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For each equation, determine whether it represents a direct variation, an inverse variation, or neither.
1 answer:
we know that in direct variation as x increase y also increases.
in indirect variation x decreases y increase and vice versa.
in part a we have x at top (numerator ) and y at denominator it mean indirect variation (as x increases y decreases).
to find k we know that for indirect variation xy=k
if we rewrite the equation x=9/y we get xy=9
which mean k=9 .
in part b we have 4xy=20 if we simplify this equation we get
so here if we rewrite in terms of x.
we get x=5/y which represents indirect variation.
and we know xy=k
we have xy=5 .so k=5
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The cost to produce n shirts is given as:
The cost function is a quadratic function with a positive leading coefficient, so the minimum value will be at the vertex of the function.
The vertex of a quadratic function can be calculated as:
a = coefficient of squared term = 0.4
b = coefficient of n term = -32
Using these values, we get:
This means, the cost will be minimized if 40 t shirts are produced.
The minimum cost can be found by calculating C at n=40
So, the minimum cost will be:
C(40) = 0.4(40)² - 32(40) + 650
C(40) = 10
Therefore, the minimum cost to produce a t shirt will be $10
The cost function is a quadratic function with a positive leading coefficient, so the minimum value will be at the vertex of the function.
The vertex of a quadratic function can be calculated as:
a = coefficient of squared term = 0.4
b = coefficient of n term = -32
Using these values, we get:
This means, the cost will be minimized if 40 t shirts are produced.
The minimum cost can be found by calculating C at n=40
So, the minimum cost will be:
C(40) = 0.4(40)² - 32(40) + 650
C(40) = 10
Therefore, the minimum cost to produce a t shirt will be $10