What two methods are the best choices to factor this expression 18x2-8
Answer:
Please check the explanation
Explanation:
The best two methods will be:
Factor by groupingFactor out the GCFFactor by grouping
Factor by grouping deals with establishing a smaller groups from each term.
[tex]18x^2=\:\left(2\cdot 3\cdot 3\cdot x^2\right)[/tex]
[tex]8\:=\:\:2\cdot 2\cdot 2[/tex]
Therefore, the expression becomes
[tex]18x^2=\:\left(2\cdot 3\cdot 3\cdot x^2\right)-\left(2\cdot \:2\cdot \:2\right)[/tex]
Now factor out the greatest common factor (GCF) which is 2
[tex]=\:2\left(3\cdot \:\:3x^2-\left(2\right)\left(2\right)\right)[/tex]
[tex]=2\left(9x^2-2\cdot \:2\right)[/tex]
[tex]=2\left(9x^2-4\right)[/tex]
Factor out the GCF
Given the expression
[tex]18x^2-8\:\:\:[/tex]
factor out common term 2
[tex]=2\left(9x^2-4\right)[/tex]
[tex]=2\left(3x+2\right)\left(3x-2\right)[/tex] ∵ [tex]Factors\:\:\left(9x^2-4\right)=\left(3x+2\right)\left(3x-2\right)[/tex]
A radio signal has a frequency of 1.023 x 108 HZ. If the speed of the signal in air is 2.997 x 108m/s, what is the wavelength of the signals? а 7.15 m b 5.23 m C 2.93 m d 0.93 m
Answer:
2.93 m (which agrees with answer "C" on the list)
Explanation:
Recall that the speed of the wave equals the product of the wave's length times its frequency. Therefore, the wavelength is going to be the quotient of the speed of the signal divided its frequency:
Wavelength = 2.997 10^8 / 1.023 10^8 = 2.93 m
Elevator is accelerating upward 3.5 M/S2 and has a mass of 300 KG. The force of gravity is 2940 N. What is the tension force pulling elevator up?
Answer:
T = 3990 N
Explanation:
The free body diagram for the elevator consists of a tension force pointing up, and its weight pointing down. So the elevator's net force is:
F = T - 2940N
ad at the same time, using Newton's second law, we have that this net force should equal the elevator's mass (300 kg) times its acceleration (a):
T - 2940N = 300kg (3.5m/s^2)
then
T = 2940 N + 1050 N
T = 3990 N
The chart shows Daniela’s run through her race.
A graph with horizontal axis time (seconds) and vertical axis position in (meters). The line runs straight from 0 seconds 5 meters to 10 seconds 30 meters.
What is her velocity?
1.5 m/s
2 m/s
2.5 m/s
5 m/s
Answer:
Explanation:
velocity is the rate of change of displacement with respect to time.
Velocity = displacement/time
If a line runs straight from 0 seconds 5 meters to 10 seconds 30 meters.
The velocity will be expressed as;
v = d2-d2/t2-t1
v = 30-5/10-0
v = 25/10
v = 2.5m/s
Hence her velocity is 2.5m/s
Daniela's velocity is 2.5 m/s.
Velocity is the ratio of displacement to time taken. It is given by:
Velocity = displacement / time
The velocity of Daniela can be gotten by calculating the slope of the graph. Considering the points (0, 5) and (4, 15).
[tex]Velocity(slope)=\frac{15-5}{4-0}=2.5\ m/s[/tex]
Therefore Daniela's velocity is 2.5 m/s.
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A potential difference of 1.20 V will be applied to a 33.0 m length of 18-gauge copper wire (diameter = 0.0400 in.). Calculate (a) the current, (b) the magnitude of the current density, (c) the magnitude of the electric field within the wire, and (d) the rate at which thermal energy will appear in the wire.
