On a topographic map, two points on the same contour line are at the same
A. distance from the ocean
B. air pressure
C. temperature
D. elevation
Answer (2)
The question pertains to finding the maximum weekly revenue for a skateboard shop where the revenue function is given by y=(70-x)(50+x). To find the maximum value, we first put the quadratic equation into vertex form, which is y=a(x-h)^2+k, where (h, k) is the vertex of the parabola. The x-coordinate of the vertex, which is 'h' in the vertex form, gives us the price adjustment that will maximize revenue. The y-coordinate 'k' will be the maximum revenue itself.
To convert y=(70-x)(50+x) to vertex form, we complete the square: y = 70×50 + 70x - x×50 - x×x y = 3500 + 20x - x^2 y = -x^2 + 20x + 3500
Now, we complete the square: y = -(x^2 - 20x) + 3500 y = -(x^2 - 20x + 100) + 3500 + 100 y = -(x - 10)^2 + 3600
This is now in vertex form, where the vertex is (10, 3600). This means the shop can maximize weekly revenue by decreasing the price by $10, which will yield a maximum revenue of $3600.
To maximize weekly revenue, the skateboard shop should decrease its price by $10, leading to a maximum revenue of $3600. This conclusion was reached by converting the revenue function into vertex form and identifying the vertex. The vertex point indicates the optimal price adjustment for maximum revenue.
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