A certain type of bacteria doubles in population every hour. Their growth can be modeled by an exponential equation. Initially,
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The missing term in the provided quadratic equation is 10x if the roots of a quadratic equation are 5 ± 3i.
<h3>What is a complex number?</h3>It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have the roots of a quadratic equation:
5 ± 3i
To find the quadratic equation:
(x - (5+3i))(x - (5-3i))
= x² -10x + 34
The missing value is 10x
The quadratic equation is:
= x² -10x + 34
Thus, the missing term in the provided quadratic equation is 10x if the roots of a quadratic equation are 5 ± 3i.
Learn more about the complex number here:
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Answer:
the rate of change of the water depth when the water depth is 10 ft is;
Step-by-step explanation:
Given that:
the inverted conical water tank with a height of 20 ft and a radius of 8 ft is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec.
We are meant to find the rate of change of the water depth when the water depth is 10 ft.
The diagrammatic expression below clearly interprets the question.
From the image below, assuming h = the depth of the tank at a time t and r = radius of the cone shaped at a time t
Then the similar triangles ΔOCD and ΔOAB is as follows:
( similar triangle property)
h = 2.5r
The volume of the water in the tank is represented by the equation:
The rate of change of the water depth is :
Since the water is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec
Then,
Therefore,
the rate of change of the water at depth h = 10 ft is:
Thus, the rate of change of the water depth when the water depth is 10 ft is;
