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2 years ago

What is the solution of the inequality x^3+3x^2>7x+6

Mathematics

1 answer:

sveta [45]2 years ago

3 0

Answer:

x>2

Step-by-step explanation:

x3+3x2=7x+6

x3+3x2−(7x+6)=7x+6−(7x+6)

x3+3x2−7x−6=0

(x−2)(x2+5x+3)=0

x−2=0 or x2+5x+3=0

x=2 or x=−0.6972243622680054 or x=−4.302775637731995

x<−4.302776

−4.302776<x<−0.697224

−0.697224<x<2

x>2(Works in original inequality)

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Zahir made this wooden perch for his pet bird. What is the volume of the bird perch? Round to the nearest tenth if necessary.

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Answer:

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Step-by-step explanation:

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3 years ago

What is the volume of a right circular cylinder with a diameter of 46.25 cm and a height of 18.5 cm?

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3 years ago

Sean tossed a coin off a bridge into the stream below. The path of the coin can be represented by the equation 2 h tt = − 16t^2+

tekilochka [14]

Answer:

It will take 5.61 seconds for the coin to reach the stream.

Step-by-step explanation:

The height of the coin, after t seconds, is given by the following equation:

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How long will it take the coin to reach the stream?

The stream is the ground level.

So the coin reaches the stream when h(t) = 0.

$h(t) = -16t^{2} + 72t + 100$

$-16t^{2} + 72t + 100 = 0$

Multiplying by (-1)

$16t^{2} - 72t - 100 = 0$

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}$

$\bigtriangleup = b^{2} - 4ac$

In this question:

$16t^{2} - 72t - 100 = 0$

$a = 16, b = -72, c = -100$

$\bigtriangleup = (-72)^{2} - 4*16*(-100) = 11584$

$t_{1} = \frac{-(-72) + \sqrt{11584}}{2*16} = 5.61$

$t_{2} = \frac{-(-72) - \sqrt{11584}}{2*16} = -1.11$

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It will take 5.61 seconds for the coin to reach the stream.

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3 years ago

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IgorC [24]

Answer:

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1 year ago