When the two resistors are in parallel, the current through the the larger resistor will be less and the current through the smaller resistor will be more.
According to ohm's law, the electric current is proportional to the voltage applied, so we can write,
V ∝ I
V = IR
R is the resistance.
In parallel, the voltage is same. So, we can write,
I ∝ 1/R
So, as we can see that the current and the resistance are inversely related, we can conclude that when the two resistors are connected in parallel, the current from the larger resistor will be less and current through the smaller resistor will be more.
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y
013 10.0 points
An Atwood machine is constructed using two
wheels (with the masses concentrated at the
rims). The left wheel has a mass of 1.9 kg and
radius 24.05 cm. The right wheel has a mass
of 2.6 kg and radius 25.74 cm. The hanging
mass on the left is 1.97 kg and on the right
1.1 kg.
What is the acceleration of the hanging
mass on the left? Use down as the posi-
tive direction. The acceleration of gravity is
9.8 m/s².
Answer in units of m/s².
The system's acceleration is determined by the difference in torque and mass applied.
What is the acceleration of the hanging mass?
Acceleration = m/s²
T= Newtons compared to the weight W = Newtons for the hanging mass. The acceleration is zero if the weight of the hanging mass is less than the frictional resistance force acting on the mass on the table.
Because the weight of the hanging mass must move three times the mass, the acceleration is reduced to one-third of its original value. When the table mass is increased to 99 times the hanging mass, the acceleration becomes a = (1/100)g.
Newton's second law of motion states that an object's acceleration equals the net force acting on it divided by its mass, or a = F m.
When the mass of an object and the net force acting on it are known, this acceleration equation can be used to calculate its acceleration.
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A parent is looking at their kids backpacks and wants to compare their masses. What is the best tool to find the mass of each bag
Answer:
balence
Explanation:
A balance scale would be the most accurate tool for a parent to use when trying to compare the masses of their kids' backpacks.
Explanation:The best tool for comparing the masses of the backpacks would be a balance scale. A balance scale allows for precise comparison of items' weight or mass. In order to use the tool, the parent would first place one backpack on one side of the balance scale and the second backpack on the other side. The balance scale will tip towards the side of the heavier backpack, allowing the parent to determine which one has a larger mass. For a more quantitative measurement, weights can be added to the lighter side until the scale balances again. The total mass of the weights then corresponds to the mass of the heavier backpack.
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the orbital speed of a satellite orbiting the earth in a circular orbit at the height of 400 km above the surface of the earth is vo. if the same satellite is at a distance of 800 km above the surface of the earth and the radius of the earth is 6400 m, the orbital speed of the satellite would be
The orbital speed of the satellite would be 1.4v₀. The result is obtained by using the ratio of the orbital speeds in two situations.
What is the orbital speed of a satellite?The orbital speed of satellite orbiting the Earth can be expressed as
v = √(GM/r)
Where
v = orbital speed of satellite (m/s)G = gravitational constant (6.6743 × 10⁻¹¹ m³kg⁻¹s⁻²)r = distance of planet and satellite (m)A satellite is orbiting around the Earth.
When it is at a height of 400 km above the surface of the Earth, the orbital speed is v₀.If the same satellite is at a height of 800 km above the surface of the Earth, find the orbital speed!The radius of the Earth, R = 6400 m.
Let's determine the distance of the two situations.
Situation 1
r₁ = h₁ + R
r₁ = 400 km + 6400 m
r₁ = 400000 m + 6400 m
r₁ = m
Situation 2
r₂ = h₂ + R
r₂ = 800 km + 6400 m
r₂ = 800000 m + 6400 m
r₂ = 806400 m
Make a ratio using the formula above. We will get the orbital speed in the situation 2.
