This response is accompanied by the T-s or H-s graphic.
2. The steam extraction rate is 4.088 kg per second.
3. Steam leaving the boiler has a net power output of 1089.5 KJ/Kg.
4. The boiler's mass flow rate of steam is 16.352Kg/s.
5. The plant generates 11016.2KJ/s of net electricity.
6. 0.218 is the usage factor.
We must ascertain all of the system's thermodynamic coordinates in order to examine the issue. The optimal cogeneration steam plant technology can be seen in the second image that is attached to this response.
We may get the details for each point from a chart of the thermodynamic characteristics of water.
+ Steam from the boiler reaches the turbine at 7 MPa and 500 °C:
h₆=3410.56KJ/Kg
s₆=6.7993 KJ/Kg
As a result, this cogeneration steam system is suitable. s₆=s₇=s₈
At 600 kPa, one-fourth of the steam is removed from the turbine:
2773.74 KJ/Kg = h7(s7) (overheated steam)
+The remaining steam expands further and exhausts to the condenser at a pressure of 10 kPa.
(This is wet steam with title X=0.8198; h8(s8)=2153.58 KJ/Kg.)
s1=0.64925KJ/Kg and h1(P=10Kpa)=191.83 KJ/Kg (condensed water).
Pumping this flow to 600KPa results in:
s₂=s₁
h₂(s₂)=192.585KJ/Kg
+The heater condenses the steam that was taken for the process heater.
h₃(P=600KPa)=670.42KJ/Kg (condensed water) (condensed water).
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The supply chain is ...
Answer:
A supply chain is the network of all the individuals, organizations, resources, activities, and technology involved in the creation and sale of a product. A supply chain encompasses everything from the delivery of source materials from the supplier to the manufacturer through to its eventual delivery to the end user.
What state of liquid does point a represent in the Rankine cycle?
Saturated liquid, subcooled liquid, superheated liquid, or Sat. liquid vapor mix?
The state of liquid that point 2a" represents in the Rankine cycle is "Subcooled Liquid" (Option B).
What is the Rankine cycle?The Rankine cycle, also known as the Rankine Vapor Cycle, is a process that is frequently utilized in power facilities such as coal-fired power plants and nuclear reactors. Fuel is utilized in this mechanism to generate heat within a boiler, transforming water into steam, which then expands via a turbine, providing useful work.
The Rankine cycle (RC) is a thermodynamic cycle used in thermal power plants to transform thermal energy into mechanical labor. Many researchers have recently focused on exploiting the Rankine cycle to recuperate low-grade waste heat.
Subcooling refers to a liquid that exists at a temperature lower than its typical boiling point. Water, for example, boils at 373 K and is referred to as "subcooled" at ambient temperature. A subcooled liquid is a suitable condition in which refrigerants, for example, can complete the remaining stages of a cooling system.
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what single addition to the automobile gave the internal combustion engine the edge and resulted in most automobiles being produced with these engines?
The gas vacuum engine, the first internal combustion engine used industrially, was patented by Samuel Brown in 1823. In a vehicle and a boat, the invention was shown. It was then utilized commercially to pump water to the Croydon Canal's upper level in 1830.
What three kinds of internal combustion engines are there?
Internal combustion engines come in three main categories and are widely used today:
1. the spark ignition engine, which is generally used in automobiles;
2. the diesel engine, which is utilized in big vehicles and industrial systems and
3. is preferable to the more compact and lighter due to gains in cycle efficiency.
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There is interdependence between an organization and its information systems". Discuss this statement.
There is interdependence between an organization and its information systems have a mutual dependency on each other.
What is the organization?An institution made up of individuals or a group of individuals who gather together to accomplish a single, common goal is referred to as an organization.
Information systems and organizations are mutually influenced by one another. Inability to efficiently advantage of innovative technologies, an organization should be receptive to the effects of data systems, which have an impact on how information systems are designed.
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what is the formula for reynolds number? a. b. c. d. 5 points save answer question 3 of 7 moving to the next question prevents changes to this answer.
