In mathematics, a ratio indicates how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8∶6, which is equivalent to the ratio 4∶3). Similarly, the ratio of lemons to oranges is 6∶8 (or 3∶4) and the ratio of oranges to the total amount of fruit is 8∶14 (or 4∶7).
The numbers in a ratio may be quantities of any kind, such as counts of people or objects, or such as measurements of lengths, weights, time, etc. In most contexts, both numbers are restricted to be positive.
A ratio may be specified either by giving both constituting numbers, written as "a to b" or "a∶b", or by giving just the value of their quotient a/b. Equal quotients correspond to equal ratios.
Consequently, a ratio may be considered as an ordered pair of numbers, a fraction with the first number in the numerator and the second in the denominator, or as the value denoted by this fraction. Ratios of counts, given by (non-zero) natural numbers, are rational numbers, and may sometimes be natural numbers. When two quantities are measured with the same unit, as is often the case, their ratio is a dimensionless number. A quotient of two quantities that are measured with different units is called a rate.
Homework Statement
At the given 10 Hz frequency calculate the magnitude of the voltage across a:
(1)4.7kohm resistor
(2)100nF capacitor
Homework Equations
Vr/v=R/z=R/sqrtR^2+(1/wC)
Vc/v=(1/wC)/z=(1/wC)//sqrtR^2+(1/wC)
The Attempt at a Solution
(1)4.7/sqrt(4.7^2+2*PI*4.7^2)...
For my investigation regarding the aerodynamic forces on a spherical projectile, I really need to know the theoretical ratio of rotational kinetic energy to linear kinetic energy of a spherical projectile (assuming the only spin is forward spin and there is no Magnus effect).
Can someone please...
Homework Statement
Determine divergence/convergence of this series:
\sum\frac{(2n)!}{(n!)^{2}} * (\frac{1}{4})^{n}
Homework Equations
ratio test?
The Attempt at a Solution
I attempted to use the ratio test and the resulting limit was 1, which means the ratio test is inconclusive. So far, I...
Homework Statement
Electric and magnetic fields in many materials can be analyzed using the same relationships as for fields in vacuum, only substituting relative values of the permittivity and the permeability, ε = κε0 and μ = κmμ0, for their vacuum values, where κ is the dielectric...
Homework Statement
Test for convergence and divergence.
Homework Equations
\sum_{i=1}^{n} \frac{n!}{3^n}
\sum_{i=1}^{n} \frac{1}{{(log (n))}^{1/n}}
The Attempt at a Solution
For the first one I get \frac{(n+1)}{3} After applying the ratios. Taking the limit as n approaches infinity, it is...
The sqeuence of ratios of a fabinacci number
F_n+1/F_n
on looking at this.
F_2/F_1 =1/1 =1
F_3/F_2 =2/1 =2
F_4/F_3 =3/2 =1.5
F_5/F_4 = 5/3 = 1.667
Why would F_n+1 = at F_4 =3 with also F_3=2 I think i understand the squence is fabin accie on the denominater but on the...
has a transfer characteristic |H(f) given in the link below. The transmission is at maximum error-free rate of 4,800 bps. Compute the SNR (signal-to-noise-ratio) at the channel output. Does the output signal suffer from any distortion?
http://imageshack.us/photo/my-images/263/79465468.jpg/...
The Supergolden ratio is the solution of x3=x2+1.
\psi = \left({{\sqrt{31}}\over{2\ \times 3^{{{3}\over{2}}}}} {{29}\over{54}} \right)^{{{1}\over{3}}} {{1}\over{9\,\left({{\sqrt{31}}\over{2\ \times3^{ {{3}\over{2}}}}} {{29}\over{54}}\right)^{{{1}\over{3}}}}} {{1}\over{ 3}}\approx...
Homework Statement
The weight of an object of mass 1kg at the surface of Mars is about 4N. The radius of Mars is about half the radius of Earth. Estimate the ratio:
mass of Mars/Mass of Earth
Homework Equations
The Attempt at a Solution
The answer is 0.1 but I don’t see...
Hi everyone,
I'm not sure if this is the right section to post this in, but the question doesn't really seem to fit any singular category, so I'll try this one (if someone has a better recommendation, please let me know!)
The question I'm seeking to answer is this:
A baseband signal of...
Homework Statement
If the work put in is 3000j, calculate the useful energy output.
