Answer:
(i) [tex]\frac{2}{3}[/tex][tex]\pi[/tex]rh
(ii) [tex]\frac{16}{3}[/tex][tex]\pi[/tex]
Explanation:
Given:
V = [tex]\frac{1}{3}[/tex][tex]\pi[/tex]r²h
Where;
V = volume of a right circular cone.
r = radius of the cone
h = height of the cone.
(i) The rate of change of V with respect to r if r changes and h remains constant is [tex]\frac{dV}{dr}[/tex], and is given by finding the differentiation of V with respect to r as follow:
[tex]\frac{dV}{dr}[/tex] = [tex]\frac{d}{dr}[/tex][[tex]\frac{1}{3}[/tex][tex]\pi[/tex]r²h]
[tex]\frac{dV}{dr}[/tex] = [tex]\frac{2}{3}[/tex][tex]\pi[/tex]rh --------------------(i)
(ii)
Given;
h = 2
r = 4
Substitute these values into equation (i) as follows;
[tex]\frac{dV}{dr}[/tex] = [tex]\frac{2}{3}[/tex][tex]\pi[/tex](4 x 2)
[tex]\frac{dV}{dr}[/tex] = [tex]\frac{2}{3}[/tex][tex]\pi[/tex](8)
[tex]\frac{dV}{dr}[/tex] = [tex]\frac{16}{3}[/tex][tex]\pi[/tex]
[tex]\frac{dV}{dr}[/tex] = [tex]\frac{16}{3}[/tex][tex]\pi[/tex]
A right circular cone is one where the axis of cones is the line connecting the vertex to circular base's midway, the volume of right circular cone as follows:
Volume calculation:Formula:
[tex]V = \frac{1}{3} \pi r^2h[/tex]
Where;
V = right circular cone volume
r = Cone radius.
h = Cone height.
The calculation for part 1:
[tex]\frac{dV}{dr}[/tex] is indeed the rate of change of V with reference to r when r changes but h remains constant, and it is calculated via calculating the differentiation of V with respect to r as follows:
[tex]\to \frac{dV}{dr} =\frac{d}{d}r [ \frac{1}{3} \pi r^2h] =\frac{2}{3} \pi r h[/tex]
The calculation for part 2:
When h = 2 and r = 4 then substituting the value into the part 1 equation then:
[tex]\to \frac{dV}{dr} = \frac{2}{3} \pi (4 \times 2) = \frac{2}{3} \pi (8) = \frac{16}{3} \pi[/tex]
Find out more about the volume here:
brainly.com/question/24086520
How many 10" diameter circles can be cut from a semicircular shape that has a 20"
diameter and a flat-side length of 25"?
9514 1404 393
Answer:
1
Explanation:
Only one such circle can be drawn. The diameter of the 10" circle will be a radius of the semicircle. In order for the 10" circle to be wholly contained, the flat side of the semicircle must be tangent to the 10" circle. There is only one position in the figure where that can happen. (see attached).
Answer:
1The diameter measurement of a semi circle having a measure of 10" diameter , 20" diameter and a length of 25.MAPP gas, natural gas, propane, and acetylene can be used with oxygen to cut metal.
True
False
Which two technologies were combined to create product life cycle management (PLM) software?
CAD and a database
spreadsheets and graphics
a database and spreadsheets
CAD and spreadsheets
Answer:
CAD and a database
Explanation:
The correct answer is CAD and a database. When American Motors Corportation introduced the Jeep Cherokee, it implemented CAD to increase engineering productivity and combined that with a new communications system.
What regulates the car engines temperature
Answer:
car’s thermostat is used to regulate the temperature of the engine to help the engine stay cool.
Explanation:
Answer:
Coolant
Explanation:
A brass alloy is known to have a yield strength of 275 MPa (40,000 psi), a tensile strength of 380 MPa (55,000 psi), and an elastic modulus of 103 GPa (15.0×106 psi). A cylindrical specimen of this alloy 5.4 mm (0.21 in.) in diameter and 225 mm (8.87 in.) long is stressed in tension and found to elongate 6.8 mm (0.27 in.). On the basis of the information given, is it possible to compute the magnitude of the load that is necessary to produce this change in length? If not, explain why.
