Well, let's see what we've got here:
( 4⁻³ · 3⁴ · 4² ) / ( 3⁵ · 4⁻² ) .
The two simple rules of exponents that we're
going to use here are:
-- Two multiply two numbers with the same base,
add their exponents. Like (A³) · (A²) = A⁵ .
But the bases have to be the same.
-- A negative power just means it belongs in the
other section of a fraction.
A negative power on top means it belongs on the bottom.
A negative power on the bottom means it belongs on top.
Like A⁻² means 1/A² . And 1/B⁻³ means B³ .
That's all you need in order to clean up the big fraction
in the question. But in order to see where you can use
these rules, you need to re-arrange things first.
Original: ( 4⁻³ · 3⁴ · 4² ) / ( 3⁵ · 4⁻² )
Let's send the 4⁻³
to the bottom
where it belongs: ( -- 3⁴ · 4² ) / 4³ · ( 3⁵ · 4⁻² )
Not take that 4⁻² from
the bottom, and put it on
top, where it belongs: ( 4² · 3⁴ · 4² ) / 4³ · ( 3⁵ -- )
Multiply the 4²s on top: ( 4⁴ · 3⁴ ) / ( 4³ · 3⁵ )
Now let me break this up.
Not changing anything, just
writing it in a different way: ( 4⁴ / 4³ ) · ( 3⁴ / 3⁵ )
Look at the first fraction: 4⁴ / 4³ .
Divide top and bottom by 4³ , and it becomes just 4 .
Now look at the second fraction: 3⁴ / 3⁵ .
Divide top and bottom by 3⁴ , and it becomes just 1/3 .
So in the end, we're left with just 4 / 3 .
And THAT is exactly equal to the original big messy fraction
in the question. It has exactly the same numerical value, but
you'd never know it when you see it, because it's a lot simpler.
There are a lot of other ways we could have manipulated and
massaged the original fraction, but the steps are the same:
-- Multiply numbers with the same base, by adding the exponents.
-- Remember that a number with a negative exponent belongs
in the other section of the fraction, with a positive exponent.
The density of dry air at room temperature and atmospheric pressure Is 1.2 kg m-3. What volume would 6 kg of dry air occupy under these conditions?
Answer:
V = 5 m³
Explanation:
The density of air, d = 1.2 kg/m³
Mass of the dry air, m = 6 kg
We need to find the volume o the gas. We know that, the density of an object is given by mass divided by its volume. So,
[tex]d=\dfrac{m}{V}\\\\V=\dfrac{m}{d}\\\\V=\dfrac{6}{1.2}\\\\V=5\ m^3[/tex]
So, the volume of the dry air is 5 m³.
Explain why magnetic damping might not be effective on an object made of several thin conducting layers separated by insulation.
Answer:
The eddy currents will be very small.
Explanation:
An object made of several thin conducting layers separated by insulation may not be affected by magnetic damping because the eddy current produced in each layer due to induction will be very small and the opposing magnetic flux produced by the eddy currents will be very small.
[tex]\boxed{\color\red\huge\tt\bold\purple{Question}}[/tex]
Define Inertia.
Answer:
Inertia : a property of matter by which it continue in its existing state of rest or uniform motion in a straight line, unless that state is changed by external force.
HOPE ITS HELPS!!
[tex]\boxed{\color{red}\huge\tt\bold\purple{Answer}}[/tex]
Inertia is the tendency of an object to continue in the state of rest or of uniform motion. The object resists any change in its state of motion or rest.
Find the magnitude and angle of a vector given the components: Bx = 7, By=-5
Answer:
[tex] |B| = \sqrt{ {B _{x} }^{2} + {B _{y} }^{2} } \\ = \sqrt{ {7}^{2} + {5}^{2} } \\ = \sqrt{74} \\ = 8.6[/tex]
[tex]let \: the \: angle \: be \: \theta \\ \tan(\theta) = \frac{B _{y} }{B _{x} } \\ \tan( \theta) = \frac{ - 5}{7} \\ \theta = { \tan }^{ - 1} ( \frac{ - 5}{7} ) \\ = 35.5 \degree[/tex]
Find equivalent resistance.
