We need to find 2 digit numbers (10-99) each of which has a) 8 divisors b) 9 divisors
Here's what I found: For 8 divisors, the number must have a. 3 distinct prime factors, or b. of the form {p^3, q} which are: 2^3*3=24 (1,2,3,4,6,8,12,24) 2*3*5=30 (1,2,3,5,6,10,15,30) 2^3*5=40 (1,2,4,5,8,10,20,40) 2*3*7=42 (1,2,3,6,7,14,21,42) 2*3^3=54 (1,2,3,6,9,18,27,54) 2^3*7=56 (1,2,4,7,8,14,28,56) 2*3*11=66 (1,2,3,6,11,22,33,66) 2^3*11=88 (1,2,4,8,11,22,44,88) 2*3*13=78 (1,2,3,6,13,26,39,78) 2*5*7=70 (1,2,5,7,10,14,35,70)
For 9 divisors, it is necessary that the 2-digit number be a perfect square, and the square-root is composite. For this, we can list only (2*3)^2=36 (1,2,3,4,6,9,12,18,36)
So there are 10 2-digit numbers with 8 factors, and 1 with 9 factors.
Note: looks like 72 has 12, the most factors in two digit numbers: 72 (1,2,3,4,6.8,9,12,18,24,36,72)
For the given system of linear equations to give an infinite number of solutions the value of k should be 2.
<h3>What is a Dependent Consistent System of equations?</h3>
A system of the equation to be a Dependent Consistent System the system must have multiple solutions for which the lines of the equation must be coinciding.
Given the two systems of linear equations,
2x + 3y = 4
(k+ 2)x + 6y = 3k+2
For any system of equations to have infinitely many solutions, the equation of the linear system must be in ratio, so that the lines of the equations overlap each other. Therefore, the ratio for the two of the given equations can be written as,
2/(k+2) = 3/6 = 4/(3k+2)
Solving the ratio to get the value of k,
2/(k+2) = 3/6
2/(k+2) = 1/2
2 × 2 = 1 × (k+2)
4 = k + 2
4 - 2 = k
k = 2
Hence, for the given system of linear equations to give an infinite number of solutions the value of k should be 2.
(Sorry if I get something wrong, it’s straining my eyes to see what letter) 1. A 2. U 3. S 4. J 5. I 6. M 7. H 8. B 9. Y 10. L
To find where a coordinate is on a graph you need to start with the first number (x) (let’s say the coordinate is (2, -3), so 2) and find where it is ( you always find where the first number is on the x-axis and the second number on the y, remember that by x, y and x comes first.) Then, you need to find the second number (-3) then you need to find where they meet. So 2, -3 is on the letter I.
To find what coordinates a point that’s already been plotted is to see, for example, L, the two numbers that meet where L is are -4, -3, remember whatever was on the x axis comes first, -3, -4 is not the same.
Hopefully this makes sense, I don’t normally answer stuff.
Ignore the fact that it says limit because when sin (pi) is here it is not an Undefined Point, whatever value the calculator says is sin(pi) is the answer.