[tex]\frac{v_{1}}{v_{2}} = \frac{\sqrt{GM/r_{1}} }{\sqrt{GM/r_{2}} }[/tex]
[tex]\frac{v_{1}}{v_{2}} = \sqrt{\frac{r_{2}}{r_{1}}}[/tex]
[tex]\frac{v_{0}}{v_{2}} = \sqrt{\frac{806400}{406400}}[/tex]
[tex]\frac{v_{0}}{v_{2}} = \sqrt{1.98425}[/tex]
[tex]\frac{v_{0}}{v_{2}} = 1.40863[/tex]
v₂ = 1.40863v₀
v₂ ≈ 1.4v₀
Hence, the satellite would have an orbital speed of 1.4v₀.
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how to make a maga........................
How to make a magazine:
1. Determine a theme and focus on such theme
2. Determine how our magazine will form
3. Determine the deadline
4. Determine the content of the article and the number of column
5. Add photos / images
6. Create design front page / cover
7. Advertisement loading
8. Print process
9. Distribution
The steps to make a magazine1. Determine a theme and focus on such theme
A magazine must clearly target readers. by determining the theme, we automatically determine the target audience for our magazine. after the theme and target audience have been determined, the next step is to focus on that.
2. Determine how our magazine will form
This step tends to be more complex. because we have to choose the type of paper material, the size of the magazine, the appearance of the front page, etc. once again this is very related to our target readers. our magazine
3. Determine the deadline
We must be able to determine when our magazine will be published by first determining the deadline. by setting a deadline, we are like making a 'dead promise' with our magazine readers
4. Determine the content of the article and the number of column
The content of the article must always relate to the main theme of our magazine and be very acceptable to our target readers. regarding the number of columns, make it in such a way that it is not too extravagant on the page but the reader is not troubled by the form of the column which is not reader friendly
5. Add photos / images
A magazine equipped with photos/pictures will look more attractive when compared to a plain magazine without photos/pictures. avoid reader boredom because it can result in a reduction or even loss of readers of our magazine
6. Create design front page / cover
Make the cover design as attractive as possible because the front page / cover is the first thing that potential readers will see and then decide whether or not to buy our magazine
7. Advertisement loading
Sometimes our magazine is sponsored by certain products/institutions so we have to display advertisements for these products/institutions in our magazine.
8. Print process
After all the steps above we have successfully completed, then next is we do the printing process. research all articles including the spelling first so you don't spend a lot of time in the editing process
9. Distribution
After the printing process is complete, the last step we have to do is distribute our magazines. we can work with agents and distributors of newspapers/magazines in several cities that we think have potential target readers
Your question is incomplete but most probably your full question was:
How to make a magazine?
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what current density would produce the vector potential, a® = ˆ (where is a constant), in cylinderical coordinates?
The current density that produces the vector potential ˆ in cylindrical coordinates is proportional to ^=μ 02kϕ^.
The current density, J, that produces the vector potential, A, in cylindrical coordinates can be found using the curl of the magnetic vector potential, . To calculate the curl, we first find the derivative of A with respect to each cylindrical coordinate. Using the fact that A is proportional to ˆ, we can write A = (ˆ) and take the derivative with respect to to get .
Next, we use the formula for the curl in cylindrical coordinates, . Plugging in our values, we get .
Since J is related to A through the equation , we have .
Therefore, the current density that produces the vector potential ˆ in cylindrical coordinates is proportional to ˆ.
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The complete question is
What current density would produce the vector potential, A=k ϕ^ (where k is a constant), in cylindrical coordinates?
A region has a uniform electric field of 200,000 N/C directed to the northeast.A. An additional +0.25 µC placed into this region. What is the electric force on this charge?B. Now replace the first charge by a -0.25 µC. What is the electric force on this charge?A. 0.8 N southwest for A. 0.8 N northeast for B.B. 0.05 N northeast for bothC. 0.05 N southwest for A. 0.05 N northeast for B.D. 0.8 N northeast for bothE. 0.05 N northeast for A. 0.05 N southwest for B.F. 0.8 N northeast for A. 0.8 N southwest for B.
A region has a uniform electric field of 200,000 N/C directed to the Southwest. The electric force on this electron would point southwest (opposite to the direction of the electric field.)
Imagine yourself in an electric field. This field would exert an electric force on a positive point charge placed there. By definition, the field's direction at that location corresponds to the force that it applies to the positive point charge there in terms of electric field.