Reynolds Number = Inertial Force / Viscous Force L = length or diameter of the fluid
The ratio of viscous forces to inertial forces is known as the Reynolds number. A dimensionless number called the Reynolds number is used to group fluid systems where the influence of viscosity plays a significant role in regulating the velocities or the flow pattern of a fluid.
What is implied by the Reynolds number?
The fluid flow is classified as turbulent or laminar using the Reynolds number, abbreviated as Re. When a numerical model is chosen based on pre-calculated Reynolds numbers, it is one of the key regulating parameters in all viscous flows.
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Re = VD/ or Re = VD/v is the formula for the Reynolds Number, where "V" stands for fluid velocity, "D" for characteristic distance, "" for fluid density, "v" for kinematic viscosity, and "" for dynamic viscosity, all of which can be found in data tables.
What are Reynolds number?When a fluid experiences relative internal movement as a result of various fluid velocities, the ratio of inertial forces to viscous forces is known as the Reynolds number. A boundary layer, such as the bounding surface inside a pipe, is an area where these forces affect how they behave. The ratio of inertial and viscous forces is measured by the Reynolds number, which aids in the prediction of flow patterns in various fluid flow scenarios. Laminar flow typically predominates in flows with low Reynolds numbers, while turbulent flow typically predominates in flows with high Reynolds numbers.Re = VD/ or Re = VD/v is the formula for the Reynolds Number, where "V" stands for fluid velocity, "D" for characteristic distance, "" for fluid density, "v" for kinematic viscosity, and "" for dynamic viscosity, all of which can be found in data tables.To learn more about Reynolds number refer to:
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for a steel alloy it has been determined that a carburizing heat treatment of 1-h duration will raise the carbon concentration to 0.38 wt% at a point 3.0 mm from the surface. estimate the time (in h) necessary to achieve the same concentration at a 6.1 mm position for an identical steel and at the same carburizing temperature. enter your answer in accordance to the question statement h
The time (in h) necessary to achieve the same concentration at a 6.1 mm position for an identical steel is 4 h.
As the carburizing heat treatment of 1-hour duration increases the carbon concentration to 0.38 wt% at a point 3.0 mm from the surface, the time necessary to achieve that same concentration for identical steel can be calculated as follows;
It is known that;
[tex]\frac{x_{1}^{2} }{Dt} = constant[/tex]
where x represents distance and t is time. As the carburizing temperature is constant, therefore D will also be constant;
[tex]\frac{x_{1}^{2} }{t} = constant[/tex]
Therefore;
[tex]\frac{x_{1}^{2} }{t_{1} } = \frac{x_{2}^{2} }{t_{2} }[/tex]
Now by substituting the given values, we can find the time required to achieve the same concentration as follows;
(3)² / 1 = (6.1)² / [tex]t_{2}[/tex]
9 = 37.21 / [tex]t_{2}[/tex]
9([tex]t_{2}[/tex]) = 37.21
[tex]t_{2}[/tex] = 37.21 / 9
[tex]t_{2}[/tex] = 4.13 hours ≈ 4 hours.
Therefore, the time necessary to achieve the same concentration at a 6.1 mm position for an identical steel is 4 hours.
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stranded wire use is being discussed. technician a says there is less exposed surface area for electron flow in stranded wire. technician b says there is more resistance in the stranded wire than in the same gauge solid wire. who is correct?
The answer is neither A nor B. The strands cannot be twisted without forming a helix. Or, to put it another way, the helix is an inevitable result of the twisting movement.
A solid wire with the same cross-sectional area and conventional length as the wire in the illustration will have a little less resistance. This is due to the fact that the wire in the illustration will have a Path Length that is somewhat more than the length of the solid wire, and Path Length is what counts in terms of resistance. Now, you probably won't notice the helix when holding a real stranded and twisted wire. The helix in the aforementioned image is exaggerated, and the helix in a real wire is typically so "slight" that it's difficult to see.
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tech a says that yaw is when a vehicle deviates from its straight path. tech b says that roll is when the front of the vehicle noses down or rises up. who is correct?