Answer:
The magnitude of the load can be computed because it is mandatory in order to produce the change in length ( elongation )
Explanation:
Yield strength = 275 Mpa
Tensile strength = 380 Mpa
elastic modulus = 103 GPa
The magnitude of the load can be computed because it is mandatory in order to produce the change in length ( elongation ) .
Given that the yield strength, elastic modulus and strain that is experienced by the test spectrum are given
strain = yield strength / elastic modulus
= 0.0027
When an arbitrary substance undergoes an ideal throttling process through a valve at steady state, (SELECT ALL THAT APPLY) inlet and outlet mass flowrates will be equal. inlet and outlet specific enthalpies will be equal. inlet and outlet pressures will be equal. inlet and outlet mass flowrates will be equal. inlet and outlet specific enthalpies will be equal. inlet and outlet temperatures will be equal.
Answer:
15x
Explanation:
A coal fired powerplant emits 0.5 kg/s of SO2 into the atmosphere from a stack that has a physical height of 100 meters. There is no temperature inversion and the atmosphere is characterized by class B stability for open country conditions. Exhaust emissions are 120 degrees C, ambient temperature is 25 degrees C, the stack diameter is 2.5 meters, and the volumetric flow of the exhaust is 35 cubic meters per second. The wind speed is 2 m/s.
Calculate the plume rise of the emissions using the Holland equation and determine the effective emission height.
pelo o que diz na database é que você n é ser humano normal por perguntar isso!!
Q-) please give me a reference about Tack coat? Pleae i need it please??!!
Answer:
Tack coat is a sprayed application of an asphalt binder upon an existing asphalt or Portland cement concrete pavement prior to an overlay, or between layers of new asphalt concrete.
Explanation:
An industrial boiler consists of tubes inside of which flow hot combustion gases. Water boils on the exterior of the tubes. When installed, the clean boiler has an over all heat transfer coefficient of 300 W/m^2 . K. Based on experience, i is anticipated that the fouling factors on the inner and outer surfaces will increase linearly with time as Ra,t and Ryo-at where a, 2.5 x 10^-11 m2 K/W s and a,-1.0 x 10^-11 m^2 - K/W s for the inner and outer tube surfaces, respectively. If the boiler is to be cleaned when the overall heat transfer coeffi- cient is reduced from its initial value by 25%, how long after installation should the first cleaning be scheduled?
Answer:
the first cleaning be scheduled 1.006 years after installation
Explanation:
Given the data in the question;
U[tex]_{clean[/tex] = 300 W/m².K
first we determine the heat coefficient of the dirt surface;
overall heat transfer coefficient is reduced from its initial value by 25%
U[tex]_{dirt[/tex] = ( 1 - 25%) × U[tex]_{clean[/tex]
U[tex]_{dirt[/tex] = ( 1 - 0.25) × 300
U[tex]_{dirt[/tex] = 0.75 × 300
U[tex]_{dirt[/tex] = 225 W/m².K
next we find the inner fouling factor
[tex]R"_{f ,i[/tex] = [tex]a_it[/tex]
[tex]R"_{f ,o[/tex] = (2.5 × 10⁻¹¹)t
for the outer fouling water;
[tex]R"_{f ,o[/tex] = [tex]a_ot[/tex]
[tex]R"_{f ,o[/tex] = ( 1.0 × 10⁻¹¹ )t
now, we determine the total heat transfer coefficient
[tex]\frac{1}{U}[/tex] = [tex]R"_{f ,i[/tex] + [tex]R"_{f ,o[/tex]
we substitute
[tex]\frac{1}{U}[/tex] = (3.5 × 10⁻¹¹)t
so the first cleaning duration after insulation will be;
[tex]\frac{1}{U} = \frac{1}{U_{dirt}} - \frac{1}{U{clean}}[/tex]
we substitute
(3.5 × 10⁻¹¹)t = [tex]\frac{1}{225} - \frac{1}{300}[/tex]
(3.5 × 10⁻¹¹)t = 0.001111
t = 0.001111 / (3.5 × 10⁻¹¹)
t = 31742857.142857 seconds
t = 31742857.142857 / 3.154 × 10⁷
t = 1.006 years
Therefore, the first cleaning be scheduled 1.006 years after installation
Compute the volume percent of graphite, VGr, in a 3.9 wt% C cast iron, assuming that all the carbon exists as the graphite phase. Assume densities of 7.9 and 2.3 g/cm3 for ferrite and graphite, respectively.