Answer asap and please, please don't spam.
Answer:
R = 4.77 ohms
Explanation:
Four resistors are given such that,
R₁ = 2 ohms
R₂ = 3 ohms
R₃ = 5 ohms
R₄ = 10 ohms
Here, R₁ and R₂ in series. The equivalent is given by :
R₁₂ = R₁ + R₂
= 2 + 5
R₁₂ = 7 ohms
Similarly, R₃ and R₄ are in series. so,
R₃₄ = R₃ + R₄
= 10+5
R₃₄ = 15 ohms
Now, R₁₂ and R₃₄ are in parallel. So,
[tex]\dfrac{1}{R}=\dfrac{1}{R_{12}}+\dfrac{1}{R_{34}}\\\\\dfrac{1}{R}=\dfrac{1}{7}+\dfrac{1}{15}\\\\R=4.77\ \Omega[/tex]
So, the equivalent resistance s 4.77 ohms.
Una mochila tiene una masa de 5.9 Kg y se mueve con una aceleración de: 0.53 m/ seg2. ¿ Cuál es la fuerza que debe aplicar ?.
Answer:
3,13 N
Explanation:
Del enunciado de la segunda ley del movimiento de Newton;
F = ma
Dónde;
F = Fuerza aplicada
m = masa del cuerpo
a = aceleración del cuerpo
Sustitución de valores;
F = 5,9 kg * 0,53 m / seg2 = 3,13 N
Por tanto, la fuerza aplicada es 3,13 N
can someone please help
Answer: D
Explanation: because doing a yoga desk program is physical activity, 10k steps is pysical activity, riding a bike or walking/running is also physical activity. so it should be D, all of the above.
How much energy is transferred when the potential difference is 230 volts and the charge is 5 coulombs?
Answer:
1150J
Explanation:
Voltage = energy / charge
energy = Voltage * charge
energy = 230v * 5C = 1150J
An athlete running the velocity 3m/s due east is confronted with two trade winds. One wind travelling at 10m/s in a direction north 65degrees east and another wind travelling at 8m/s in a direction south 70degrees east. Find the resultant velocity and direction of the athlete
Answer:
v = 10.09 m / s, 8.78 North of East
Explanation:
The easiest way to solve this exercise is to decompose the velocities into a coordinate system, where the x-axis coincides with the West-East direction and the y-axis coincides with the South-North direction.
athlete's velocity v₁ₓ = 3 m / s
wind speed 2 v₂ = 10 m / s with direction 65 north of east
sin 65 = v_{2y} / v₂
cos 65 = v₂ₓ / v₂
v_{2y} = v₂ sin 65
v₂ₓ = v₂ cos 65
v_{2y} = 10 sin 65 = 9.06 m / s
v₂ₓ = 10 cos 65 = 4.23 m / s
wind speed 3 v₃ = 8 m / s with direction 70 south of east
This angle measured from the positive side of the x-axis is
θ = 360 - 70
θ = 290
sin 290 = v_{3y} / v₃
cos 290 = v₃ₓ / v₃
v_{3y} = v₃ sin 290
v₃ₓ = v₃ cos 290
v_{3y} = 8 sin 290 = -7.52 m / s
v₃ₓ = 8 cos 290 = 2.74 m / s
now we can find each component of the velocity
X axis
vₓ = v₁ + v₂ₓ + v₃ₓ
vₓ = 3 + 4.23 + 2.74
vₓ = 9.97 m / s
Y axis
v_y = v_{2y} + v_{3y}
v_y = 9.06 - 7.52
v_y = 1.54 m / s
to find the modulus let's use the Pythagorean theorem
v = [tex]\sqrt{v_x^2 + v_y^2 }[/tex]
v = [tex]\sqrt{9.97^2 + 1.54^2}[/tex]
v = 10.09 m / s
let's use trigonometry for the direction
tan θ = v_y / vₓ
θ = tan⁻¹ v_y / vₓ
θ = tan-1 1.54 / 9/97
θ = 8.78
the address is 8.78 North of East
Draw Lewis diagram of an oxygen difluoride molecule
Explanation:
that is my answer thank me later
Answer:
oxygen difluoride a polar molecule
When a golfer tees off, the head of her golf club which has a mass of 151 g is traveling 43.9 m/s just before it strikes a 46.0 g golf ball at rest on a tee. Immediately after the collision, the club head continues to travel in the same direction but at a reduced speed of 28.2 m/s. Neglect the mass of the club handle and determine the speed of the golf ball just after impact
Answer:
51.54 m/s
Explanation:
Applying,
Law of conservation of momentum,
Total momentum before collision = Total momentum after collision
mu+m'u' = mv+m'v'.................... Equation 1
Where m = mass of the head of the golf club, m' = mass of the gulf ball, u = initial velocity of the head of the gulf club, u' = initial velocity of the gulf ball, v = final velocity of the head of a gulf club, v' = final velocity of the gulf ball
From the question,
Given: m = 151 g = 0.151 kg, u = 43.9 m/s, m' = 46 g = 0.046 kg, u' = 0 m/s (at rest), v = 28.2 m/s
Substitute these values into equation 1
0.151(43.9)+0.046(0) = 0.151(28.2)+0.046(v')
solve for v'
6.6289+0 = 4.2582+0.046v'
0.046v' = 6.6289-4.2582
0.046v' = 2.3707
v' = 2.3707/0.046
v' = 51.54 m/s
A 15.0 kilogram cart initially traveling at 2.0 meters per second east accelerates uniformly at 0.75 meter per second squared east for 6.0
seconds. What is the speed of the cart at the end of this 6,0 second interval? Please include all work - including givens, formula, substitution,
and units for full credit. (2)
Answer:
Explanation:
Since this is not parabolic motion, it is one-dimensional motion. Very simple. What we are given is
mass: 15.0 kg
initial velocity: 2.0 m/s
acceleration: .75 m/s/s
time: 6.0 seconds
Since we are looking for final velocity, the equation we need for this is
v = v0 + at that says final velocity is equal to the initial velocity plus the acceleration of the object times how long it travels. We don't have a need for the mass here at all.
[tex]v=2.0\frac{m}{s}+.75\frac{m}{s^2}(6.0s)[/tex]
Notice that one of the seconds labels to the right of the plus sign cancel out, leaving us with like units...which we HAVE to have if we want to add.
Simplifying a bit gives us
v = 2.0 m/s + 4.5 m/s so
v = 6.5 m/s
What 3 things does the force of gravity depend on?
Answer:
Size of an object, and the distance between the objects.
When the mass of an object increases the force of gravity increases as well.
Explanation:
The magnitude of this force depends upon the mass of each object and the distance between the centers of the two objects. Mathematically, we say the force of gravity depends directly upon the masses of the objects and inversely upon the distance between the objects squared.
(b) How much energy must be supplied to boil 2kg of water? providing that the specific latent heat of vaporization of water is 330 kJ/kg.
Complete question:
(b) How much energy must be supplied to boil 2kg of water? providing that the specific latent heat of vaporization of water is 330 kJ/kg. The initial temperature of the water is 20 ⁰C
Answer:
The energy that must be supplied to boil the given mass of the water is 672,000 J
Explanation:
Given;
mass of water, m = 2 kg
heat of vaporization of water, L = 330 kJ/kg
initial temperature of water, t = 20 ⁰C
specific heat capacity of water, c = 4200 J/kg⁰C
Assuming no mass of the water is lost through vaporization, the energy needed to boil the given water is calculated as;
Q = mc(100 - 20)
Q = 2 x 4200 x (80)
Q = 672,000 J
Q = 672,000 J
Q = 672,000 J
Therefore, the energy that must be supplied to boil the given mass of the water is 672,000 J
1 Ten (10) ml aqueous solutions of drug A (10% w/v) and drug B (25% w/v) are stored in two identical test tubes under identical storage conditions at 37°C for 3 months. If both drugs degrade by first-order, which drug will retain the highest percentage of initial concentration?