Both tech a and tech b are correct
Confirming the statement of tech a:
Yaw angle is defined as the angle between the pointing line in the movement of car direction in which it is pointed.
Yaw angle describes the car rotation about vertical axis which is about y-axis. It is the angle between the axis parallel to the vehicle surface in fixed-earth coordinate system.
Yaw then describes a vehicle deviating from a straight path. Hence tech a is correct.
Confirming the statement of tech b:
In high speeds, vehicles tends to tip over. This is angular displacement of vehicle about its longitudinal axis.
When a vehicle tips over, then its weight is thrown out to the outside of corner which results into rolling of the vehicle.
Therefore, when the moving vehicle is turned to the left, then the driver throws to the right. Similarly, when the vehicle turns to the right, then the driver throws to the left which results into rolling of front wheel, causing the front of the vehicle to nose down or rise up.
Hence, tech b is correct.
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for a given amount of power (s) to be transmitted, an increase in the transmission line voltage would result in:
Efficiency improvement is the main driver behind high voltage power transmission. There are inherent energy losses when electricity is transferred across vast distances.
Electricity is transferred from one site to another with the least amount of power loss possible thanks to high voltage transmission. Transformers, which raise voltage levels to enable long-distance transmission, are a crucial component of this process. The electrical grid is made up of power plants, distribution networks, and sub-stations as well as the electrical transmission system. The power loss will decrease as the current decreases. Therefore, to lower current during electricity transmission, the voltage is increased. When sending the same amount of power over a longer distance at a lower voltage, there will be a greater power loss.
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a differentiator has a break frequency of 100 khz and a unity gain frequency of 10 khz. over what frequency range would the circuit provide the derivative of a function and increase the signal?
An op amp-based circuit known as a differentiator produces an output signal that is proportional to the differentiation of the input signal. In essence, an op amp differentiator is an inverting amplifier with an appropriate capacitor at its input end.
A differentiator circuit: what is it?Depending on the circuit time constant and the amplifier's bandwidth, the differentiator circuit produces the derivative of the input signal over a range of frequencies. Applying the input signal to the inverting input causes the output to be polarity-inverted with respect to the input signal.
Why is a differentiator opamp used? The major application of this op-amp is to boost weak signal levels. Depending on the components used in the design, an op-amp differentiator can be either active or passive. We will utilize this differentiator amplifier in frequency modulators and wave shaping circuits because it essentially functions as a high pass filter.
Why do op-amps utilize capacitors? A feedback capacitor is used in a typical op-amp circuit to restrict bandwidth. A feedback capacitor is a typical approach to minimize noise because restricting op-amp bandwidth will do so. Consider that a capacitor functions as a short to "high frequency" AC impulses in order to comprehend how the feedback capacitor operates.
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When the soluble BOD in the influent to the treatment plant rises from 129 mg/L to 201 mg/L, the operator called to ask your advice on a new MLVSS for the plant. It has been operating with an F/M of 0.45 mg/mg-d and the operator would like to continue using the same F/F. The plant data are as follows: flow rate = 7,673 m^3/d; aeration tank volume = 1,157 m^3; mixed liquor volatile suspended solids = 2,601 mg/L
The new mixed liquor volatile suspended solids from the given plant data is; 4052.72 mg/L
What is the discharge flow rate?MLVSS is expressed as mixed liquor volatile suspended solids and it is the total amount (mg/L) of organic or volatile suspended solids in the mixed liquor residing in an aeration tank. This volatile portion in the aeration tank serves the purpose of measurement or indication of the microorganisms that are present.
