the pipe is closed at one end;
F₀ = 73.92 Hz
F₁ = 221.76 Hz
F₂ = 369.6 Hz
F₃ = 517.44
(b) when the pipe is open at both ends;
F₀ = 147.85 Hz
F₁ = 295.7 Hz
F₂ = 443.55 Hz
F₃ = 591.4 Hz
Explanation:
Given;
length of the pipe, L = 116 cm = 1.16 m
speed of sound in air, v = 343 m/s
The formula below will be used to determine the different frequencies of the pipe at different wavelengths
[tex]F = \frac{V}{\lambda}[/tex]
where;
F is frequency
λ is wavelength
(a) when the pipe is closed at one end;
Wavelength for fundamental frequency;
L = Node -------> Antinode
L = λ/4
λ = 4L
the fundamental mental frequency;
[tex]F_0 = \frac{V}{4L} = \frac{343}{4 \times 1.16} = 73.92 \ Hz[/tex]
Wavelength for first overtone or audible frequency;
L = Node -----> Node + Node ----> Antinode
L = λ/2 + λ/4
L = 3λ/4
λ = 4L/3
[tex]F_1 = \frac{V}{4L/3} = 3(\frac{V}{4L} ) = 3F_0 = 3 (73.92) = 221.76 \ Hz[/tex]
Thus, the next two audible frequencies will be multiple of next consecutive odd numbers after 3 (i.e 5 and 7);
F₂ = 5F₀ = 5(73.92) = 369.6 Hz
F₃ = 7F₀ = 7(73.92) = 517.44 Hz
(b) when the pipe is open at both ends;
Wavelength for fundamental frequency;
L = Antinode ----> Node + Node -----> Antinode
L = λ/4 + λ/4
L = λ/2
λ = 2L
the fundamental frequency;
[tex]F_0 = \frac{V}{2L} = \frac{343}{2\times 1.16} = 147.85 \ Hz[/tex]
The first three audible overtones will be multiples of the 3 consecutive positive integers after 1 (i.e 2, 3, 4)
F₁ = 2F₀ = 2(147.85) = 295.7 Hz
F₂ = 3F₀ = 3(147.85) = 443.55 Hz
F₃ = 4F₀ = 4(147.85) = 591.4 Hz
Select all the correct answers.
What happens when a ray of light moves from alr to water?
Its speed changes.
its color changes.
Its direction changes.
It's absorbed by water.
Answer:
it changes it's direction
Explanation:
When light travels from air into water, it slows down, causing it to change direction slightly. This change of direction is called refraction. When light enters a more dense substance (higher refractive index), it 'bends' more towards the normal line
Answer:
Hope this helps!
Explanation:
When light travels from air into water, it slows down, causing it to change direction slightly. This change of direction is called refraction. When light enters a more dense substance (higher refractive index), it 'bends' more towards the normal line.
distance travelled/time taken gives?
Answer:
speed
Explanation:
Speed = distance travelled/time taken
Answer: Speed
Explanation:
Speed is defined as the rate of change of the position of an object in a direction. The speed of an object is calculated as the distance travelled divided by the time that is taken.
Speed is regarded as a scalar quantity since it has only direction but doesn't have magnitude. The answer to the above question is speed.
What materials are difficult to charge because electrons easily flow through them?
Answer:
Conductors
Explanation:
1. A 10.-ohm resistor and a 20. -ohm resistor are connected in series
to a voltage source. When the current through the 10.- ohm resistor
is 2.0 amperes, what is the current through the 20.-ohm resistor?
(5F)
a. 1.0 A
b. 2.0 A
C. 0.50 A
d. 4.0 A
A 10.-ohm resistor and a 20. -ohm resistor are connected in series
to a voltage source. When the current through the 10.- ohm resistor
is 2.0 amperes, what is the current through the 20.-ohm resistor?
Answer:
B --> 2.0 A
the current going through the 10.-ohm resistor is what goes through 20.-ohm resistor
The current through the 20Ω resistor is 2.0 A. Hence option B is correct.
What is Current ?Current is a flow of charges. it is denoted by i and expressed in ampere A. Mathematically it is expressed as i = q/t, where q is the amount of charge and t is time. Current is nothing but amount of charges flown in the unit time in the electric wire. Charge is expressed in coulomb C and time in second s. hence coulomb per second (C/s) is ampere A. Charge on electron is 1.60217663 × 10⁻¹⁹C which is called as elementary charge.
There are two types of the current, Convectional current and non-conventional current. Convectional current is the current flows from positive to negative. Non convectional current flows from negative to positive. Note that flow of electrons is from negative to positive. Hence direction of flow of conventional current is from positive to negative.
In this problem, two resistors are connected in series. In the series combination of resistor, same current flows through all resistor.
Hence current through 20Ω Resistor is 2.0A.
Hence option B is correct.
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Which ones are correct??
Answer:
blanket:thermal conductivity
as it conduct heat.
aquarium glass:transparency
as light can be transfered from one side to
another.
An initially uncharged sphere is on an insulated stand and isolated in a chamber. The charge on the sphere is monitored as a beam of monochromatic light shines on the sphere. Initially nothing happens. The wavelength of the light is slowly decreased. When the wavelength reaches a certain value, a positive charge is suddenly measured on the sphere. The wavelength is then held constant, and the charge continues to increase at a constant rate. The intensity of the beam is then increased without the wavelength being changed, and the rate of increase of the charge becomes greater.
