<span>Integral of sqrt(36 + x^2)dx = 1/2sqrt(36 + x^2)x + 18sinh^1 (x/6) + c </span>
Answer:
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Step-by-step explanation:
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Let x be the number of weeks; therefore, the two linear equations are

Where T stands for the punches on the tea punch card and C for the punches on the coffee punch card.
Solving by substitution. Set T=C, then

Thus, substitute the value of x=3 into the first equation,

Thus, after 3 weeks, Josiah will have the same number of punches on each card, and he will have 23 punches on each card.