The gas tank of a certain luxury automobile holds 22.3 gallons according to the owner’s manual. if the density of gasoline is 0.8206 g/ml, determine the mass in kilograms and pounds of the fuel in a full tank.

First, the cubic volume of water to be removed is calculated by multiplying length, width, and reduced depth of the pool. This equates to 81.25 cubic meters, which is 81250 liters. The time is then calculated by dividing total volume by pump rate, equating to 19345 seconds or approximately 5.40 hours.

The subject of this question is related to applied mathematics, specifically about volume and rates.

In order to determine how long it will take to lower the water level in the pool, first, we need to calculate the volume of the water to be removed. The volume can be calculated by multiplying the length, width, and height of the swimming pool. However, since we want the height to be 6.50 cm or 0.065 m, we use that as our height.

Volume = length x width x height = 50.0 m x 25.0 m x 0.065 m = 81.25 cubic meters. Since 1 cubic meter is equivalent to 1000 liters, the volume of water to be removed is 81250 liters.

Given that the pump removes water at a rate of 4.20 liters per second, we can determine the time by dividing the total volume by the rate of the pump.

Time = volume / rate = 81250 liters / 4.20 liters/sec = 19345 seconds or approximately 5.40 hours.

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Since the rabbit is moving at constant velocity, therefore the acceleration is zero, hence the increase in distance over time would simply be:

x = v t

where v is velocity and t is time, x is distance

Since we are starting at x = 8.1 m, the equation of motion would therefore be:

x = 8.1 – 1.6 t

The least amount of time required for a point on a wave to move from y = 0 to y = 12 cm is 12 seconds.

To determine the least amount of time required for a point on a wave to move from y = 0 to y = 12 cm, we need to consider the wave's velocity. Since the wave velocity is constant, the distance the wave travels is the wave velocity times the time interval. Therefore, we can calculate the time required by dividing the distance by the wave velocity.

In this case, we can assume the wave travels 12 cm in the positive y-direction. Let's say the wave velocity is 1 cm/s. To reach 12 cm, it would take 12 / 1 = 12 seconds. So, the least amount of time required for the point on the wave to move from y = 0 to y = 12 cm is 12 seconds.

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During the launch, the person was accelerating against the gravity, therefore the equation we use in this case is:

F = m * (g + a)

where m is mass = 60 kg, g is gravity = 9.81 m/s^2, a is acceleration = 4 * g

therefore:

F = m * (g + 4 g)

F = m * 5 g

F = 60 kg * 5 * (9.81 m/s^2)

F = 2943 N

The apparent weight of a 60 kg rider during the launch of a power tower ride experiencing 4g of acceleration is 2940 N. This is calculated by adding the force due to the rider's weight and the force due to the ride's acceleration.

To calculate the apparent weight of a rider during the launch, we need to consider the gravitational force (weight) and the additional force due to the 4g acceleration of the ride. The weight of the rider is calculated using the formula: Weight = Mass x Gravity, where mass is 60 kg and gravity is 9.8 m/s². This gives a weight of approximately 588 N (Newton).

The force due to the ride's acceleration is calculated using the formula: Force = Mass x Acceleration, where in this case acceleration is 4g or 4 x 9.8 m/s², which gives approximately 2352 N.

The apparent weight of the rider is therefore the sum of these two forces: 588 N + 2352 N = 2940 N.

So a 60 kg rider's apparent weight during the launch is 2940 N.

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a force must act on it

The maximum theoretical flow rate through a supersonic nozzle is determined by the nozzle's design and the properties of the fluid flowing through it.

In supersonic flow, the flow properties change drastically, and the flow behavior is described by compressible fluid dynamics equations, including the Mach number.

The maximum Mach number that can be achieved in a supersonic flow is 1, also known as Mach 1.

Any Mach number greater than 1 corresponds to supersonic flow. The design of the nozzle, specifically its converging and diverging sections, determines how well the flow can be accelerated to supersonic speeds and how efficiently it can expand to match the downstream pressure.

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Final answer:

The acceleration of the ball rolling down the ramp is 0.2 m/s^2, calculated using the equation of motion for uniformly accelerated movement without initial velocity.

Explanation:

To calculate the acceleration of a ball that starts from rest and travels a certain distance down a ramp over a known time period, we can use the equations of motion for uniformly accelerated motion. It is given that the ball travels 0.9 meters in 3 seconds from rest.

The equation that relates distance (s), initial velocity (u), time (t), and acceleration (a) is:

s = ut + \frac{1}{2}at^2

Since the initial velocity u is 0 m/s (because the ball starts from rest), the equation simplifies to:

s = \frac{1}{2}at^2

Rearranging this equation to solve for acceleration yields:

a = \frac{2s}{t^2}

Plugging in the given values:

a = \frac{2 * 0.9 m}{(3 s)^2} = \frac{1.8 m}{9 s^2} = 0.2 m/s^2

Therefore, the acceleration of the ball is 0.2 m/s2.

Final answer:

When a plastic comb is run through hair, the comb gains electrons and becomes negatively charged due to the transfer of electrons, which is a result of static electricity caused by friction. The hair loses electrons but does not gain protons or lose protons, as protons do not move freely like electrons.

