a^2 −a−^(1000) (√((1+8000a)))=1000 find a
Find the value of r, if ^(10) C_r = ^(10) C_(2r + 1)
6 different letters were written to 6 different people and 6 different envelopes were prepared with the addresses of these people written on them. In how many different ways can you put a letter in each envelope without putting a letter written to this person in the envelope with the name of any person?
Find f(x)=∫^( x) _( 0) (dt/(t+e^(f(t)) ))
If x + ((49)/(x + 48)) = − 34 find (2x + 83)^3 + (1/((2x + 83)^3 ))
Arrange in descending order: (√5) − (√2), (√7) − (√5) , (√(13)) − (√(11)) , (√(19)) − (√(17))
u_0 = a, u_(n+1) = (√(u_n v_n )) v_0 = b ∈ ]0,1[ , v_(n+1) = (1/(2(u_n +v_n ))) • show that a≤u_n ≤u_(n+1) ≤v_n ≤v_(n+1) ≤b • show that v_n − u_n ≤ ((a+b)/2^n )
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A pin 6cm high is placed in front of a diverging lens of focal length 15cm, Calculate the position of the image formed
:: α , β and γ are roots of the following equation . Find the value of ” F ” : Equation : x^( 3) −2x −1=0 F := α^( 5) + β^( 5) + γ^( 5)
calculate : I= ∫_(0 ) ^( ∞) (( tan^( −1) (x))/((1 + x^( 2) )^( 2) )) dx = ?
please convert 2531_((5000) ) to base 5002. thanks.