Answer:A) Current = 1.739A, B)current density, J = 2.147x10^6 A/m2
magnitude of electric field , E = 0.036 N/C
)rate of thermal energy, P =2.086W
Explanation:
Resistance = R = ρL/A
But the cross-section area of the wire. is given as
Diameter / 2 = 0.04/2 =0.02in to m = 0.02 / 39.37= 0.000508
A = πr^2 = π x 0.000508^2 = 8.10 x 10^-7
since resistivity of copper,ρ= 17x10-9 ohm.m
so resistance is R = ρL/A
17x10-9 x 33 / 8.1x10-7
= 0.69 ohm.
A) Current = I = Voltage /Resistance =1.20/0.69 =1.739A
B)current density, J = Current /Area
= 1.739/8.1x10-7
= 2.147x10^6 A/m2
c)magnitude of electric field , E = Current density x resistivity =J ρ
E = 2.147 x 10^6 x 17 x 10^-9
E = 0.036 N/C
D)rate of thermal energy, P = I² R =1.739² X 0.69
=2.086W
The image blow shows a certain type of global wind:
What best describes these winds? Polar easterlies caused by air above poles being relatively warmer.
Polar easterlies caused by air above poles being relatively cooler.
Trade winds caused by air above equator being relatively warmer.
Trade winds caused by air above equator being relatively cooler.
Answer:
i got u its a
Explanation:
Based on the situation above, choose the CORRECT type of error.
The reading from the timer was not accurate because some of
the timer's display was missing and broken."
Answer:
what's your question I can't understand
A golfer hits the ball off the tee at an angle of thirty-five degrees from the horizontal with a speed of 46 m/s. It lands on the green, which is elevated 5.50 m higher than the tee. How much time elapsed from when the ball was hit to when it landed on the green?
Answer:
t = 5.16 seconds.
Explanation:
The flight time can be found using the following equation:
[tex] y_{f} = y_{0} +v_{0y}*t - \frac{1}{2}gt^{2} [/tex]
Where:
t: is the time
g: is the gravity = 9.81 m/s²
y₀: is the initial height = 0
[tex]y_{f}[/tex]: is the final height = 5.50 m
[tex]v_{0y}[/tex]: is the initial vertical velocity = v*sin(35)
v: is the speed = 46 m/s
[tex] 5.50 = 46*sin(35)*t - \frac{1}{2}9.81*t^{2} [/tex]
By solving the above cuadratic equation we have:
t₁= 0.22 s and t₂= 5.16 s
We will take the solution equal to 5.16 seconds, since in 0.22 seconds (very short time) the ball is going up and in 5.16 seconds it landed on the green.
Therefore, 5.16 seconds have passed since the ball was hit until it landed.
I hope it helps you!
A wire of radius 0.8 cm carries a current of 106 A that is uniformly distributed over its cross-sectional area. Find the magnetic field B at a distance of 0.07 cm from the center of the wire.
Answer:
The magnetic field is [tex]B = 2.319 *10^{-3} \ T[/tex]
Explanation:
From the question we are told that
The radius of the wire is [tex]r = 0.8 \ cm = 0.008 \ m[/tex]
The current is [tex]I = 106 \ A[/tex]
The position considered is d = 0.07 cm = 0.0007 m
Generally the magnetic field is mathematically represented as
[tex]B = \frac{\mu_o * I}{2\pi * \frac{r^2}{d} }[/tex]
Here [tex]\mu_o[/tex] is the permeability of free space with value [tex] 4\pi * 10^{-7} N/A^2[/tex]
So
[tex]B = \frac{ 4\pi * 10^{-7} * 106 }{2 * 3.142 * \frac{0.008^2}{0.0007} }[/tex]
=> [tex]B = 2.319 *10^{-3} \ T[/tex]
A runner taking part in the 200 m dash must run around the end of a track that has a circular arc with a radius of curvature of 50 m. If he completes the 200 m dash in 29.6 s and runs at constant speed throughout the race, what is the magnitude of his centripetal acceleration (in m/s2) as he runs the curved portion of the track?
