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The maximum profit is the highest point on the curve at (3, 45), and since the y-value is the profit in hundreds of dollars, the maximum profit is $4500.
The shop is making a profit as long as the curve is above the x-axis, so this is over the given interval (0, 10).
The maximum profit is earned at x = 3, and the x-value is the money spent on advertising in hundreds of dollars, so this means that $300 was spent of advertising.
We have two congruent trapezoids.
The formula of an area of a trapezoid:
We have:
Substitute:
Answer:
Answer:
x=7, -2.
Step-by-step explanation:
x^2-5x=14
x^2-5x-14=0
factor out the trinomial,
(x-7)(x+2)=0
zero property,
x-7=0, x+2=0,
x=0+7=7,
x=0-2=-2
These calculations are based on the drawing of the file enclosed.
There are three right triangles.
From the big right triangle:
a^2 + b^2 = 25^2
From the small right triangle on the left side:
(25-x)^2 + 10^2 = a^2
From the small right triangle on the right side
x^2 +10^2 = b^2
=> (25-x)^2 + 10^2 + x^2 + 10^2 = a^2 + b^2
=> (25-x)^2 + 10^2 + x^2 + 10^2 = 25^2
=> 25^2 - 50x + x^2 + 10^2 + 10^2 = 25^2
=> x^2 -50x + 100 =0
Use the quadratic formular to find the roots:
x = 2.1 and x = 47.9
Distance from back: 25 - 2.1 = 22.9 ft
Answer: 22.9 ft
