1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
11111nata11111 [884]
3 years ago
8

The volume of a right circular cone of radius r and height h is V = 1 3 πr 2h (a) (i) Find a formula for the instantaneous rate

of change of V with respect to r if r changes and h remain constant. (ii) Suppose that h = 2 is fixed but r varies. Find the rate of change of V w. R. To r at the point where r = 4.
Engineering
1 answer:
Diano4ka-milaya [45]3 years ago
5 0

Answer:

(i) \frac{2}{3}\pirh

(ii) \frac{16}{3}\pi

Explanation:

Given:

V = \frac{1}{3}\pir²h

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 \frac{dV}{dr}, and is given by finding the differentiation of V with respect to r as follow:

\frac{dV}{dr} = \frac{d}{dr}[\frac{1}{3}\pir²h]

\frac{dV}{dr} = \frac{2}{3}\pirh     --------------------(i)

(ii)

Given;

h = 2

r = 4

Substitute these values into equation (i) as follows;

\frac{dV}{dr} = \frac{2}{3}\pi(4 x 2)

\frac{dV}{dr} = \frac{2}{3}\pi(8)

\frac{dV}{dr} = \frac{16}{3}\pi

\frac{dV}{dr} = \frac{16}{3}\pi

You might be interested in
Characteristics of information assurance management work force
hjlf
1. Integrity

Integrity involves assurance that all information systems are protected and not tampered with. IA aims to maintain integrity through means such as anti-virus software on all computer system, and ensuring all staff with access to know how to appropriately use their systems to minimize malware, or viruses entering information systems.

IT Governance provides a variety of E-learning courses to improve staff awareness on topics such as phishing and ransomware, as a means to reduce the likelihood of system being breached, and data exposed.

2. Availability

Availability simply means those who need access to information, are allowed to access it. Information should be available to only those who are aware of the risks associated with information systems.

3. Authentication

Authentication involves ensuring those who have access to information, are who they say they are. Ways of improving authentication involve methods such as two-factor authentication, strong passwords, bio-metrics and other devices. Authentication may also be used to not only identify users, but also other devices.

4. Confidentiality

IA involves the confidentiality of information, meaning only those with authorization may view certain data. This step is closely mirrored by the six data processing principles of the General Data Protection Regulation (GDPR), where by personal data must be processed in a secure manner "using appropriate technical and oganizational measures" ("integrity and confidentiality").

5. Nonrepudiation

The final pillar simply means someone with access to your organizations information system cannot deny having completed an action within the system, as there should be methods in place to prove that they did make said action.
5 0
3 years ago
A good way of ensuring whether a listener has understood a presentation is to record all major and minor details. identify all u
PolarNik [594]

Answer:

Summarize in one's own words

Explanation:

4 0
4 years ago
Read 2 more answers
without using the routh hurwitz criterion, determing if the followign systems are asymptotically stable, marginally stable, or u
lesantik [10]

Answer:

The system is marginally stable.

Explanation:

Transfer function, M(s) = [10(s+2)]/(s³ + 3s² + 5s)

In control the stability properties of a system can be obtained from just the characteristic equation of its closed loop transfer function.

- The condition for stability is that all the roots of the characteristic equation be negative and real.

- The condition for asymptotic stability is that all the real parts of the roots must all be negative, since there'll be complex roots.

- The condition for marginal stability is that the real part of all the complex roots are negative, the roots without real parts must have distinct imaginary parts.

- The condition for instability is for at least one of the roots to be positive. Or if there are complex roots, the real part of the roots being positive indicates instability.

The characteristic equation for this transfer function is (s³ + 3s² + 5s)

Solving this polynomial

s = 0

s = [-3 - √(11i)]/2

s = [-3 + √(11i)]/2

These roots have all their real parts to be negative, and the zero root has a distinct imaginary part, hence the system is marginally stable

4 0
4 years ago
Hello , how are yall:))))
SVEN [57.7K]

Answer:

eh I'm good hbu?????????

6 0
3 years ago
Read 2 more answers
: The interior wall of a furnace is maintained at a temperature of 900 0C. The wall is 60 cm thick, 1 m wide, 1.5 m broad of mat
Snowcat [4.5K]

Answer:

<em>Heat is lost at the rate of 750 J/s or W</em>

<em>The thermal resistance is 1 K/W</em>

Explanation:

interior temperature T_{2} = 900 °C

wall thickness t = 60 cm = 0.6 m

width = 1 m

breadth = 1.5 m

thermal conductivity k = 0.4 W/m-K

outside temperature T_{1} = 150 °C

heat through the wall = ?

The area of the wall A = w x b = 1 x 1.5 = 1.5 m^2

Temperature difference dt = T_{2} - T_{1} = 900 - 150 = 750 °C

note that dt is also equal to 750 K since to convert from °C to K we'll have to add 273 to both temperature, which will still cancel out when we subtract the two temperatures.

To get the heat that escapes through the wall, we use the equation

Q = Ak\frac{dt}{t}

substituting values, we have

Q = 1.5 x 0.4 x \frac{750}{0.6} = <em>750 J/s or W</em>

Thermal resistance R_{t} = \frac{dt}{Q}

R_{t} = 750/750 =<em> 1 K/W</em>

7 0
3 years ago
Other questions:
  • Why research and development in Maintenance Engineering?
    6·1 answer
  • a cubical box 20-cm on a side is contructed from 1.2 cm thick concrete panels. A 100-W light bulb is sealed inside the box. What
    12·1 answer
  • Suspension cultures of Panax ginseng plant cells are used to produce ginseng biomass for the health tonic market. The cells are
    7·1 answer
  • Determine the angles made by the vector V = - 36i + 15j with the positive x- and y-axes. Write the unit vector n in the directio
    11·1 answer
  • What range does creep occur in? A)Elastic, B)Plastic, C)Transition D)Temperature range from room to 200 degrees?
    14·1 answer
  • How is the fuel introduced into the Diesel engine?
    9·1 answer
  • Can someone help me on my auto tech worksheet
    13·1 answer
  • Resistance in a circuit that has 35 mA of current and 5.6 V applied equals.
    9·1 answer
  • Which dimensionless parameter tells whether flow disturbances will be attenuated or amplified? a. Pr b. Re C G d. St e. Fe
    9·1 answer
  • The cars of a roller-coaster ride have a speed of 19.0 km/h as they pass over the top of the circular track. Neglect any frictio
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!