Required:
a. In a coherent paragraph-length response, describe the cause of the charge on the sphere and the changes in the observations about the charge, in terms of physics principles.
b. An electron in the chamber is moving with speed 2×10^5m/s when it collides with a positron (a particle identical to an electron except for the sign of its charge) moving with the same speed in the opposite direction. The particles annihilate each other. How much energy is released due to the annihilation?
c. In another experiment, a beam of electrons with uniform wavelength λe is incident on a slit, where the width of the slit is much larger than λe. A detector is placed near the slit, but no diffraction pattern is observed. What change should be made that would result in a diffraction pattern? Indicate why this change is the one needed.
Answer:
a) E = K + Φ, b) ΔE = 1.64 10⁻¹³ J., c) λ = a
Explanation:
a) In this case it is an example of the photoelectric effect that was correctly described by Einstein assuming that the light ray is composed of a series of particles called photons, each one with an energy given by the Planck equation
E = h f
c = λ f
substituting
E = h c /λ
We can see from this equation that as the wavelength of the ray decreases the energy of each photon increases, the moment arrives that the energy is sufficient to remove an electron from the sphere, thus leaving an unbalanced positive charge, this description explains why the positive charge appears on the sphere; the minimum wavelength to remove an electron is
E = K + Φ
if K = 0
E =Φ
where fi is the work function of the material.
When the intensity of the ray increases according to Eintein's description, the number of photons increases, so if the number of photons increases, the number of shocks and the number of electrons expelled increases, therefore the unbalanced positive charge also increases.
b) the energy released in collision is the sum of the energy of each particle
for the electron
E = K + m c² = (pc) ² + (m c²) ²
where the moment is
p = γ m u
γ = [tex]\sqrt{1- (\frac{u}{c})^2 }[/tex]
γ = [tex]\sqrt {1- ( \frac{2 \ 10^5}{3 \ 10^8 })^2 } = \sqrt{1- (6.67 \ 10 ^{-4)^2 }[/tex]
γ ≅ 1
in this case since the speed of the particles is much less than the speed of light,
E = (m u) ² + (m c²) ²
E = m² (u² + c²)
E = 9.1 10⁻³¹ [(2 10⁵) ² + (3 10⁸) ²
E = 9.1 10⁻³¹ 9 10¹⁶
E = 8.2 10⁻¹⁴ J
the positron has an energy of equal magnitude, so when the two particles annihilate the energy change is
ΔE = 2E
ΔE = 2 (8.2 10⁻¹⁴)
ΔE = 1.64 10⁻¹³ J.
c) the expression that describes the diffraction process is
a sin θ = m λ
sin θ = m λ/ a
where a is the width of the slit and m in diffraction order
The greatest value that the sine function can have is 1
1 = m λ / a
λ = a / m
therefore we can see that to see the diffraction phenomenon the width of the slit must be greater than or equal to the wavelength
Part D- Isolating a Variable with a Coefficient In some cases, neither of the two equations in the system will contain a variable with a coefficient of 1, so we must take a further step to isolate it. Let's say we now have • 30 + 4D = 5 • 2C + 5D = 2 t to None of these terms has a coefficient of 1. Instead, we'll pick the variable with the smallest coefficient and isolate it. Move the term with the lowest coefficient so that it's alone on one side of its equation, then divide by the coefficient. Which of the following expressions would result from that process?
1. D= 5/4 - 3/4C
2. C= 5/3 - 4/3D
Part E- Now that you have one of the two variables in Part D isolated, use substitution to solve for the two variables. You may want to review the Multiplication and Division of Fractions and Simplifying an Expression Primers. Enter the answer as two numbers (either fraction or decimal), separated by a comma, with C first.
Answer:
D) D = [tex]\frac{5}{4} - \frac{3}{4} \ C[/tex], E) (C, D) = ( [tex]\frac{17}{7}, \ \frac{-4}{7}[/tex]
Explanation:
Part D) two expressions are indicated
3C + 4D = 5
2C +5 D = 2
let's simplify each expression
3C + 4D = 5
4D = 5 - 3C
we divide by 4
D = [tex]\frac{5}{4} - \frac{3}{4} \ C[/tex]
The other expression
2C +5 D = 2
2C = 2 - 5D
C = [tex]1 - \frac{5}{2} \ D[/tex]
we can see that the correct result is 1
Part E.
It is asked to solve the problem by the substitution method, we already have
D = [tex]\frac{5}{4} - \frac{3}{4} \ C[/tex]
we substitute in the other equation
2C +5 D = 2
2C +5 (5/4 - ¾ C) = 2
we solve
C (2 - 15/4) + 25/4 = 2
-7 / 4 C = 2 - 25/4
-7 / 4 C = -17/4
7C = 17
C = [tex]\frac{17}{7}[/tex]
now we calculate D
D = [tex]\frac{5}{4} - \frac{3}{4} \ \frac{17}{7}[/tex]
D = 5/4 - 51/28
D =[tex]\frac{35-51}{28}[/tex]
D = - 16/28
D = [tex]- \frac{4}{7}[/tex]
the result is (C, D) = ( [tex]\frac{17}{7}, \ \frac{-4}{7}[/tex] )