Answer:
The centripetal acceleration of the runner as he runs the curved portion of the track is 0.91 m/s²
Explanation:
Given;
distance traveled in the given time = 200 m
time to cover the distance, t = 29.6 s
speed of the runner, v = d / t
v = 200 / 29.6
v = 6.757 m/s
The centripetal acceleration of the runner is given by;
[tex]a_c = \frac{V^2}{r}[/tex]
where;
r is the radius of the circular arc, given as 50 m
Substitute the givens;
[tex]a_c = \frac{V^2}{r}\\\\a_c = \frac{(6.757)^2}{50}\\\\a_c = 0.91 \ m/s^2[/tex]
Therefore, the centripetal acceleration of the runner as he runs the curved portion of the track is 0.91 m/s².
match the variables to its definition
Answer:
See connections below
Explanation:
1 [tex]\Rightarrow[/tex] b
2 [tex]\Rightarrow[/tex] a
3 [tex]\Rightarrow[/tex] d
4 [tex]\Rightarrow[/tex] i
5 [tex]\Rightarrow[/tex] g
6 [tex]\Rightarrow[/tex] h
7 [tex]\Rightarrow[/tex] c
8 [tex]\Rightarrow[/tex] e
9 [tex]\Rightarrow[/tex] f
A 45 kg object has a momentum of 225 kg-m/s northward. What is the object's velocity?
A. 180 m/s
B. 5.0 m/s
C. 10,125 m/s
D. 0.20 m/s
Jolie is on the weightlifting team at her school. She must lift as much weight as possible from the ground to a standing straight position. How much work will Jolie do if she uses a force of 5N to lift 150 pounds to a height of 1.5m? 0 2.3) O 6.5) 7.5) 0 3.3)
Answer:
=7.5J
Explanation:
Step one:
given data
the applied force F=5N
the distance = 1.5m
Step two:
Required
work done by Jolie
Now by definition, the work done is the applied times the distance which the force is applied
Wd= F*D
Wd= 5*1.5
Wd=7.5J
If she uses a force of 5N to lift 150 pounds to a height of 1.5m, the work done will be 7.5J
An electric motor spins at a constant 2695.0 rpm. If the rotor radius is 7.165 cm, what is the linear acceleration of the edge of the rotor?A) 5707 m/s^2 B) 281.6 m/s^2 C) 28.20 m/s^2 D) 572,400 m/s^2
Answer:
5707 m/s^2
Explanation:
A 40-cm-diameter, 300 g beach ball is dropped with a 4.0 mg ant riding on the top. The ball experiences air resistance, but the ant does not. What is the magnitude of the normal force exerted on the ant when the ball's speed is 4.0 m/s?
Answer:
The normal force exerted on the ant is 0.75 N.
Explanation:
Given;
diameter of the ball, D = 40 cm = 0.4m
radius of the ball, r = 0.2m
mass of the beach ball, m₁ = 300 g = 0.3 kg
mass of the ant, m₂ = 4 x 10⁻⁶ kg
speed of the ball, v = 4 m/s
The area of the ball, assuming spherical ball is given by;
A = 4πr²
A = 4π(0.2)² = 0.5027 m²
The drag force (resistance) experienced by the spherical ball is given as;
[tex]F_D = \frac{1}{2}C\rho Av^2[/tex]
where;
C is the drag coefficient of the spherical ball = 0.45
ρ is density of air = 1.21 kg/m³
[tex]F_D = \frac{1}{2}C\rho Av^2\\\\F_D = \frac{1}{2}(0.45)(1.21) (0.5027)(4)^2\\\\F_D = 2.19 \ N[/tex]
The downward force of the ball due to its weight and that of the ant is given by;
[tex]F_g = mg\\\\F_g =g(m_{ant} + m_{ball})\\\\F_g = g(4*10^{-6} \ kg\ + \ 0.3\ kg)\\\\F_g = g(0.300004 \ kg) \ \ \ (mass \ of \ the \ ant \ is \ insignificant)\\\\F_g = 9.8(0.3)\\\\F_g = 2.94 \ N[/tex]
The net downward force experienced by the ball is given by;
[tex]F_{net} = F_g - F_D\\\\F_{net} = 2.94 \ N - 2.19 \ N\\\\F_{net} = 0.75 \ N[/tex]
This downward force experienced by the ball is equal to the normal reaction it exerts on the ant.