Explanation:

When people use plastic combs on their hair, the combs can become negatively charged due to static electricity. This happens due to the transfer of electrons from one object to another. In this case, the true statements about the situation are:

The comb gains electrons.

The hair loses electrons.

Protons are not exchanged in static electricity because they are located within the atomic nucleus and do not move freely. Therefore, it is the gain or loss of electrons that causes the static charge. The friction between the comb and the hair can cause electrons to be transferred from the hair to the comb, which is why the comb becomes negatively charged.

The maximum height is: hmax  = v0² sin² α / 2 g
The horizontal range is: x = v0² sin 2 α / g

So we are given that:

x = 14.5 hmax

v0² sin 2 α / g = 14.5 v0² sin² α / 2 g
7.25 sin² α = 2 sin α cos α    
7.25 sin α = 2 cos α  
7.25 tan α = 2
tan α = 0.27586
α = tan^(-1) 0.27586
α = 15.42°
The angle of projection is 15.42°

The greatest possible distance from the mirror to the point where the reflected rays meet is infinite for a flat mirror, as the reflected rays never actually converge, creating a virtual image.

The greatest possible distance d from the mirror to the point where the reflected rays meet would be when the object distance do approaches the focal length f of the mirror from the right side, causing the image distance d to approach negative infinity, indicating that the reflected rays would never converge in real space. This situation describes the formation of a virtual image where the rays appear to come from. In a flat mirror, the focal length is technically at infinity since parallel rays remain parallel after reflection and never actually converge. Therefore, in a practical sense, when considering a flat mirror, the reflected rays appear to converge at a distance behind the mirror equal to the object's distance in front of the mirror, which is defined as d = -do.

The greatest possible distance (d) from the mirror to the point where the reflected rays meet is [tex]\( \frac{L}{2} \)[/tex], which is the focal length of the mirror when it is at the center of the spherical surface.

To understand why the greatest possible distance (d) from the mirror to the point where the reflected rays meet is [tex]\( \frac{L}{2} \)[/tex], let's consider the behavior of light rays reflecting off a mirror.

When a light ray reflects off a mirror, the angle of incidence is equal to the angle of reflection. This means that the path of the light ray before and after reflection are symmetric with respect to the normal to the mirror surface at the point of incidence.

For the reflected rays to meet at a point, they must converge. The best way to visualize this is to consider a light ray that travels parallel to the mirror's surface. After reflection, this ray will appear to come from a point behind the mirror, known as the focal point. The distance from the mirror to this focal point is the focal length of the mirror.

In the case of a flat mirror, the focal length is infinite because parallel rays remain parallel after reflection and do not converge to a single point. However, if we consider a spherical mirror, the focal length (f) is finite and is related to the radius of curvature (R) of the mirror by the equation [tex]\( f = \frac{R}{2} \)[/tex].

Now, let's consider the scenario where the mirror can be moved horizontally. The greatest possible distance (d) from the mirror to the point where the reflected rays meet would occur when the mirror is at the center of the spherical surface it is a part of. At this point, the focal point of the mirror would be at a distance equal to the focal length (f) from the mirror's surface.

Given that the length of the mirror is (L), and the radius of curvature (R) is equal to (L) (since the mirror is a segment of a sphere), we can substitute (R) with (L) in the focal length equation. Thus, the focal length (f) is [tex]\( \frac{L}{2} \)[/tex].

I like to solve first in SI units. So convert pressure into Pascal.

P = 207 psi = 1.427x10^6 Pa

The formula for hydrostatic pressure is:

P = ρ g h

where ρ is density of ocean water = 1025.1 kg/m^3, g is gravity = 9.81 m/s^2, h is height or depth

1.427x10^6 = 1025.1 * 9.81 * h

h = 141.92 m

Convert meters to inches:

h = 141.92 m = 5587.4 inches

The number of electrons flowing in a current can be found by multiplying the current by the time, and then dividing by the charge of a single electron. Use the value of 50 microamps for current, 60 seconds for time, and 1.6x10^-19 Coulombs for the charge of an electron.

To answer this question, we first need to understand a couple key concepts such as electric current and the charge of an electron. Electric current is defined as the rate at which charge is flowing, and in this case, 50 microamperes microamps) means that there are 50 microCoulombs of charge flowing each second. The charge of an electron is approximately 1.6x10^-19 Coulombs.

Now, we can use these values to calculate how many electrons are flowing in a minute. The first step is to convert minutes to seconds, giving us 60 seconds. Multiply the current (50 microCoulombs or 50x10^-6 Coulombs per second) by the time in seconds (60 seconds). This will tell you how much charge flows in one minute. Finally, divide the total charge by the charge of a single electron (1.6x10^-19 Coulombs) to find the number of electrons. Remember to round your final answer to two significant figures as requested.

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Final answer:

The atomic mass unit is based on the carbon-12 atom, where 1 atomic mass unit is equal to one-twelfth of the mass of a carbon-12 atom.