It should be obvious that the electric field in this area in this query points northeast. A positive point charge would therefore experience an electric force in the same direction—to the northeast—if it were placed in this area.
Negative charge characterizes electrons. An electron would experience electric force in the opposite direction from a positive point charge positioned in the same location. The positive point charge in this area has an electric force that points northeast (same as the direction of the electric field). Southwest is the polar opposite of northeast. Therefore, the direction of the electric field acting on an electron in this location would be southwest
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If the coefficient of static friction between a patient and the bed sheets is 1.2, what is the maximum angle (θ) at which the bed can be tilted with respect to the floor before the patient begins to slide?a) 45°b) 60°c) 30°d) 50°e) 25°
The maximum angle at which the bed can be tilted with respect to the floor before the patient begins to slide is 45°.
This is because the coefficient of static friction (μs) between the patient and the bed sheets is 1.2, and the coefficient of static friction is equal to the tangent of the angle of inclination (θ):
μs = tan θ. Therefore, 45° is the maximum angle before the patient begins to slide.Static friction is the friction force that resists the initiation of motion. It is the force that one object exerts on another when they are not yet moving relative to each other. The coefficient of static friction is typically represented by the Greek letter μs, and is usually greater than the coefficient of kinetic friction (μk). The value of μs depends on the materials of the two objects that are in contact with each other.
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eclipsed structures are higher in energy than staggered because of
The electron density of C- H bonds is more closer together than they are in staggered form hence, eclipsed structures are higher in energy than staggered.
When two C-H bonds are brought into a dihedral angle of zero degrees, their electron clouds experience repulsion, which raises the energy of the molecule.
Eclipsed conformations are higher in energy than staggered due to bond straining.
What is bond strain?
The speeding up of a chemical process by a protein's active site is known as enzyme catalysis. The mechanism of enzyme catalysis is, in theory, comparable to that of other forms of chemical catalysis. By offering a different reaction pathway, the enzyme lowers the energy needed to reach the reaction's highest energy transition state. The quantity of reactant molecules that reach a level of energy adequate for them to attain the activation energy and produce the product increases when the activation energy is reduced. Compared to uncatalyzed chemistry under the same circumstances, enzymes catalyse chemical reactions at amazing rates. A least of three steps, and sometimes more, are needed for each catalytic event, and they are all completed within the brief milliseconds that are common for enzymatic reactions.
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If vector C is added to vector B, the result is -91 – 8j. If B is subtracted from C, the result is 5i + 4j. What is the direction of B (to the nearest degree)? Select one: O a. 221 O b. 206 O c. 230 O d. 225 O e. 236
The closest degree in which B is pointed when the vectors are added is calculated to be 221 degrees.
We have to find the vector B. We will substructure equations,
⇒ -9 i - 8 i -(5i + 4j) = -9 i - 8 i - 5i - 4i = -14i - 12 j = 2(-7 i - 6 j)
You can obtain the value of vector B from here. That translates to -7 i and -6 j. Now, it is clear that both apply. Given the warning indicators, a third chord event should be expected.
Additionally, the third quarter went in their favour, or, as we might say with Angelo factor B, A D, plus theatre. Therefore, we get one or d. plus 41 degree when -6 divided by -7 and I. D. Plus are both present. 221 degrees is that.
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a large sheet of metal has a hole cut in the middle of it. when the sheet is heated, the area of the hole will
Answer:
A1 = π R^2 original area
A2 = π (R + ΔR)^2 area of hole increased in radius by ΔR
A2 - A1 = π (2 R ΔR + ΔR^2) change in area due to heating
Δ A = π 2 R ΔR ΔR^2 is small and will be omitted
ΔR = R c ΔT where ΔT is the temperature change
Thus the coefficient of area expansion is twice that of the coefficient of linear expansion
How many unit vectors are there for which cos alpha = 1/2 and cos beta = 1/2, where alpha and beta are angles made with x-axis and y-axis respectively.
There are two unit vectors for the given values of cos α and cos β where alpha and beta are angles made with x-axis and y-axis respectively.