Thus, the normal force exerted on the ant is 0.75 N.
What percentage of an iron anchor’s weight will be supported by buoyant force when submerged in salt water?
Answer:
0.87
Explanation:
To solve this, we use the principle of Archimedes. Archimedes Principal of flotation states that "the buoyant force of an object is equal to the total weight of the fluid it displaces."
In the attachment, I stated the mathemacal formula, of which
F(B) = The buoyant force
w(fl) = The weight of the salt water displaced
p(iron) = density of iron
p(salt) = density of the salt water = 1025 kg/m³
F' = weight of the iron in air
F = weight of the iron in salt water
p(man) = density of man = 7680 kg/m³
The rest are the easy calculations done by substituting the values
Mr Johnson launches an arrow horizontally at a rate of 40m/s off of a 78.4 m cliff towards the south, how much time does it take before the arrow hits the ground below (step 1 of a quesiton will need this answer for a future question)
a 2 seconds
b. 1 second
c.4 seconds
d 19.6
Answer:c
Explanation:
Explane Hawaii characteristics
Answer:
Hawaii is located in the Pacific Ocean to the southwest of the continental U.S., southeast of Japan and northeast of Australia. Hawaii is known for its tropical climate, unique topography, and natural environment, as well as its multicultural population.
What is the electric force between two point charges when 91 = -4e, 92 = +3 e,
and r= 0.05 m?
e = 1.6 x 10-1C, k = 9.00 x 10°Nom/C2)
Kouch
A. -1.1 * 10-24 N
B. 1.1 * 10-24 N
C. 5,5 x 10-25 N
D. -5.5 x 10-25 N
Answer:option B
Explanation:
What are the things being compared in the following argument?
"The United Nations failed to intervene in Bosnia to prevent massive human rights violations and ethnic cleansing. It also failed to act to stop the murders of close to a million innocent people in Rwanda. THe UN will not intervene to stop any widespread slaughter of innocents in Nigeria."
a.
Ethnic cleansing in Nigeria and Bosnia
b.
The slaughter of innocents by the UN
c.
situations in which the United Nations might intervene
d.
Human rights violations in Rwanda and Bosnia
Answer:
C
Explanation:
The thing that is being compared in the given argument is Ethnic cleansing in Bosnia. The correct option is A.
What is Ethnic cleansing?Ethnic cleansing is the systematic removal of ethnic, racial, and religious groups from a given area with the goal of ethnically homogenizing the region.
In this group of resettled Bosnian refugees, ethnic cleansing has resulted in high rates of PTSD and depression, as well as other forms of psychological morbidity.
The long-term consequences of ethnic cleansing as a form of mass psychological trauma have yet to be studied.
Political elites seek to gain and/or consolidate political power by capitalizing on nationalism and the desire to create the domestic "other" in order to foster solidarity among the dominant nationality.
The topic under discussion in this argument is ethnic cleansing in Bosnia.
Thus, the correct option is A.
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Image formed by a plane mirror is
Answer: A plane mirror always forms a virtual image (behind the mirror). The image and object are the same distance from a flat mirror, the image size is the same as the object size, and the image is upright.
Explanation:
1. When an object is at rest, not moving, and is crashed into by another
object...which object is experiencing a force and in what direction? Or are
both experiencing a force - what direction?
Answer:
both experience forces or at least a force
Explanation:
it would go in the direction the other object
(second object, the one that crashed) was going
si if going right then right if left then left
plus or minus
A 60-W light bulb emits spherical electromagnetic waves uniformly in all directions. If 50% of the power input to such a light bulb is emitted as electromagnetic radiation, what is the radiation intensity at a distance of 2.00 m from the light bulb?
