Find all values of $x$ such that $\sqrt{4x^2} - \sqrt{x^2} = 6$.

Mathematics

1 answer:

Eddi Din [679]3 years ago

4 0

9514 1404 393

Answer:

x = -6 or 6

Step-by-step explanation:

The square root is always positive, so the equation simplifies to ...

$\sqrt{4x^2}-\sqrt{x^2}=6\\\\2|x|-|x|=6\\\\|x|=6\\\\x=\{-6,\ 6\}$

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The graph shows the solutions to f(x) = 0, where f(x) = √(4x²) -√(x²) -6.

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A car is traveling up a steep ramp to a parking garage.the ramp is 445 feet long and rises a vertical distance of 80 feet. What

Alecsey [184]

With the information provided in the problem, we can create a right triangle with the ramp as its hypotenuse, and the vertical rise as its opposite side from its angle of elevation.
Let $E$ be the angle of elevation from the car to the end of the ramp. We now know that the hypotenuse of our triangle measures 445 feet, and the opposite side measures 80 feet, so we need a trig function that relates our angle of elevation with the hypotenuse and the opposite side. That function is sine:
$sine(E)= \frac{80}{445}$
$E=arcsine( \frac{80}{445} )$
$E=10.36$

We can conclude that the angle of elevation from the car to the end of the ramp is 10.36°.