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  1. kaliprasad

    MHB Find all possible solutions of c and d

    we have $70^2 + 61^2 + c^2 = d^2$ or $4900 +3721 + c^2 -= d^2$ or $d^2-c^2 = 8621$ or ($d+c)(d-c) = 8621$ to solve the same you can put 8621 as product of 2 numbers (one case 8621 * 1$ equiate one to d +c and another to d- c and solve for c and d. by choosing all pair of numbers fot erach pair...
  2. kaliprasad

    MHB Group Elements of Z24: Find the Order

    kindly infrom what you have tried and where you are facing problems
  3. kaliprasad

    MHB Solve Polynomial Division: -5a + 4b = x^2+1 Rem -A-2

    yes. 4b – a + 1 = 0 as there is no x term. you need to divide by x+1 and get the constant term (putting x = -1 shall do also) this shall give 2 equations and you need to solve and proceed further;
  4. kaliprasad

    MHB Finding 3-Digit Numbers with Sum of Digits Squared = 2

    In the above I find 100 solutions specified under the categories. $S(n)$
  5. kaliprasad

    MHB Gre.qu.1 are also in Q

    You are right. the question is easy. The product of numbers that are in P that are in Q cannot be more than the product of numbers that are in Q. this is so because the numbers in P that are in Q has to be be subset of numbers in Q. Now does Q contain at least one element that is not in P...
  6. kaliprasad

    MHB -gre.qu.10 quantity on 2 means

    we have sum of 100 measurements = 2300 sum of 50 additional measurements = 27 * 50 = 1350 total sum = 2300 + 1350 = 2650 so arithmetic mean = $\frac{3650}{150} = \frac{73}{3}$ so B is bigger for a short cut 25 is mean of 23 and 27 more elements(100) have mean 23 and less (50) elements have...
  7. kaliprasad

    MHB Similar triangles

  8. kaliprasad

    MHB Integer solutions of system of equations

    There was a typo error in first line and I corrected the same. Otherwise I do not find error if any. This may be pointed
  9. kaliprasad

    MHB Integer solutions of system of equations

    May be. I would like to know the correct answer
  10. kaliprasad

    MHB Area of rectangle

    Width being less than square root of 600 I see that it is less than 25 so I have only one candidate d to check and width 10 so length 60 meets the criteria and hence the answer
  11. kaliprasad

    MHB Find Optimal t for Profit: C vs. R

    For the profit we must have $R > C$ or $4t^2+t > 3t^2 + 9t$ Now you can proceed from here and find the result
  12. kaliprasad

    MHB Find the area of triangle

    Area of $\triangle STV$ = area of $\triangle UVT$ because they are on equal base and same base now area of $\triangle UVT$ is 3 times area of $\triangle UVX$ as height is same and base is 3 times so area of $\triangle STV$ = 3 * area of $\triangle UVX$ = $42cm^2$
  13. kaliprasad

    MHB Solving 2^x + 2/2^x = 3

    In future kindly inform what you have tried and where you are stuck so that we can provide steps to proceed For this put $2^x = y$ and see what you get
  14. kaliprasad

    MHB Guide to Dealing with Double Subscripts

    you can write as E_{x_{y}} to get $E_{x_{y}}$
  15. kaliprasad

    MHB Passengers on the bus

    My Attempt After if left the 1st stop $\dfrac{5}{8}$ remained so $\dfrac{3}{8}$ was the number of more persons alighted than boarded The number is 180 so $\dfrac{3}{8}$ of number of persons when it left the $1^{st}$ stop is 180 so number of persons when it left $1^{st}$ stop...
  16. kaliprasad

    MHB Prove No Integers Solve $ax^3+bx^2+cx+d=1$ for x=19,2 for x=62

    because this is a challenge question you are required to answer it fully . this is not a question for help