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Write the equation which connects the statement above

Mathematics

ScanSolve AI Answer

Answer

P=kDTP = k \frac{D}{T}

Step-by-step solution

5 steps
  1. Define variables for the quantities mentioned in the statement.

    Let PP represent the candidate's pressure.
    Let DD represent the number of days left.
    Let TT represent the topics covered.

  2. Translate the direct proportionality into a mathematical relationship.

    "a candidate's pressure is directly proportional to the number of days left" means P∝DP \propto D.

  3. Translate the inverse proportionality into a mathematical relationship.

    "and inversely proportional to the topics covered" means P∝1TP \propto \frac{1}{T}.

  4. Combine the proportionalities into a single relationship.

    Combining P∝DP \propto D and P∝1TP \propto \frac{1}{T} gives P∝DTP \propto \frac{D}{T}.

  5. Introduce a constant of proportionality to form an equation.

    To change a proportionality into an equation, we introduce a constant, let's call it kk.

    P=kDTP = k \frac{D}{T}
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