We are given;
Initial BOD; y = 129 mg/L
New BOD; y' = 201 mg/L
F/M = 0.45 mg/mg-day
Volume of tank; V = 1157 m³ = 1157 × 10³ Liters
MLVSS = 2601 mg/L
1) The discharge from the initial BOD is gotten from the formula;
Q = ((F/M) * V * MLVSS)/y
Plugging in the relevant values gives;
Q = (0.45 * 1157 × 10³ × 2601)/129
Q = 10497756.98 Liters/day
2) Now, let us find the new MLVSS which would be gotten from the formula;
MLVSS' = (Q * y')/((F/M) * V)
MLVSS' = (10497756.98 * 201)/(0.45 * 1157 × 10³)
MLVSS' = 4052.72 mg/L
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A mass of 5 kg of saturated liquid-vapor mixture of water is contained in a piston-cylinder device at 125 kPa. Initially, 2 kg of the water is in the liquid phase and the rest is in the vapor phase. Heat is now transferred to the water, and the piston, which is resting on a set of stops, starts moving when the pressure inside reaches 300 kPa. Heat transfer continues until the total volume increases by 20 percent.
Determine:
(a) the initial and final temperatures,
(b) the mass of liquid water when the piston first start moving
a) The initial and final temprature are 99.61°C and T3 = 259.07°C
b) The mass of liquid water when the piston first start moving is 0g
Using the data provided:
Initial Pressure = P1 = 125kPa
Mass of Saturated Vapor Liquid = m = 5kg
Initial Mass of Liquid water = mf = 2kg
Initial Mass of Vapor = mg = 3kg
The temperature for a mixture of liquid steam saturated with water according to the thermodynamic table is:
T₁ = 99.61°C
The specific volume is:
vf = 0.001043m³/kg
And the saturated volume is:
vg = 1.6941m³/kg
Therefore, the volume in state 1 will be equal to:
V1 = mfvf + mgvg
V1 = (2kg)(0.001043m³/kg) + (3kg)(1.6941m³/kg)
V1 = 5.084m³
In state 3 then the volume will be equal to:
V3 = 1.2V1
V3 = 1.2(5.084m³)
V3 = 6.1008m³
Then the specific volume will be equal to:
v3 = V₃/m
v3 = 6.1008m³/5kg
v3 = 1.2202m³/kg
For a pressure of 300 kPa and the previous specific volume found through the thermodynamic table, the value of the temperature is:
T3 = 259.07°C
Question b) When the piston first stats moving at P₂ = 300kPa and V₂ = V₁ = 5.084m³
v₂ =V₂/m
v₂ = 5.084m³/5kg
v2 = 1.0168m³/kg
While at 300 kPa the value of the vapor saturated vg = 0.88578m³/kg This implies that the condition is met:
v2 > vg
Therefore, no liquid is there in-cylinder when piston stats moving, mf = 0kg
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technician a says that variable valve timing improves performance. technician b says that cylinder deactivation helps improve performance. which technician is correct?
In essence, it alters the valve timing by changing the camshafts' phase angle. For instance, to permit early intake at high speed, the inlet camshaft will be cranked 30° in advance. According to requirement, the engine management system regulates this movement, which is triggered by hydraulic valve gears.
Who introduced variable valve timing?Aston Martin
Variable valve timing (VVT), a technology used in conventional vehicle internal combustion engines, was first developed by Fiat in the late 1960s. The 1980 Spider 2000 from Alfa Romeo was the first manufacturer to use VVT in a production vehicle.
Unclean Oil Can Be Very Dangerous
These oil-fed solenoids and actuators, which are also incompatible with turbocharged engines, are among the variable timing components. Internal coking, clogging, and sludge difficulties in those components can be brought on by dirty oil.
VVT regulates airflow and exhaust
Engine valves regulate the ingestion of fuel and fresh air as well as the outflow of combustion gases. In order to match the engine's operating circumstances, VVT and lift systems modify the timing of the valves. As a result, efficiency is increased across a broad range of engine running speeds.
Where can I find variable valve timing soldenoids? At the front of the engine, often close to the front of the valve cover, is where you'll find the variable valve timing solenoid.
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Explain why you think a designer would choose to use an isometric sketch rather than a perspective sketch to share their idea with a design team member?
It is because an isometric sketch is more useful for functional drawings that are used to explain how something works, while one-point perspective drawings are typically used to give a more sensory idea of an object or space.