[PLAIN]http://www.mkwebman.com/question
Load = 1962N
Homework Equations
VR = Distance covered by effort / Distance covered by load
MA = load/effort
Efficiency = MA / VR
Efficiency = useful...
Homework Statement
A receiving system consists of an antenna with an effective noise temperature of
70 K. This antenna is connected to a microwave front end of noise figure 7 dB
via a feeder. The feeder’s specific attenuation function is 0.2 dB/10m. The actual
feeder length is 2 m. Calculate...
Homework Statement
Here is the objective: To experiment with the resultant of two gravitational forces. In particular, you will find the equilibrium position for a test mass located on a line between two point masses.
Here are the instructions:
(1) Drag the test mass (red disk) to an...
Homework Statement
Copper forms two oxides. For the same amount of copper, twice as much oxygen was used to form the first oxide than to form the second one. What is the ratio of the valencies of copper in the first and second oxides?
(This is not my homework question. I am solving a book...
Homework Statement
The temperature of a fixed mass of gas drops from 127 C to 27 oC under constant pressure. Find the ratio of the new volume to the original volume.
C. 3:4
D. 4:3
E. 1:1
A and B arent here because i have gotten them wrong.
Homework Equations
Ideal gas law: PV=...
Two carts each 12 cm long travel toward each other on a frictionless air glider track. The first cart on the left has an initial velocity of 18 cm/s toward the other cart that is stationary. The carts then collide. The cart on the left has a new velocity of -4cm/s and the stationary cart now has...
I am doing the following practice problem in prep for an exam:
sum from n=0 to infinity: (3^n)/(n+1)^n
The book says to use the ratio test on it, which I did, but would the root test also apply to this?
Homework Statement
Determine whether 1/n! diverges or converges.
So far, we have only learned the comparison tests, p-series, geometric series, divergence test, and integral test, so I can only use these tests to prove it.
Homework Equations
N/a
The Attempt at a Solution
I...
Hi all,
Speed is a ratio of the distance traveled per unit time. But what then is work done and moments?
For example, work done is force multiplied by the distance traveled in the direction of the force. But how would you explain the rationale of multiplying these two quantities?
As...
Homework Statement
question
A ciclindrical metal specimen 10 mm in diameter is stressed elastically in tension. A force of 15000 N produces a reduction in diameter of 0.007 mm. Compute Poisson ratio if its elastic modulus is 100 GPa
Homework Equations
E=stress/strain
The...
question
A ciclindrical metal specimen 10 mm in diameter is stressed elastically in tension. A force of 15000 N produces a reduction in diameter of 0.007 mm. Compute Poisson ratio if its elastic modulus is 100 GPa
my attempt
D original = 0.01m
change in D = 0.000007m
F=15000N
E=...
Hi all, this is my first post.
I find a lot of conflicting definitions of damping factor, damping coefficient, and damping ratio on the internet, and in some textbooks, when related to RLC circuits.
Sometimes I see the neper frequency described as the damping factor or damping coefficient...
Homework Statement
To start, I did find a few very similar or equal topics, but I could not gather enough information.
And, the pi symbols are intended to be pi symbols with negative superscripts (couldn't get it to work/finalize).
---
The charge-to-mass ratio of a \pi- particle is known to...
Homework Statement
Show that the volume of an upright cylinder that can be inscribe in an upright cone is 4/9 times the volume of cone
Homework Equations
volume of cone
volume of cylinder
differentiation ??
similarity of triangle
The Attempt at a Solution
I draw the picture of...
I don't really know how to approach this problem...
A satellite is in a circular orbit around its parent body. The ratio of the satellite's kinetic energy to its potential energy, K/Ug, is a constant independent of the masses of the satellite and parent, and of the radius and velocity of the...
We have 2 solenoids : S1 and S2
The coils are wind up as close as they can get and both have length L.
They are both made from the same material and have the same length.
They are both connected to a DV source.
S2 has a wire with a double diameter
The ratio between B1 and B2 then is?
I...
Homework Statement
Suppose that an electron is a small spherical shell of mass m with a charge e spread over its surface. Show that the ratio of the magnetic moment to angular momentum of such an electron should be e/2m whether the electron is a) moving in a circular orbit or b) spinning...
Homework Statement
1962N Load 5 m from effort (hydraulic ram) and fulcrum 1m from effort.
Calculate the Velocity ratio, if work input is 3000j calculate work output.
Homework Equations
VR = distance moved by effort / distance moved by load
effort = 11772N
MA = load / effort =...