Answer:
Vgr = 0.122 = 12.2 vol %
Explanation:
Density of ferrite = 7.9 g/cm^3
Density of graphite = 2.3 g/cm^3
compute the volume percent of graphite
for a 3.9 wt% cast Iron
W∝ = (100 - 3.9) / ( 100 -0 ) = 0.961
Wgr = ( 3.9 - 0 ) / ( 100 - 0 ) = 0.039
Next convert the weight fraction to volume fraction using the equation attached below
Vgr = 0.122 = 12.2 vol %
consider a stead flow ideal carnot cycle using steam as the working fluid in which the high temperature constant pressure heat addition process starts with a saturated liquid and ends with a saturated vapor. plot this cycle in t-s coordinates showing the steam dome. calculate the thermal efficiency for this cycle if the pressure of the high temperature steam is 6 mpa and the low temperature heat rejection process occurs at 300 k.
Answer:
45.32%
Explanation:
Given data:
pressure of high temperature steam = 6 MPa
low temperature heat rejection process ( Tr ) = 300 k
A) plot of cycle in t-s coordinates showing steam dome
attached below
B) Calculate thermal efficiency
thermal efficiency = 1 - (Tr / Tsat )
Tsat = 275.59°C ≈ 548.59 K ( from steam table at Pa = 6 MPa )
back to equation 1
1 - (300 / 548.59 )
1 - 0.5468 = 0.4532 = 45.32%
A cylindrical bar of metal having a diameter of 19.9 mm and a length of 186 mm is deformed elastically in tension with a force of 42600 N. Given that the elastic modulus and Poisson's ratio of the metal are 67.1 GPa and 0.34, respectively, determine the following: (a) The amount by which this specimen will elongate (in mm) in the direction of the applied stress. (b) The change in diameter of the specimen (in mm). Indicate an increase in diameter with a positive number and a decrease with a negative number.
Answer:
a) 0.347 mm
b) - 0.0126 mm
Explanation:
Diameter of metal bar = 19.9 mm
length = 186 mm = 0.186 m
Tension force = 42600 N
elastic modulus = 67.1 GPa
Poisson's ratio = 0.34
a) calculate the amount by which the specimen will elongate
first calculate the area of metal bar
Area = πd^2 / 4 = π/4 ( 19.9 )^2 = 3.11 * 10^-4 m^2
Elongation ( E ) = б / e = P/A * L / ΔL
and ΔL = PL / AE
hence the elongation ( ΔL) = [ (42600 * 0.186 ) / ( 3.4*10^-4 * 67.1 * 10^9 ) ]
= 3.47 * 10^-4 m ≈ 0.347 mm
b) Calculate the change in diameter of specimen
μ = -( Δd / d) / ( ΔL/L )
0.34 = - (Δd / 19.9 ) / ( 0.347 / 186 )
∴ Δd = 0.34 * 0.00186 * 19.9 = - 0.0126 mm
As part of a heat treatment process, cylindrical, 304 stainless steel rods of 100-mm diameter are cooled from an initial temperature of 500 C by suspending them in an oil bath at 30 C. If a convection coefficient of 500 W/m2 K is maintained by circulation of the oil, how long does it take for the centerline of a rod to reach a temperature of 50 C, at which point it is withdrawn from the bath
Answer:
Explanation:
Given that:
diameter = 100 mm
initial temperature = 500 ° C
Conventional coefficient = 500 W/m^2 K
length = 1 m
We obtain the following data from the tables A-1;
For the stainless steel of the rod [tex]\overline T = 548 \ K[/tex]
[tex]\rho = 7900 \ kg/m^3[/tex]
[tex]K = 19.0 \ W/mk \\ \\ C_p = 545 \ J/kg.K[/tex]
[tex]\alpha = 4.40 \times 10^{-6} \ m^2/s \\ \\ B_i = \dfrac{h(\rho/4)}{K} \\ \\ =0.657[/tex]
Here, we can't apply the lumped capacitance method, since Bi > 0.1
[tex]\theta_o = \dfrac{T_o-T_{\infty}}{T_i -T_\infty}} \\ \\ \theta_o = \dfrac{50-30}{500 -30}} \\ \\ \theta_o = 0.0426\\[/tex]
[tex]0.0426 = c_1 \ exp (- E^2_1 F_o_)\\ \\ \\ 0.0426 = 1.1382 \ exp (-10.9287)^2 \ f_o \\ \\ = f_o = \dfrac{In(0.0374)}{0.863} \\ \\ f_o = 3.81[/tex]
