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Determine the number of ways to choose 5 numbers from the first 18 positive integers such that any 2 differ by at least 2.

4 years ago

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4 years ago

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How to apply telescopic series in series involving sine of angles
 
 
suppose your seies is : sin x + sin 2x + sin 3x..........sin nx, multiply and divide by sin x/2, use sin x * sin y = ½ * (cos(x-y) – cos(x+y) ), sin x * sinx/2 = 0.5 * cos(x/2) – 0.5 *...
 
Akshay 9 months ago
 
se sin x * sin y = ½ * (cos(x-y) – cos(x+y) ), sin x * sinx/2 = 0.5 * cos(x/2) – 0.5 * cos(1.5x), sin 2x * sin x/2 = 0.5 * cos(1.5 x) – 0.5*cos(2.5 x), sin 3x * sin x/2 = 0.5 * cos(2.5 x) – ...
 
manu 3 months ago
 
or if you want to do it using exponentials, write sin ax =1/2 * (e iax -e -iax ), u will get two geomtric series, one for +ve powers of exp, other for negative powers. apply sum of gm...
 
Akshay 9 months ago
what is meant by even and odd numbers????????????????????????????????????????????????????????????????????????????????????????????????????????
 
 
hey student.. Odd numbers can NOT be divided evenly into groups of two. The number five can be divided into two groups of two and one group of one. Even numbers always end with a digit of 0,...
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Sakshi one month ago
What is √(-20) ?
 
 
4.47213595 i
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Ashutosh Sharma 9 months ago
 
4.4721359551 this the value of the sqt of -20 and solve it more types like if ur stdying in 10 th class then teachers will told two methods
 
RIYAZSHAIK one month ago
 
There is no answer for this value.Because there is no solution for under root negative value.
 
OUTPASS 7 months ago
Can u solve it? Question number 13 plz
 
 
By expanding the tan2x and cos2x terms we get simplifying we get now each of the multiplying term has limit 1 as x tends to 0 thus L = 1/2
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Riddhish Bhalodia 3 months ago
what is integration? and what is the real life applications of an integration?
 
 
Dear Sudharshan Integration is the one symboll used in solving problems . Integration is opposite to differentiation. It is usefull in mathematics, physics and chemistry
 
Prabhakar ch 3 months ago
 
DEAR SUDARSHAN, Integration is the act of bringing together smaller components into a single system that functions as one. Integration is used to compute such things as the areas and...
 
naresh raju 3 months ago
 
dear sudarshan..... Integration is a way of adding slices to find the whole. Integration can be used to find areas, volumes, central points and many useful things. But it is easiest to...
 
mohan 3 months ago
Distance of a focal chord of the parabola y 2 = 4x from the vertex is 2 units then its length is
 
 
Dera Student, Assume any point on parabola P(at 2 , 2at) and PQ is focal chord then coordinates of Q will be (a/t 2 , -2a/t). Since value of a = 1. Now write the equation of line PQ using...
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Vijay Mukati 2 months ago
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