Show me the calculation of joint variation

Mathematics

ScanSolve AI Answer

Answer

Tofauti ya pamoja hutokea wakati kiasi kimoja kinatofautiana moja kwa moja na bidhaa au mgawo wa vigeu vingine.

Step-by-step solution

2 steps

Formula ya jumla ya tofauti ya pamoja ni:
z = kxy

ambapo:

  • z ni kiasi kinachotofautiana
  • x na y ni vigeu vingine
  • k ni mara kwa mara ya tofauti

Mfano:

Tuseme z kinatofautiana kwa pamoja na x na y. Ikiwa z = 24 wakati x = 2 na y = 3, tafuta thamani ya z wakati x = 4 na y = 5.

  1. Tumia taarifa zilizotolewa ili kupata mara kwa mara ya tofauti (k).

    24 = k × 2 × 3
    24 = 6k
    k = 24 / 6
    k = 4

  2. Tumia thamani ya k na maadili mapya ya x na y ili kupata z.

    z = kxy
    z = 4 × 4 × 5
    z = 80

    Kwa hiyo, thamani ya z ni 80.

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