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-BARSIC- [3]
2 years ago
14

Applying Inverse Properties In Exercise,apply the inverse properties of logarithmic and exponential functions to simplify the ex

pression.See example 2.
In e2x - 1
Mathematics
1 answer:
kodGreya [7K]2 years ago
5 0

Answer:

The simplified form of the given expression is (2x-1).

Step-by-step explanation:

Consider the given expression is

\ln e^{2x-1}

According to the Inverse Properties of In

\ln e^x=x

In the given expression the power of e is (2x-1).

Using the Inverse Properties of In, we get

2x-1

Therefore, the simplified form of the given expression is (2x-1).

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A ball is thrown in the air from a height of 3 m with an initial velocity of 12 m/s. To the nearest tenth of a second, how long
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Answer:  1.4 seconds

<u>Step-by-step explanation:</u>

The equation is: h(t) = at² + v₀t + h₀          where

  • a is the acceleration (in this case it is gravity)
  • v₀ is the initial velocity
  • h₀ is the initial height

Given:  

  • a = -9.81 (if it wasn't given in your textbook, you can look it up)
  • v₀ = 12
  • h₀ = 3

Since we are trying to find out when it lands on the ground, h(t) = 0

EQUATION:   0 = 9.81t² + 12t + 3

Use the quadratic equation to find the x-intercepts

                        a=-9.81, b=12, c=3

x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\\\\\\x=\dfrac{-(12)\pm \sqrt{(12)^2-4(-9.81)(3)}}{2(-9.81)}\\\\\\x=\dfrac{-12\pm 16.2}{-19.62}\\\\\\x=\dfrac{-12+ 16.2}{-19.62}=-0.2\qquad x=\dfrac{-12- 16.2}{-19.62}=\large\boxed{1.4}\\

Note: Negative time (-0.2) is not valid

4 0
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