Isometric Sketch or isometric drawing can be described as a pictorial representation of an object in which all three dimensions are drawn at full scale. It looks like an isometric projection. Isometric sketch is kind of 3D drawing, which is set out using 30-degree angles. It is kind of axonometric drawing so the same scale is used for every axis, resulting in a non-distorted image.
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A method of coupling tubing without welds, solderor leaks is the use of
A method of coupling tubing without welds, solder or leaks is the use of a fitting or adapter.
What is a an fitting?The term fitting is seen as a form of Flexible hoses and metal tubing used to transport fluids are connected together and this is through the use of AN fittings, that is a specific kind of fitting.
Note that Fittings are typically used in conjunction with standards that are similar to act as a link between two threads that aren't naturally compatible. A fitting is required in order to connect a hose to a pump. The pump must be connected to an adaptor in order to connect to many hoses, each of which may have a different standard.
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A contractor estimates maintenance costs for a new piece of equipment to be $275 for the first month with a monthly increase of 0.5%. At i = 0.75% per month, what is the present cost of maintenance for the new equipment across 4 years?
The present cost of maintenance for the new equipment across 4 years is $12,266.01.
What is the formula for calculating a growing annuity?The formula for calculating a growing annuity is as follows:
[tex]\frac{M}{r-g}[/tex] [tex](1- (\frac{1+g}{1+r} )^N).[/tex]where M = the first payment, g = the growth rate, r = the discount rate, and N = the number of payments.
According to the question,
The first payment is = 275
The growth rate is = 0.5%.
The discount rate is = 0.75%.
The number of payments in 4 years = 4*12 = 48.
Now, put all values in the above equation:
[tex]\frac{275}{0.75 - 0.5}[/tex] [tex](1- (\frac{1+0.5}{1+0.75} )^4^8)[/tex] = 12.366.01.
Therefore, the present cost of maintenance for the new equipment across 4 years is $12,266.01.
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If | A + B|2 = A2 + B2, then
If |a|b then 2−2=(−)(+)|0⟺+|0
for the following stress-strain curve, determine the following: a. the modulus of elasticity b. the stress where the linear stress-strain relationship ends, called the proportional limit c. the yield strength, taken at .002 strain offset the proportional limit d. the ultimate tensile strength e. the modulus of resistance
Answer:https://www.usna.edu/NAOE/_files/documents/Courses/EN380/Course_Notes/Ch10_Deformation.pdf
Explanation: This may help you
-i+ (9-5i)-3(2-6i) in standard form with explanation
The given expression can be represented as 3+12i.
Complex NumberA complex number is represented by the following form: a+bi, where a and b are real numbers. The variables: a is the real part and bi imaginary part. See an example: 5 + 2i , then:
5 real part2i imaginary partRegarding operations math, the same properties used for real numbers can be applied to complex numbers. And for solving the operations math with these numbers, it is important to know that i²= -1. Thus, 3i² = 3*(-1)= -3.
When you subtract or sum complex numbers, you can only subtract or sum: the real part with the real part of each complex number and the imaginary part with the imaginary part of each complex number. Here, you can see examples:
(5 + 2i) + (5 + 2i) = 10+4i
(4 + 10i) - (2 + 5i) = 2+5i
Therefore, the result for the -i+ (9-5i)-3(2-6i) will be:
-i + 9 -5i -6+18i
-6i +3 +18i
3+12i
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a technician back probes the ground side of a port fuel injector with a dmm set to dcv. the engine is idling. what reading should the technician see?
Answer: A technician attaches one lead of a digital voltmeter to the ground terminal of the TP sensor and the other meter lead to the negative terminal of the battery.