Answer:
YOUR answer is given below:
Explanation:
Drug B will retain the highest percentage of initial concentration.
First order degradation means that both solution will degrade by same amount in same time because first order is directly proportional relationship between given both aqueous solution.
Given that Ten (10) ml aqueous solutions of drug A (10% w/v) and drug B (25% w/v) are stored in two identical test tubes.
Since, initially concentration of Drug B is more. Therefore, at all instant concentration of Drug will be highest.
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1) Num sistema isolado tenho 4 tipos de corpos diferentes. A, B, C e D. A está em equilíbrio térmico com B. B está em equilíbrio térmico com C. D está em equilíbrio térmico com A. Esse sistema está transmitindo energia entre seus corpos? Justifique sua resposta.
Answer:
Yes.
Explanation:
Yes, this system transmitting energy between your bodies because everybody is in thermal equilibrium with other body. Thermal equilibrium occurs when there is same amount of thermal energy is gained by the body and same amount of energy lost by the body so there is no increase or decrease occur in the thermal energy of each body so we can say that the system transmitting energy between the bodies.
WILL GIVE BRAINLIEST! Which statement about gravity is correct?
A. Gravity is the substance that most organisms breathe.
B. Gravity is used in automobiles, as it is required to fuel them.
C. Gravity generally works as a force attracting a body toward earth.
D. Gravity is the result of built up emotions that spread when organisms release energy.
Answer:
Its Letter C Because Gravity's characteristic is to draw objects (including us) toward its center (which in this case, Earth).
Do only number 5 and thank
Answer:
Quantity of charge = 1800 Coulombs
Explanation:
Given the following data;
Current = 1 A
Time = 0.5 hours
Conversion:
1 hour = 60 * 60 = 3600 seconds
0.5 hour = 0.5 * 3600 = 1800 seconds
To find the charge passing through the wire;
Mathematically, the quantity of charge passing through a conductor is given by the formula;
Quantity of charge = current * time
Substituting into the formula, we have;
Quantity of charge = 1 * 1800
Quantity of charge = 1800 Coulombs
which of the following is incorrect for nuclear forces
a) they are attractive in nature
b) they are short range forces
c) they obey inverse square law
d) they are non conservative in nature
Answer:
c they obey inverse square law
1d. Conservation of energy is demonstrated in this roller coaster example.
The Conservation of Energy is a principle which states that energy cannot be created
or destroyed, but can be altered from one form to another
Friction plays a significant role in the efficiency of the rollercoaster cars. Explain how, even
with friction, the law of conservation of energy still holds true. (2 points)
Answer:
can you clear your question I can't understand
In Rutherford's model of the atom, the positive charge
A) occupies most of the space in the atom
B) is concentrated at the center of the atom
C) is distributed throughout the atom's volume
D) revolves about the nucleus in specific orbits
Answer:
the correct address is B
In Rutherford's model of the atom, the positive charge is concentrated at the center of the atom.
What is Rutherford's model?The model described the atom as a tiny, dense, positively charged core called a nucleus, in which nearly all the mass is concentrated, around which the light, negative constituents, called electrons, circulate at some distance, much like planets revolving around the Sun.
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the gravity on mars is 3.8 m/s2 and you weigh 200 N. your mass will be??
Answer:
Mass = 52.63 kilograms
Explanation:
Given the following data;
Acceleration due to gravity = 3.8 m/s²
Weight = 200 N
To find mass;
Mathematically, the weight of a physical object is given by the formula;
Weight = mass * acceleration due to gravity
Substituting into the formula, we have;
200 = mass * 3.8
Mass = 200/3.8
Mass = 52.63 kg
Why does the soccer ball not increase in size when air is pumped into it?
Answer:
(I'm not 100% sure about this)
Maybe its because the soccer ball is faulty. Such troublemakers can include holes in the ball, preventing it from inflating.