Explanation:

The universal standard that serves as the basis for the atomic mass unit is the mass of a carbon-12 atom. An atomic mass unit (usually abbreviated as amu or u) is defined as one-twelfth of the mass of a single carbon-12 atom. This provides a convenient scale for measuring atomic masses, as it results in both protons and neutrons having masses very close to 1 u, given their similar mass. Electrons have a much smaller mass and thus make a negligible contribution to the atomic mass. To express this in more familiar units, 1 u is equivalent to 1.6605×10-27 kilograms.

Final answer:

Explanation of calculating the distance between two deer in a field using trigonometry and the Pythagorean theorem.

Explanation:

Given information:

Deer b is 64.9 m from deer a at an angle of 53.4° north of west. Deer c is 77.9 m north of east relative to deer a. The distance between deer b and c is 96.8 m.

To find: Distance between deer a and c.

Calculation:

Using trigonometry, we can find the distances and then apply the Pythagorean theorem to calculate the distance between deer a and c.

Distance between deer a and c is approximately 59.2 meters.

Answer:

Explanation:

A hypothesis or system of hypothesis is the core of a research. It's the possible solution to a problem that researchers established when looking for theories or events to prove it.

The percent uncertainty in this question refers to how much measured values could deviate from a standard or expected value. For this example, considering a good-quality measuring tape that can be off by 0.50cm over a distance of 20m, the percent uncertainty is calculated as 0.0025%

The concept this question is referring to is percent uncertainty, which is a quantitative measure of how much measured values deviate from a standard or expected value. It's widely used in physics and engineering. In a practical context, when you're using a measuring tape, it's unlikely you'll get a perfect measurement every time. This could be due to factors like the smallest division on the tape or the person using it having bad eyesight. In this particular example, measuring tape error was 0.50 cm over a distance of 20 m (or 2000 cm).

The percent uncertainty is calculated by dividing the uncertainty (the amount the measurement could be off by) by the measured value, and then multiplying by 100% to express it as a percentage.

So, percent uncertainty = (uncertainty/measured value) * 100%.
For this scenario, percent uncertainty = (0.50 cm / 20000 cm) * 100% which equals to 0.0025%.

So, in this example, the percent uncertainty is 0.0025%.

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The percent uncertainty of the measuring tape is 0.025%.

To find the percent uncertainty of a measurement, you use the following formula:

[tex]\text{Percent Uncertainty} = \left( \frac{\text{Absolute Uncertainty}}{\text{Measured Value}} \right) \times 100 \%[/tex]

Given:

First, convert the Measured Value to centimeters because the absolute uncertainty is given in centimeters.

[tex]20 \text{ m} = 2000 \text{ cm}[/tex]

Now, plug the values into the formula:

[tex]\text{Percent Uncertainty} = \left( \frac{0.50 \text{ cm}}{2000 \text{ cm}} \right) \times 100 \%[/tex]

Calculate the result:

[tex]\text{Percent Uncertainty} = \left( \frac{0.50}{2000} \right) \times 100 \% = 0.025 \%[/tex]

Final answer:

The initial velocity of the ball is approximately 14.9 m/s, found using kinematic equations considering the ball's upward motion against gravity over 1.3 seconds to pass a 2.00 m high window.

Explanation:

To determine the initial velocity of a ball thrown straight up, we can use the kinematic equations for uniformly accelerated motion. The ball passes a 2.00 m high window that starts 7.5 meters above the ground, and it takes 1.3 seconds to pass by the window. We'll use the following kinematic equation:

s = ut + 1/2at²

where s is the displacement (the height of the window), u is the initial velocity we want to find, t is the time (1.3 seconds), and a is the acceleration due to gravity (approximately -9.81 m/s², since it's upwards).

Plugging in the values, we have:

2.00 m = u(1.3 s) + 1/2(-9.81 m/s²)(1.3 s)²

Solving for u, the initial velocity of the ball is calculated to be the positive root of the resulting quadratic equation. After performing the algebraic manipulation, we find that the initial velocity is approximately 14.9 m/s.

Answer:

For a: The original speed of the truck is 4.76 m/s

For b: The acceleration of the truck is [tex]-0.23m/s^2[/tex]

Explanation:

Speed is defined as the rate at which an object moves with respect to time.

To calculate the time taken for the given speed, we use the equation:

[tex]s=\frac{d}{t}[/tex]

where,

s = speed of the truck

d = distance traveled = 40.0 m

t = time taken by truck = 8.50 s

Putting values in above equation, we get:

[tex]s=\frac{40.0m}{8.50s}=4.76m/s[/tex]

Hence, the original speed of the truck is 4.76 m/s

Acceleration is defined as the rate of change of velocity with respect to time.

Mathematically,

[tex]a=\frac{v-u}{t}[/tex]

where,

v = final velocity  of the truck = 2.80 m/s

u = initial velocity  of the truck = 4.76 m/s

t = time taken  = 8.50 s

Putting values in above equation, we get:

[tex]a=\frac{2.80-4.76}{8.50}=-0.23m/s^2[/tex]

Negative sign represents slowing down or deceleration.

Hence, the acceleration of the truck is [tex]-0.23m/s^2[/tex]