A) 15 W/m2
B) 4.8 W/m2
C) 2.4 W/m2
D) 0.60 W/m2
E) 1.2 W/m2
Answer:
a
Explanation:
A 60-W light bulb emits spherical electromagnetic waves uniformly in all directions. If 50% of the power input to such a light bulb is emitted as electromagnetic radiation, what is the radiation intensity at a distance of 2.00 m from the light bulb
so i did 60(50%)=30÷2=15
The radiation intensity is 15 W / m².
To find the radiation intensity, the values are given as,
Power = 60 W
Distance = 2 m
50% of the power input is emitted as electromagnetic radiation.
What is radiation intensity?The amount of energy emitted per unit solid angle by per unit area of the radiating surface can be said as radiation intensity.
As, when there is a power output, the input power will emit some energy as a kinetic energy and electromagnetic radiation. By the way, the power input emits 50 % as a radiation, so the power input given as,
P = 60 / 2 ( As it was 50 % )
= 30 Watt.
The radiation intensity is,
In = 30 / 2
= 15 W / m².
Thus, the radiation intensity is calculated as, 15 W/ m².
So, Option A is the correct answer.
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What physical property does the symbol I_enclosed in problem 5 represent? a. The current along the path in the same direction as the magnetic field b. The current in the path in the opposite direction from the magnetic field c. The total current passing through the loop in either direction d. The net current through the loop
Answer:
C
Explanation:
Current passing through the loop in either direction
In your new job, you are the technical advisor for the writers of a gangster movie about Bonnie and Clyde. In one scene Bonnie and Clyde are being pursued by a police car. They are 750m from a level railroad crossing travelling at 100 km/hr. A train is 500 meters from the crossing travelling at 130 km/hr. The level crossing is on the state line, and so if they can beat the train, they could evade capture, at least for a while until they become Federal fugitives. They accelerate at a constant rate of 4 m/s2 toward the crossing. The writers want to know if Bonnie and Clyde make it across the crossing before the train.
Answer:
Explanation:
Velocity of train 130 km /hr
distance of crossing s = 500 m = .5 km
Time taken by train to reach crossing = .5 / 130 = .003846 hr = 13.85 s
Time taken by gangster to reach the crossing = t
initial velocity u = 100km/h = 27.77 m /s
distance of crossing s = 750 m
acceleration a = 4 m /s
s = ut + .5 a t²
750 = 27.77 t + .5 x 4 x t²
2 t² + 27.77 t - 750 = 0
t = - 27.77 ± √(27.77² + 4 x 2 x 750) / 2 x 2
= - 27.77 ±√ ( 771.17 + 6000) / 4
= - 27.77 ±82.28 / 4
= 13.62 s
So this time is less than time taken by train so it will be able to cross the crossing before train arrives .
What is the difference between the two graphs
Answer:
one of the graph is postion-time graph while the other one is velocity-time graph
Why do stretching exercises increase flexibility more than cardio exercises?
5. How does the existence of humans compare with Earth's age?
Answer:
Human activity has fundamentally changed our planet. We live on every continent and have directly affected at least 83% of the planet’s viable land surface. Our influence has impacted everything from the makeup of ecosystems to the geochemistry of Earth, from the atmosphere to the ocean. Many scientists define this time in the planet’s history by the scale of human influence, and label it as a new geological epoch called the Anthropocene.
Explanation:
Test Due! Which statement is true?
The correct answer is C. Mercury and Mars have the same gravitational force
Explanation:
This chart compares the different features of two planets in our solar system (Mercury and Mars). In this chart, the only numerical value or feature that is the same for both planets is gravity because for both planets gravity is 1.7 m/s2. This implies the gravitational force or the force that attracts objects towards the center of the planet is the same or that objects are pulled with the same force in both planets. Moreover, this factor depends on others such as mass, density, among others.
gravities limit is under which sphere as the perimeter?