a math club has 40 members. The number of girls is 5 less the number of boy. what are the two equations solve
1 answer:
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Complete Question:
Which statement about the following equation is true?
A) The discriminant is less than 0, so there are two real roots
B) The discriminant is less than 0, so there are two complex roots
C) The discriminant is greater than 0, so there are two real roots
D) The discriminant is greater than 0, so there are two complex roots
Answer:
C) The discriminant is greater than 0, so there are two real roots
Step-by-step explanation:
The given equation is which by simplification becomes
For a quadratic equation of the form , the discriminant is given by the equation,
If the discriminant D is greater than 0, the roots are real and different
If the discriminant D is equal to 0, the roots are real and equal
If the discriminant D is less than 0, the roots are imaginary
For the quadratic equation under consideration, a = 2, b = -9, c = 3
Let us calculate the discriminant D
D = (-9)² - 4(2)(3)
D = 81 - 24
D = 57
Since the Discriminant D is greater than 0, the roots are real and different.
Answer:
26 ft square by 13 ft high
Step-by-step explanation:
The tank will have minimum surface area when opposite sides have the same total area as the square bottom. That is, their height is half their width. This makes the tank half a cube. Said cube would have a volume of ...
2·(8788 ft^3) = (26 ft)^3
The square bottom of the tank is 26 ft square, and its height is 13 ft.
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<em>Solution using derivatives</em>
If x is the side length of the square bottom, the height is 8788/x^2 and the area is ...
x^2 + 4x(8788/x^2) = x^2 +35152/x
The derivative of this is zero when area is minimized:
2x -35152/x^2 = 0
x^3 = 17576 = 26^3 . . . . . multiply by x^2/2, add 17576
x = 26
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As the attached graph shows, a graphing calculator can also provide the solution.
