Cos (aX) = 1 + bX, give value of X in terms of a and b.Practical Problem at site: An arc shape insert- plate of which R was 1250 and D was 625mm and thus S = 2618 (chord length (L)= 2165), has been damaged and flattered.
And site staff gives feedback that it is now D = 525 instead of 625 and Chord length =2280.but this all not match in a geometrical figure. One dimension is wrong. If we consider D= 525 is correct then what is new radius. S=2618 will remain unchanged. Hence if S and D is given what is new R.
By trigonometry and geometrically this relation will arrive like this
S = R . Theta ---------- Equation no. 1
where R is radius of arc and Theta is angle in radians of arc ends at centre and S is length of arc.
second relation if distance of arc centre to chord centre is = D, then
Cos (Theta/2) = (R - D)/R -------------Equation no 2
Simplifying both relation,
Cos (S/2R) = (R-D)/R
Here equation is with one unknown, because S and D is known variables. Only R is to find out.
In Simple form it can be written to solve further this equation is
Cos (aX) = 1 + bX, give value of X in terms of a and b. Please help to solve this simple Equation
R
L/2
D
Theta
Suppose the first term is a, the second is a+r and the nth is a+(n-1)r. Then the sum of the first five = 5a + 10r = 85 and the sum of the first six = 6a + 15r = 123 Solving these simultaneous equations, a = 3 and r = 7 So the first four terms are: 3, 10, 17 and 24
It is 58465.
An arithmetic series is the sum of the terms in an arithmetic progression.
The nth term of the series is [ 4/2(n-1) ].
The sum of 50 consecutive odd integers is equal to: (First Term + Last Term) * (The number of Terms)/2 or in this case, more specifically: (2 * First Term + 98) * 25 If you meant 1+3+5+7+...+99, then the sum is 2500.
Best example is that an "odd" (or "even") function's Maclaurin series only has terms with odd (or even) powers. cos(x) and sin(x) are examples of odd and even functions with easy to calculate Maclaurin series.
YAWA!!
This series is known as the Harmonic Series and it diverges but very, very slowly. For example, the first 100 terms sum to 5.187...., the first 1000 terms to 7.486...., and the first 1000000 terms to 14.392.... There are many proofs of the divergence of this series and an internet search of Harmonic Series will no doubt find many of them.
There are lots of series out there for people to enjoy. In terms of a series by J.K. Rowling, she is working on a crime series, the first book was released in early 2013.
Suppose the first term is a, the second is a+r and the nth is a+(n-1)r. Then the sum of the first five = 5a + 10r = 85 and the sum of the first six = 6a + 15r = 123 Solving these simultaneous equations, a = 3 and r = 7 So the first four terms are: 3, 10, 17 and 24
The only derivatives of the verb 'est', which means '[he/she/it] is', are other forms of the infinitive 'esse', which means 'to be'. For example, 'esto' may be the second or the third person singular form in the future imperative tense. In terms of the second person, it translates as '[you] shall be'. In terms of the third, its translation is '[he/she/it] shall be'.
A Taylor expansion is a way of representing a function in terms of a sum of its derivatives. Please see the link.
The Nth partial sum is the sum of the first n terms in an infinite series.
The natural base, e, 2.718281828..., was selected because the derivatived/dx ex is equal to x. This simplifies many calculations, derivatives, integrals, etc. Additional: This base is used because there is a series (of terms) for powers of (e), therefore, powers of any value can be found just by plugging in values in the series.
The summation of a geometric series to infinity is equal to a/1-rwhere a is equal to the first term and r is equal to the common difference between the terms.
An equation where some terms are derivatives of functions. Usually the problem is to find the function that makes the equation true.
The sum of the terms in a sequence is called a series. Sequence is a function whose domain is the natural numbers. So f(1)= first entry in the sequence, and f(2) is the next.... f(n) is the nth term. We usually don't write sequences that way. Instead of f(1) we write, a1 to refer to the first term. The function tells us the rule we use to find the terms of the sequence. So for example, f says take n and square it. Then the first 3 terms of the sequence are 1, 4 and 9 and the first 3 terms of the series are 1, 5 and 14