It is given that,
cos α = 1/2
cos β = 1/2
We know the relation between cos α, cos β and cos γ as,
cos²α + cos² β + cos² γ = 1
Putting the known values in the above equation, we have,
1/4 + 1/4 + cos² γ = 1
1/2 + cos² γ = 1
cos² γ = 1/2
cos γ = ± 1/√2
So, two values of cos γ are possible.
Thus, two unit vectors are possible. One corresponding to the direction cosines 1/2, 1/2, 1/√2 and other corresponding to the direction cosines 1/2, 1/2, -1/√2.
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what are the two ways in which technical debt relates to velocity
Technical debt relates to velocity in two ways: Slowing down velocity and Accelerating velocity.
Technical debt is an important concept for developers to understand, as it can directly affect the velocity of their projects. On one hand, technical debt can slow down velocity by increasing the amount of time spent on maintenance and rework, as well as by introducing complexity that can reduce productivity.
On the other hand, it can also be used to accelerate velocity, as making quick, short-term fixes can reduce the need for more in-depth refactoring and, as a result, speed up the project timeline. Ultimately, it is essential to understand how technical debt can influence velocity and be prepared to navigate the complexities it can introduce.
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falling raindrops frequently develop electric charges. does this create noticeable forces between the droplets? suppose two 1.8 mg drops each have a charge of 29 pc . the centers of the droplets are at the same height and 0.36 cm apart.
The electric force between the droplets, and the horizontal acceleration this force produce on the droplets are: 5.84*10^-7 N and 0.32 m/s² respectively
What is electric force?In physics the electric force is the force that attracts or repels two charges (q) separated at a distance called (r), this is expressed in the international system of units in Newton.
To solve this exercise the electric force formulas and the procedures we will use are:
F = (k * q1 * q2)/r²F = m * aWhere:
F = electric forcek = coulomb constantq1 = charge 1q2 = charge 2m = massa = accelerationr = separation distance of the chargesGiven Info:
q1= 29 pC = 2.9*10^-11 Cq2= 29 pC = 2.9*10^-11 Cr = 0.36 cm = 3.6*10^-3 mm= 1.8 mg= 1.8*10^-6 kgF =?k= 9 *10^9 N*m²/C²a=?Applying the electric force formula we have:
F = (k * q1 * q2)/r²
F = [(9 *10^9 N*m²/C² * (2.9*10^-11 C) * (2.9*10^-11 C)]/ (3.6*10^-3 m)²
F = 7.569*10^-12 N*m² /1.296*10^-5 m²
F = 5.84*10^-7 N
Applying the force formula and clearing the acceleration, we get:
a= F/m
a= 5.84*10^-7 N/ 1.8*10^-6 kg
a= 0.32 m/s²
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how phonation occurs
The adduction of the vocal folds, which approximates the vocal folds to shrink or shut the glottis, is the first step in the phonation process. Lung contraction starts airflow and creates pressure accumulation underneath the glottis.
The cricothyroid angle, which controls the angle between the thyroid and cricoid cartilages, and medial movement of the arytenoids during expiration are both used to phonate. The vocal folds vibrate as a result of these motions, which cause slight variations in the tension of the vocal folds during air flow.
An airstream is converted into audible sounds by the larynx. The perceived voice quality is especially dependent on this procedure, which is known as phonation.
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what is the density of a block of material that is 12 cm × 6 cm × 2 cm and has a mass of 356 g?
The density of the block when the dimensions and weight of the block are specified is calculated to be 2.47 g/cm³.
It is given that the length of the block (l) = 12 cm
Breadth of the block (b) = 6 cm
Height of the block (h) = 2 cm
Weight of the block (w) = 356 g
The volume of the block is calculated using the formula,
V = l b h = 12 × 6 × 2 = 144 cm³
Now, the density of the block is,
ρ = m /V
⇒ 356/144 = 2.47 g/cm³
Thus, the density of the block is 2.47 g/cm³.
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if the sun were suddenly moved 2 times further away, how many times fainter would it be?