What is the frequency of a wave that passes a given point 412 times in 4.0
seconds?
O A. 0.0097 s
OB. 103 Hz
O C. 408 S
O D. 1650 Hz
SUBMIT
Answer: A.0,0097s
Mas a unidade aí deveria ser Hertz (Hz)
Explanation:
Answer:
103 hz
Explanation:
Thermal physics vs atomic physics ...which is easier?
Answer:
Thermal physics
Explanation:
Because it uses temperature
Answer:
In my opinion both are easier if you'll work hard on it...
(I have 2 questions which are very similar)
Which of the chemical reactions above stores energy?
A. Cellular respiration
B. Photosynthesis
C. Both cellular respiration and photosynthesis
D. Neither cellular respiration nor photosynthesis
15 Which of the chemical reactions above releases energy?
A. Cellular respiration
B. Photosynthesis
C. Both cellular respiration and photosynthesis
D. Neither cellular respiration nor photosynthesis
(help!!!) SCIENCE
Answer:
B
A
Explanation:
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A battery has a potential resistance of 12 V and a current of 1280 mA. What is the resistance? PLS HELP ME ASAPPPPPPPPPP
Resistance (R) = 9.375 ohm (Ω)
Steps:
[tex]R = \frac{V}{I} [/tex]
[tex] = \frac{12 \: volt}{1280 \: milliampere} [/tex]
[tex] = \frac{12 \: volt}{1.28 \: ampare} [/tex]
[tex] = 9.375 \: ohm (Ω)[/tex]
Please solve it as soon as possible with steps
Answer:
In 1 round 62.857m
In 1.5 round 94.2855m
In 2 round 125.714m
In 2.5 round 157.1425
A piece of iron has a mass of 30 g and its volume is 6.2 cm3. What is its density?
Answer:
Density = 4.84 g/cm³
Explanation:
Given the following data;
Mass = 30 g
Volume = 6.2 cm³
To find the density of the piece of iron;
Density can be defined as mass all over the volume of an object.
Simply stated, density is mass per unit volume of an object.
Mathematically, density is given by the equation;
[tex]Density = \frac{mass}{volume}[/tex]
Substituting into the equation, we have;
[tex]Density = \frac{30}{6.2}[/tex]
Density = 4.84 g/cm³
Croquet balls must have a mass of 0.50 kg. A red croquet ball is moving at 5 m/s. It strikes an at-rest green croquet ball head-on and then continues to move in the same direction, but with a speed of 2 m/s. What is the final speed of the green ball?
A.
5 m/s
B.
0.5 m/s
C.
2 m/s
D.
3 m/s
Answer:
Explanation:
The Law of Momentum Conservation for us has the equation
[tex][m_rv_r+m_gv_g]_b=[m_rv_r+m_gv_g]_a[/tex] and filling in:
[tex][(.50)(5.0)+(.50)(0)]=[(.50)(2.0)+(.50)v_g][/tex] and
2.5 = 1.0 + .50v and
1.5 = .50v so
v = 3 m/s
The final speed of the green ball is 3m/s. This can be calculated by the law of conservation of momentum. Thus, the correct option is D.
What is the law of Conservation of Momentum?
The principle of the law of conservation of momentum states that if any two objects undergo collision, then the total momentum of the objects before and after the collision will be the same if there is no external force acting on the colliding objects.
The Law of Conservation of Momentum has the equation which is:
m₁ × u₁ + m₂ × u₂ = m₁ × v₁ + m₂ × v₂
where, m₁ = mass of object 1,
u₁ = initial velocity of object 1 before collision,
m₂ = mass of object 2,
v₁ = final velocity of object 1 after collision,
v₂ = final velocity of the object 2 after collision.
0.50 × 5 + 0.50 × 0 = 0.50 × 2 + 0.50 × v₂
2.5 + 0 = 1.0 + 0.50 × v₂
2.5 - 1.0 = 0.50 × v₂
1.5 = 0.50 × v₂
1.5/ 0.5 = v₂
v₂ = 3m/s
Therefore, the correct option is D.
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