[tex]t_f = \dfrac{f_o r^2}{\alpha} \\ \\ t_f = \dfrac{3.81 \times (0.05)^2}{4.40 \times 10^{-6}} \\ \\ t_f= 2162.5 \\ \\ t_f = 36 mins[/tex]
However, on a single rod, the energy extracted is:
[tex]\theta = pcv (T_i - T_{\infty} )(1 - \dfrac{2 \theta}{c} J_1 (\zeta) ) \\ \\ = 7900 \\times 546 \times 0.007854 \times (500 -300) (1 - \dfrac{2 \times 0.0426}{1.3643}) \\ \\ \theta = 1.54 \times 10^7 \ J[/tex]
Hence, for centerline temperature at 50 °C;
The surface temperature is:
[tex]T(r_o,t) = T_{\infty} +(T_1 -T_{\infty}) \theta_o \ J_o(\zeta_1) \\ \\ = 30 + (500-30) \times 0.0426 \times 0.5386 \\ \\ \mathbf{T(r_o,t) = 41.69 ^0 \ C}[/tex]
List six possible valve defects that should be included in the inspection of a used valve?
Answer:
Valvular stenosis , Valvular prolapse , Regurgitation,
Explanation:
Some project managers prefer the PERT chart over the Gantt chart because it clearly illustrates task dependencies. A PERT chart, however, can be much more difficult to interpret, especially on complex projects. Alternatively, some project managers may choose to use both techniques. If you are the project manager of a residential construction project, will you prefer PERT chart to Gantt chart? Explain why?
Answer:
PERT Chart and GANTT Chart
As the project manager of a residential construction project, I will prefer the PERT chart to the GANTT chart because a PERT chart displays task dependencies unlike a Gantt chart. With the PERT chart, the sequence of tasks is clearly mapped out. Dependent tasks are carried out when other tasks that they depend on have been executed.
Explanation:
By definition, a Gantt chart is like a bar chart that lays out project tasks and timelines using bars. On the other hand, a PERT chart follows a structure in the form of flow charts or network diagrams. It displays all the project tasks in separate boxes. The boxes are then connected with arrows which clearly show the task dependencies.
Consider a mild steel specimen with yield strength of 43.5 ksi and Young's modulus of 29,000 ksi. It is stretched up to a point where the strain in the specimen is 0.2% (or 0.002). If the specimen is unloaded (i.e. load reduces to zero), the residual strain (or permanent set) is: 0.05% 0.1% 0% 0.2%
Answer:
0.05%
Explanation:
From the question, we have;
The yield strength of the mild steel, [tex]\sigma _c[/tex] = 43.5 ksi
Young's modulus of elasticity, ∈ = 29,000 ksi
The total strain, [tex]\epsilon _c[/tex] = 0.2% = 0.002
The inelatic strain [tex]\epsilon_c^{in}[/tex] is given as follows;
[tex]\epsilon_c^{in}[/tex] = [tex]\epsilon _c[/tex] - [tex]\sigma _c[/tex]/∈
Therefore, we have;
[tex]\epsilon_c^{in}[/tex] = 0.002 - 43.5/(29,000) = 0.0005
Therefore, the inelastic strain, [tex]\epsilon_c^{in}[/tex] = 0.0005 = 0.05%
Taking the inelastic strain as the residual strain, we have;
The residual strain = 0.05%
Which color is used to indicate that a wire will be energized when power is brought to the circuit
A. Yellow
B. Black
C. Blue
D. White
Answer:
I think the answer is B. Black
The criminal and traffic code requires that a driver must have a valid driver's license in his/her
immediate possession at any time when operating a motor vehicle.
True
False
Answer:
true
Explanation:
the answer is true because if u don't have a valid license when operating a vehicle and you get pulled over you will get in trouble i know this because my parents got in trouble for it once