The ship is twice as old as the boiler was when the ship was as old as the boiler is.
What is the ratio of their ages?
I do believe I have solved this (without Googling) and have uploaded my answer online with a timestamp of 10:35PM 4/27/2011 (i.e. before I posted this).
Let me know...
Homework Statement
1. A photocpier increases the paper with the ratio 4:5, what % is the paper increased
2. An alloay has a copper, alloy and lead with the ratio 5:7:3, what % is the alloy to lead
2. The attempt at a solution
1. Difference in equation = 5 - 4 = 1...
Homework Statement
For copper we find that J=\sigmaE , where \sigma has the value 5.8x10^7 mksc units. If an alternating electric field represented by E0ei\omegat exists within the copper. Find the ratio of the conduction to the displacement current density at a frequency of 1megacycle/sec...
Homework Statement
Ice cube at 0 degree is mixed with steam at 100 degree, both become water at 50 degree.
Find the ratio of mass of the ice : mass of steam
Homework Equations
Q=ml
Q=mcdT
The Attempt at a Solution
I tried this way :
let the ratio of ice to steam = a:b
a x...
Homework Statement
If the ratio of the energy densities of matter and radiation was much higher than it is today (by several orders of magnitude), in a few sentences describe what effect this would have on the redshift (or scale factor) when the universe switched from being...
Homework Statement
For e^+ e^- collisions at \sqrt{s}=5 GeV, estimate the ratio of the rates at which interactions produce hadrons and \mu^+ \mu^-Homework Equations
\sqrt{s} = 2E = E_{cm}
\Gamma = \frac{S |p|}{8 \pi \hbar m_1^2 c} |M|^2 where M is the matrix element
\frac{d \sigma}{d...
Homework Statement
we are looking at two stars in the eridani system, eri B and eri C. the period of the system is 247.9 years. the system's measured trigonometric parallax is 0.201 arcseconds and the tru angular extent to the semimajor axis of the reduced mass is 6.89". the ratio of...
Hi all. I need help on an issue I can't figure out.
What is the difference between 15x15 and 17x17 fuel when it comes to moderation properties? Standard fuel with these lattices have dimensions
15x15: pitch: 14.3 mm, d_rod: 10.77 mm
17x17: pitch: 12.6 mm, d_rod: 9.5 mm
These geometries...
Homework Statement
The ratio sin theta =-12/13
Homework Equations
The Attempt at a Solution
which comes out to according to my calcuations -0.9230, i then use 2nd sin function on my calculator and come up with -67.3 degrees
this answer is legitimate but another way of writing...
You can see it here starting at 2:30
https://www.youtube.com/watch?v=http://www.youtube.com/watch?v=kkGeOWYOFoA
My question is, how do you determine the position of the points used to draw the triangles and circles.
Martin Rees in his book Just Six Numbers says that in the early universe there 1 billion antiquarks and a billion and one quarks. Is that really known? How is known what the ratio of antiquarks to quarks was?
The following is an approximation problem. Given a ratio:
D =\frac{ \sum a_ib_i}{\sum b_ib_i}
I wonder what steps to follow to give a reasonable approximation.
This is an intuition
D =\frac{ \sum a_i}{\sum b_i}.
Clearly, given that all b_i terms are the same, the approximation is the...
hello
a plane would need a thrust to weight ratio of 1 of fly straight up without losing speed
but how can a plane in level flight maintain its altitude with <1 TWR
since to maintain a level flight you need to have lift = weight
so your engine needs to supply enough power to generate...
Homework Statement
A=0.1+x^2 in a convergent -divergent nozzle .I need to plot mach number as a function of x for isentropic flow across the nozzle. I know the A/A* as a function of Ma. But finding the opposite (Ma in terms of A/A*) from that equation did not seem to be that easy...
Homework Statement
I need help once again with this question below:
Thanks,
aeromat
The Attempt at a Solution
This is what I have so far:
GP = GQ + QP
GQ = GP + PQ
GR = GP + PR
GP + GQ + GR = GQ + QP[-] + PQ[+] + GP + PR + GP
GP + GQ + GR = GQ + 2GP + PR
I am stuck...
Homework Statement
Tea served in a canteen is made from a mixture of two different types of tea, type A and type B. Type A costs €12.15 per kg. Type B costs €12.90 per kg. The mixture costs €12.65 per kg.
If the mixture contains 7kg of type A, how many kilograms of type B does it contain...