4 Times. If the sun were moved 2 times further away, it would be 4 times fainter.
The relationship between fainting and the distance from the sun can be given as:
[tex]1/d^2[/tex], where [tex]d[/tex] is the distance from the sun.
This is called the Inverse Square Law.
According to the inverse square law, a phenomenon's intensity falls in proportion to the square of the distance as it gets further away from its source. Understanding the behavior of light and sound to develop systems that use or interact with these phenomena all depend on this idea, which is crucial in many fields of physics and engineering.
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calculate the temperature ofan unsaturated air parcel at 100-111 increments as it isforced to rise from the earth's surface, where its temperature is 35 oc.
Examining parcels is done to assist assess the stability of the atmosphere. Unsaturated air will cool at a fixed rate of 9.8°C per 1,000 meters as it rises.
What would the air's relative humidity be if it actually included 10 grams of water vapor per kilogram of dry air (at sea level and 25 degrees Celsius) It would be 50% relative humidity. An air parcel needs to use energy to expand. As the parcel rises and expands, this energy expenditure simultaneously causes the temperature to decrease. In contrast, an air parcel gets squeezed when it is dropped through the atmosphere because the air pressure outside the packet rises. Examining parcels is done to assist assess the stability of the atmosphere.
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the width of a particular microwave oven is exactly right to support a standing-wave mode. measurements of the temperature across the oven show that there are cold spots at each edge of the oven and at three spots in between. the wavelength of the microwaves is 12 cm . part a how wide is the oven? express your answer with the appropriate units.
The particular microwave oven is 20 cm wide as there are cold spots at each edge of the oven and at three spots in between.
What is wave?A wave is a dynamic disturbance of one or more quantities that propagates in physics, mathematics, and related sciences.
Wavelength of the microwave is 12 cm .
There are cold spots at each edge of the oven and at three spots in between.
So, there have five cold spots inside the oven.
In a wavelength, there should be be three cold spots.
The wide of the particular microwave oven = (5 × 12/3) cm = 20 cm.
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Below are some statements about how the solar system formed. List The letters in the correct order.
A The sun formed.
B A cloud of gas and dust was spinning around in space.
C Gravity pulled the dust and gas together.
D The Earth and other planets formed.
E Asteroids are leftover pieces of dust and rock.
a cabin entry light of 10 watts and a dome light of 20 watts are connected in parallel to a 30-volt source. if the voltage across the 10-watt light is measured, it will be
The same as the voltage across the 20-watt light, which is 30 volts.
When two or more electrical components are connected in parallel, they are connected to the same voltage source and share the same potential difference. In this case, the 10-watt cabin entry light and the 20-watt dome light are connected in parallel to a 30-volt source.
Since they are connected to the same voltage source, the voltage across both components will be the same, which is 30 volts. This is because the potential difference across each component is determined by the voltage of the source, and not by the power or current that the component requires.
The power and current of each component will be determined by the component's resistance and the voltage across it. However, since the voltage across both components is the same, their power and current will be determined by their own individual resistances.
So even though the dome light requires more power than the cabin entry light, they will both receive the same voltage and the same potential difference.
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air flows through this tube at a rate of 1200 cm3/s . assume that air is an ideal fluid.
The height h of mercury in the right side of the U-tube is 4.37 cm.
The Bernoulli's principle of fluid dynamic states that as a fluid's static pressure or potential energy falls, so too does its speed.
Given,
Rate if volume flow Q = 1200 cm³/s
The broader end diameter D1 = 2.0 cm
The narrower end diameter D2 = 0.4 cm
By using bernoulli's theorem,
1/2pv1² + P1 = 1/2pv2² + P2
P1 - P2 = 1/2pv1² - 1/2pv2²
By using continuity equation,
Q = π(D1²/2)²v1 = π(D2²/2)²v2 = 1200 cm³/s
v2 = 4 × 1200 cm³/s / π × (0.4)² = 9550 cm/s = 95.5 m/s
v1 = 4 × 1200 cm³/s / π × (2)² = 382 cm/s = 3.82 m/s
P1 - P2 = 1/2 p(v2² - v1²)
P1 - P2 = 1/2 × 1.28 kg/m³ × ( (95.5m/s)² - (3.82m/s)² )
P1 - P2 = 5827.6 N/m²
then,
pgh = 5827.6 N/m²
h = 5827.6 N/m² / pg
h = 5827.6 N/m² / 13600 kg/m³ × 9.8 m/s² = 0.0437 m
h = 4.37 cm.