Explanation: both technicians are correct
problem 3 (25 points). in the design of a civil jet transport, such as the boeing 777links to an external site., the choice of engine size is usually based on having a 300 feet per minute rate-of-climb capability at the top of climb to cruising altitude. this is a safety margin. assume the following cruise conditions at top of climb for the boeing 777: l/d
The calculated thrust that we are required to find in this question are solved as:
150.45The static thrust at the sea level = 2446521.9 / 18 = 135.917 NHow to solve for the thrust
Rate = excess power / weight
= dn / dt
= V∞sin θ
V∞sin θ = Tn - Tr / w * V∞
sin θ = Tn - D / w
Tr = D
sin θ = T / w - D / w
T / w = sin θ + D / w
We would have the formula here as
ma x √vRTw
= 0.85 x √1.4 x 287 x 226.73
= 256.5 m/s
Next we have to solve for the angle of climb
∅ = sin⁻¹ (1.524 / 256.5)
= 5.94 x 10⁻³
T = w (θ + 1/10)
= 2446521.9 * 5.94 x 10⁻³ * 1/18
= 150.45
The static thrust at the sea level = 2446521.9 / 18
= 135.917 N
Therefore the required thrust at the cruising altitude is equal to 150.45
while the corresponding thrust at the sea level is equal to 135.917 N
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a 400 l tank initially contains water at 200 kpa and a quality of 1%. heat is transferred to the tank by a burner, thereby raising the temperature and pressure of the water. at a pressure of 3 mpa, a valve opens and saturated vapor at 2 mpa flows out. the burner remains on, maintaining a pressure of 3 mpa inside the tank, until the quality of the tank is 90%, after which it shuts off
To prevent a waterlogged tank or surging at the faucets, you must keep air in the bladder of bladder-type pressure tanks. First, look at the pressure gauge to determine the pressure at which your well pump activates and deactivates.
The difference in pressure between turning on and turning off is typically 20 psi. our pipes, fittings, and switches may become damaged by pressures more than 60 psi. Plumbing failure and expensive leaks could result from this damage. It's probable that the pump won't be able to achieve the cut-off pressure if the pressure is set at 80 psi. The bladder could be torn or holed if tank pressure lowers. If a tank is totally filled with water or has too much water for it to function properly, it is said to be waterlogged.
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3) which is not a way to minimize your exposure to radiation? * 1 point a) wearing a lead apron b) keeping a good distance c) standing behind a thick concrete wall d) wearing lead-lined gloves e) staying a longer time
Cloth is able to block the comparatively sluggish alpha radiation particles. Synthetic fabric (ideally, specialist clothes, such as HAZMAT suits), which covers the entire body, can block beta radiation particles, which are smaller and move faster.
Alpha and beta radiation particles can, of course, harm the body if they are inhaled, thus it is important to protect the airways (nose and mouth), even with a dust mask and more efficiently with a regular respirator. Hands and eyes should both be covered (goggles, gloves). The devastation of stem cells, which is what caused the first responders at Chernobyl to perish, is the primary cause of acute radiation sickness. StemRad efficiently shields tissue that contains these cells, preventing radiation sickness while preserving mobility.
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if the oil leaves the exchanger at 100 what is its flow rate? what is the length of the exchanger shell required to accomplish the desired heating?
A heat exchanger is a device that transfers heat from one working fluid to another. Both cooling and heating operations employ heat exchangers. The liquids may be in direct contact or separated from one another by a solid wall to prevent mixing.
How is heat transfer calculated in a heat exchanger?CALCULATIONS FOR HEAT EXCHANGERS:
The fundamental equation for a heat exchanger is: Q is equal to the log mean temperature difference (U x A x Tm). ΔTm is: Tm is equal to (T1 - t2) - (T2 - t1) °F.
T1 is the fluid temperature on the inlet tube side; t2 is the fluid temperature on the outlet shell; and ln (T1 - t2) (T2 – t1)
How are shell and tube heat exchangers designed? Steps for the design of a heat exchanger:
Define the fundamental conditions for the process.Choose an appropriate type of heat exchanger.To develop a heat exchanger model, adjust a few design parameters.The heat exchanger's design is rated.Make a specification sheet that includes the heat exchanger's finished design.The Second rule of thermodynamics states that 100% thermal efficiency is an impossibility for heat engines (). This is not conceivable since a heat engine will always produce some waste heat,.
