Let d1,. .., dT(n) be all positive divisors of n. For each dj | n, define Cj,s(n) = {1 ≤ x ≤ ns: (x, ns)s = dsj }. K.Bibak et al. (2016) gave a formula using Ramanujan sums for the number of solutions of the above congruence equation wit...
Using the formula for binomial coefficients:(nk)=n!k!(n−k)!we have:(193)=19!3!(19−3)!=19×18×173×2×1 Calculating this:=19×18×176=58146=969Final AnswerThus, the number of solutions to the equation x+y+z+w=20 under the condition that x,y,z,w>0 is 969....
To solve the given equations and find the number of solutions, we will analyze each equation step by step. Equation 1: x−12log0.5x=1 Step 1: Rewrite the equationWe can rewrite the equation as:log0.5x=x12 Step 2: Change of base for logarithmUsing the change of base formula, we have...
Use the discriminant to determine the number of real solutions of the equation. Do not solve the equation. $$4x^2 + 5x + \dfrac{13}{8} = 0 $$ Nature of Solutions of a Quadratic Equation Algebraically, a quadratic equation is ...
b. Solve the equation using the quadratic formula. Compute the value of the discriminant and give the number of real solutions to the quadratic equation. 2 x^2 + 5 x - 7 = 0. Compute the value of the discriminant and give the number of real so...
This formula compares the 1st value in the first array in the specified range with the 1st value of the second array in the specified range and etc. I need the formula to compare any value from the first array to any value from the second array. ...
This formula finds the date closest to or exactly reaching the accumulated sum of 100 by checking the cumulative sum of values. For your example data, it should return "05-11-23" as the result since the accumulated sum at that date is the closest to 100 (which is 100.1). The text was...
Page numbers have been inserted at the bottom of your worksheet. Method 2 – Using the Ampersand Operator Steps: In cellC27enter the formula below: ="Page "&" 1"&" of"&" 1" In this formula, theAmpersand (&)operator combines the textsPage, 1, of,and1to return the outputPage 1 of...
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This has been driving me completely insane. But I just cannot seem to construct a formula which is outputting what I want. I'll give an example of what I'm...