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Q. Air flows through the tube shown in figure below at a rate of 1200 cm³/s. Assume that air is an ideal fluid. What is the height h of mercury in the right side of the U-tube?
an observer in the northern hemisphere takes a photograph of the night sky over a 3 hour period. if the illustration below depicts the photograph taken by the observer, which direction was the camera pointing?
Observers in the northern hemisphere take long-exposure photographs of the night sky. The following illustration represents a photo taken by a viewer. At this time, the direction of the camera is true north.
The summer solstice in the northern hemisphere occurs in a few days around June 21 each year. On this day, the position of the sun in the sky at noon is at its highest altitude for the year, and the position of the sun at sunrise and sunset is at its northernmost position for the year. All you have to do is locate the North Star and measure its angle with the (northern) horizon.
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a 0.42-kg mass attached to a spring undergoes simple harmonic motion with a period of 0.71 s . part a what is the spring constant of the spring?
32.8N/m is the spring constant of the spring.
How does simple harmonic motion work?
Simple harmonic motion is described as the periodic motion of a point along a straight line with an acceleration that is always toward a fixed point in that line and a distance from that point that is proportional to that acceleration.
When the restoring force is inversely proportional to the displacement, the oscillations are the simplest. Recall that the equation F = kx from Hooke's law represents this circumstance. Thus, simple harmonic motion, the most basic type of oscillation, is described by and subject to Hooke's law.
We know that:
T=2π√m/k
k=4π^2×m/T^2
m = 0.42kg
T = 0.71s
k= 4*3.14*3.14*0.42/ 0.71*0.71
k = 32.8N/m
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true/false: materials with high dielectric constants will also be good electrical insulators. true/false: materials with high dielectric constants will also be good electrical insulators. true false
The given statement about “materials with high dielectric constants will also be good electrical insulators” is true, because dielectric materials are essentially insulators.
As the name implies, dielectrics do not allow electrical current to pass when a voltage is applied, making them insulators. The atomic scale, however, does witness certain shifts. Dielectrics get polarized when a voltage is put across them. Polarization is an effect that slightly moves the electrons toward the positive voltage, which makes sense given that atoms consist of a positively charged nucleus and negatively charged electrons. They don't go far enough to generate current in the material, but even a tiny change might have profound consequences, especially in the context of capacitors.
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to help determine the roots of x=tan(x), grapgh y=x and y=tan(x), and look at the intersection points of the two curves
The roots of given equations can be solved by calculus and the intersection of the 3 equations are at the origin i.e (0,0)
The roots of x=tan(x) :
The solution is the x-value of the point of intersection.
x = 69.05396782n, 4.49340945+69.05396782n,7.72525183+69.05396782n,14.06619391+
69.05396782n,20.37130295+69.05396782n,26.66605425 +69.05396782n,42.38791356 +69.05396782n
, for any integer n
Graph the line using the slope and y-intercept, or two points.
Slope:
1
y-intercept: (0,0)
x y
0 0
1 1
Graph the trigonometric function using the amplitude, period, phase shift, and vertical shift.
Vertical Asymptotes: x = pi/2 + pi.n ,for any integer n
Amplitude: None
Period: π
Therefore, the intersection is origin here.
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Find the rate at which a crane can do work if it lifts a 5 kg crate 78 m in 92.50 s using 455,343.44 N of work.
The rate at which a crane can do work is 41.32 watt.
What is power?Power can be defined as the amount of work completed in a given amount of time. Watt (W), which is derived from joules per second (J/s), is the SI unit of power.
Horsepower (hp), which is roughly equivalent to 745.7 watts, is a unit of measurement sometimes used to describe the power of motor vehicles and other devices.
