how to make paper look old

ModalsExampleUses 1Can / can'tThey can control their own budgets. We can't fix it. Can I smoke here? Can you help me?Ability / Possibility 1 Inability / Impossibility Asking for permission! Request [Could / couldn'tCould I borrow your dictionary? Could you say it again more slowly? We could try to fix it ourselves. I think we could have another Gulf war. He gave up his old job so he could work for us.Asking for permission! i RequestSuggestion j 1 Future possibility Ability in the pastMayMay I have another cup of coffee?China may become a major economic power.Asking for permission 1 Future possiblity jMightWe'd better phone tomorrow, they might beeating their dinner now.They might give us a 10% discount.Present possibilityI lFuture possibility ,Must / mustn'tWe must say good-bye now.They mustn't disrupt the work more thannecessary.Necessity / Obligation / ProhibitionOught toWe ought to employ a professional writer.Saying what's right or correctShallShall I help you with your luggage? Shall we meet at 2.30 then? Shall I do that or will you?OfferSuggestion Asking what to doShouldWe should sort out this problem at once.I think we should check everything again. Profits should increase next year.Saying what's right or correctRecommending action Uncertain predictionWiU / won'tI can't see any taxis so I'll walk. I'll buy it for you if you like. I'll get back to you on Monday. Profits will increase next year.Instant decisionsOfferPromiseCertain predictionWould / wouldn'tWould you mind if I brought a colleague with me?Would you pass the salt please? Would you mind waiting a moment? "Would three o'clock suit you?" - "That'd be fine."Would you like to play golf this Friday? "Would you prefer tea or coffee?" - "I'd like tea, please."Asking for permissionRequest RequestMaking arrangementsInvitation Preferences

sine cosine tangent chart

The sine term and cosine term is a ratio of sides in the right angled triangles is called tangent tables. The three relations as follow First, tan A = `(sin A)/ (cos A)` Second, assume sin A = `p/r`. Third, cos A = `q/r` Dividing `p/r` by `q/r` and canceling the r's that appear, we conclude that tan A = `p/q`. That the tangent is the opposite side divided by an adjacent side: Tan A = `(opp)/(adj)`How to find Tan values of angles in radiansAny radian angle can be converted to degree and vise versa.Î radian = 180 degreesWe know the value of Î is 3.14 approximatelySo 1 radian = 180 degree / 3.14 = 52.325 degreesNow we can find any radian measure with this conversion factor in hand. A Tangent tables by using sine term and cosine term The two triangles PST and PQR are similar, we have `(TS)/(PT) = (RQ) / (PR)`.But Here TS = tan A,PT= 1, RQ = sin A, and PR = cos PQ. Therefore we have derived the fundamental identity Tan A = `( sin A) / (cos A)`

half life equation

1. Find the values of the disintegration constant and half-life of a radioactive substance for which the following counting rates were obtained at different times.What would have been the counting rate at t = 0?2. The counting rates listed below were obtained when the activity of a certain radioactive sample was measured at different times. Plot the decay curve on semilog paper and determine the half-lives and initial activities of the component activities.

periodic table picture

Help on learning table of Pythagorean related trigonometric identities:cos2θ + sin2θ = 1sin θ = ± `sqrt(1 - cos^2 theta)`cos θ = ± `sqrt(1 - sin^2 theta)`sin θ = `1/(csc theta)`cos θ = `1/(sec theta)` tan θ = `1/(cot theta)`csc θ = `1/(sin theta)` sec θ = `1/(cos theta)` cot θ = `1/(tan theta)`1 + tan2θ = sec2θ1 + cot2θ = csc2θsin θ = ± `(tan theta)/(sqrt(1 + tan^2theta))`cos θ = ± `1/(sqrt(1 + tan^2theta))`tan θ = ± `sqrt(sec^2 theta - 1)`csc θ = ± `(sqrt(1 + tan^2theta))/(tan theta)` sec θ = ± `(sqrt(1 + tan^2theta))`cot θ = ± `1/(sqrt(sec^2 theta - 1))`Help on learning table of symmetry related trigonometric identities:sin (-θ) = - sin θ cos (-θ) = + cos θ tan (-θ) = - tan θ csc (-θ) = - csc θ sec (-θ) = + sec θ cot (-θ) = - cot θ sin (� - θ) = + sin θcos (� - θ) = - cos θtan (� - θ) = - tan θcsc (� - θ) = + csc θsec (� - θ) = - sec θcot (� - θ) = - cot sin (`pi/2` - θ) = + cos θcos (`pi/2` - θ) = + sin θtan (`pi/2` - θ) = + cot θcsc (`pi/2` - θ) = + sec θsec (`pi/2` - θ) = + csc θcot (`pi/2` - θ) = + tan θHelp on learning table of shifts and periodicity related trigonometric identitiessin (θ + `pi/2` ) = + cos θ cos (θ + `pi/2` ) = - sin θ tan (θ + `pi/2` ) = - cot θ csc (θ + `pi/2` ) = + sec θsec (θ + `pi/2` ) = - csc θ cot (θ + `pi/2` ) = - tan θ sin (θ + �) = - sin θcos (θ + �) = - cos θtan (θ + �) = + tan θcsc (θ + �) = - csc θsec (θ + �) = - sec θcot (θ + �) = + cot θsin (θ + 2�) = + cos θcos (θ + 2�) = + sin θtan (θ + 2�) = + cot θcsc (θ + 2�) = + sec θsec (θ + 2�) = + csc θcot (θ + 2�) = + tan θ

the area of a triangle

Some notes for area of triangle in circle: If the circle contain a triangle inside, we can easily calculate the area of triangle. The area of triangle is based on length of sides. We can find the area of triangle in circle is same as normal triangle area calculation.Formula for area of triangle in circle in math: For finding the area of the equilateral triangle use the simple form as A = ½ bh.The base length and height is more important for area of triangle in circle calculation. In circle, the triangle has different length of sides means we can use the heron’s formula. The perimeter is divided as half. This part is called as semi perimeter. The area of triangle in circle is = `sqrt(s (s-a) (s-b) (s-c))` . where s is represent the semi perimeter as s = `(a + b + c)/2` . If the triangle has angle size in circle means use the trigonometry formula as Area = `1/2` ab.sin c. Here two side’s length are used.

solute definition

Example problem 1 to define exponential function help:Solve the exponential function, f ( x ) = x54 x7Solution:The given function is f (x) = x54 x7The given function is of the form`e^a. e^b = e^(a+b)`Therefore we can solve the given function by using the formula f (x) = x54 x7 = x 54 + 7So we get, f (x) = x61Therefore the solution for the given function will be f (x) = x54 x7 = x61Example problem 2 to define exponential function help:Solve the exponential function, y = f (x), where y = `e^54/e^7`Solution:The given function is f (x) = `e^54/e^7`The given function is of the form`(e^a) / (e^b) = e^(a - b)` Therefore we can solve the given function by using the formula f (x) = e54 - 7So we get, f (x) = e47 Therefore the solution for the given function will bef (x) = `e^54/e^7` = e47.

point of concurrency

In line design geometry section we have many types of lines which has property of its own.Lines are classified into following types. Parallel lines: In geometry parallel lines are mostly applicable in design section, two lines which does not touch each other are called parallel lines.Perpendicular lines: In geometry Perpendicular lines are mostly applicable drawing section,Two line segment that form a L shape are called perpendicular lines.Concurrent lines: The three or more lines passing through the same point are called concurrent lines.