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to determine the real power capability of an electrical service you must take into account, phase, voltage and wattage?
It is right that to determine the real power capability of an electrical service you must take into account, phase, voltage and wattage.
Generators operators often control the voltage on the North American bulk system, and they are frequently given voltage schedules by transmission system operators. In the past, variable generation plants were seen as being extremely small in comparison to traditional producing units.
They were typically either induction generators (wind) or line-commutated inverters (PV), both of which lack the ability to naturally regulate voltage. Synchronous generators provided practically all of the bulk system voltage control.
However, the need for renewable production to contribute increasingly significantly to power system voltage and reactive management has arisen as a result of the increased degree of penetration of non-traditional renewable energy, particularly wind and solar.
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is used to indicate the centers of objects such as columns and fixtures.
Answer: Centerline
Explanation: The centerline can tell you where the center of a circle or an object is.
technician a says that a macpherson strut typically does not include the spring as part of the strut assembly. technician b says that a modified strut typically does not include the spring as part of the strut assembly. which technician is correct?
Both technicians are correct.
MacPherson struts are a specific type of independent suspension found on a car's front axle. The McPherson strut replaces the steering rod and performs the functions of suspension and vibration dampening at the same time.
The MacPherson strut, which has a cheap production cost, is still a stunningly efficient solution to combine strength, spring, and stability.
Altered strut It differs from a standard MacPherson system since the coil spring is not an interior component of the strut body. It is primarily used in rear-wheel drive automobiles. The spring in a modified strut is situated between the lower control arm and the car's frame.
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A rain gutter is to be constructed from a metal sheet of width 3m by bending up one-third of the sheet on each side through an angle θ. How should θ be chosen so that the gutter will carry the maximum amount of water?.
The area of the gutter is therefore equal to the area of the rectangle plus the area of the triangles.
A = rectangle + 2 * triangle
= 10h + 2 * (1/2 hw)
Using trig work out h and w.
h = 10 sin ?
w = 10 cos ?
A = 10h + hw
= 100sin? + 100sin?cos?
Differentiate the expression (either use the product rule for sin? cos?, or write 100sin?cos? as 50sin2? using the double angle formula)
A = 100sin? + 50sin2?
dA/dt = 100cos? + 100cos2?
For A to be a max or min the derivative must equal zero
100cos? + 100cos2? = 0
cos? + cos2? = 0
Use the double angle formula to write cos2? as 2cos^2 ? - 1
cos? + 2cos^2 ? - 1 = 0
2cos^2 ? + cos? - 1 = 0
This quadratic factorizes:
(2cos? - 1)(cos? + 1) = 0
This means that
cos ? = 1/2 or cos ? = 1
giving:
? = pi/3 or ? = pi
Which means that to achieve the maximum area ? should be pi/3 = 60 degrees
You can check that this is the max by substituting in these values of theta and the two end points (theta = 0, theta = pi), and seeing that pi/3 gives the maximum.
The maximum area is therefore
A = 100sin? + 100sin?cos?
= 100sin(pi/3) + 100sin(pi/3)cos(pi/3)
= 100 sqrt(3) / 2 + 100 sqrt(3)/2 * 1/2
= 100 * 3/2 * sqrt(3) / 2
= 3 * 25 * sqrt(3)
= 75 sqrt(3)
= 129.9...
= 130 cm^3
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technician a says that vehicles with independent rear suspensions provide better handling than those with solid rear axles. technician b says that vehicles with independent rear suspensions generally have less unsprung weight. which technician is correct?
According to Tech B, non-drive axles are the only ones that use a semi-independent rear suspension. Technician B is accurate.
The geometrical positioning of steering linkages that enables the interior wheels of a turn to move in a different circle radius than the outside wheels. Cost and load-bearing are the two main downsides of a coil spring suspension. If the car already has coil springs, cost is less of a concern; however, retrofits can be very costly and time intensive. Due to lower unsprung weight and the capacity of each tire to address the road independently of the other wheel on the vehicle, independent suspension often provides better ride quality and handling qualities.
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