Mass of the crate = 5 kg.
Vertical displacement of it = 78 m.
Time taken = 92.50 second.
Hence, power of the crane = ( 5 kg × 9.8 m/s² × 78 m) ÷ 92.50 second
= 41.32 Watt.
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derive the solution of mx$ kx = 0 and plot the result for at least two periods for the case with ω n = 2 rad>s, x0 = 1 mm, and v0 = 15 mm>s.
The solution for 2 periods are x ( t) = 1 cos 2t + √5₂ Sin 2t
x ( t ) = cos 2 t + ( .1 ) 8 sin 2 t. and we can plot a graph using them
Given mx + kx = 0
x + k/m x = 0
Wn = √K/m = 2
(Dᵃ + k/m) = 0
0 = ± i (2)
x (t) = c1 cos √k/m t + c2 sin √k/m t
x (1) = c1 cos 2t + c2 sin2t
x(0) = 1 mm
x (0) = c1 = 1 mm
x ( t ) = -2 c2 sin2t +2 c2 cos 2t
x ( 0 ) = v0 =√ 5 = 0 + 2c2
c2 = (√5₂
x ( t) = 1 cos 2t + √5₂ Sin 2t
x ( t ) = cos 2 t + ( .1 ) 8 sin 2 t
using the above two equations we can plot a graph for the two periods.
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A science student investigated how far a spring would stretch when various weights are attached to it. The stretch was measured in millimetres and the weights in grams.
The results are as follows :
MASS IN GRAMS (G) 10. 12. 14. 16. 18. 20. 22. 24
EXTENSION IN
MILLIMTREST (MM). 15. 18. 20. 25. 28. 30 33 40
(iii) Find the equation of the regression line
Equation of the regression line can be found by using linear regression which is Extension (MM) = a + b * Mass (G)
The equation of the regression line can be found by using linear regression, which is a method of finding the line of best fit that describes the relationship between two variables. In this case, the two variables are the mass in grams (G) and the extension in millimeters (MM).
To find the equation of the regression line, the student could use the method of least squares, which is a method of finding the line that minimizes the sum of the squared errors between the observed data and the predicted data.
Regression line equation is:
Extension (MM) = a + b * Mass (G)
Where "a" is the y-intercept, "b" is the slope of the line, and "Mass (G)" and "Extension (MM)" are the variables.
To find the values of "a" and "b", the student could use the following formulas:
B is equal to (NXY - XY) / (NX2 - (X)XY).
A is equal to (ΣY - bΣX) / N
Where N is the number of data points, ΣX is the sum of the mass values, ΣY is the sum of the extension values, and ΣXY is the sum of the product of the mass and extension values for each data point.
Once the values of "a" and "b" have been found, the equation of the regression line can be substituted into the equation to find the predicted extension for any given mass. This will give the student a model for how the extension of the spring is related to the mass that is attached to it.
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What average power would a 1000 kg speedboat need to go from rest to 20.0 m/s in 5.00 s, assuming the water exerts a constant drag force of magnitude fd = 500 N and the acceleration is constant.
The average power required by a 1000 kg speedboat to go from rest to 20.0 m/s in 5.00 s is 60000 Watts.
The average power required to accelerate an object is equal to the force required to overcome resistance multiplied by the velocity gained. In this case, the drag force fd opposes the acceleration of the speedboat, and so the net force on the boat is equal to the difference between the force applied to the boat and the drag force:
Fnet = Fapplied - fd = ma - fd
where m is the mass of the boat (1000 kg) and a is the acceleration. The acceleration can be calculated from the velocity gained and the time taken:
a = (vf - vi) / t = (20 m/s - 0 m/s) / 5.00 s = 4 m/s^2
So, the net force is:
Fnet = ma - fd = 1000 kg * 4 m/s^2 - 500 N = 3000 N
The power required to overcome the drag force and accelerate the speedboat is equal to the net force multiplied by the velocity gained:
P = Fnet * v = 3000 N * 20 m/s = 60000 Watts
Therefore, the average power required is 60000 Watts.
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