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2 years ago

Help please explanation as detailed as you can make it but easy to understand

Mathematics

1 answer:

Doss [256]2 years ago

5 0

Answer:

tan(x) = (√6)/2

Step-by-step explanation:

The tangent identity is ...

tan = sin/cos

<h3>Substitution</h3>

Substituting the given values of sine and cosine, we have ...

$\tan{x}=\dfrac{\sin{x}}{\cos{x}}=\dfrac{\dfrac{42}{55}}{\dfrac{14\sqrt{6}}{55}}$

<h3>Simplification</h3>

At this point, it becomes a problem in simplifying a compound fraction. This can be done by dividing the fractions in the usual way, and cancelling common factors from numerator and denominator.

We note the denominators (55) are the same, and that 42=3·14, so we can simplify this to ...

$\tan{x}=\dfrac{3}{\sqrt{6}}=\dfrac{3\cdot\sqrt{6}}{\sqrt{6}\cdot\sqrt{6}}=\dfrac{3\sqrt{6}}{6}\\\\\boxed{\tan{x}=\dfrac{\sqrt{6}}{2}}$

The step of multiplying by (√6)/(√6) is for the purpose of "rationalizing the denominator," making the denominator a rational number: (√6)² = 6.

<em>Additional comment</em>

If sin(x) = 42/55, then cos(x) = (√1261)/55. There is no angle x that will have these values of its trig functions. (Another example of poor curriculum editing.)

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<h2>Explanation:</h2>

Step 1. Write $x^2 - 8x - 33=0$ in the form $x^2+2ax+a^2=0$

$2a=-8\quad :\quad a=-4$

Step 2. Add and subtract $(-4)^2$ to the left side of the equation

$x^2-8x-33+\left(-4\right)^2-\left(-4\right)^2=0 \\ \\ \\ But: \\ \\ x^2+2ax+a^2=\left(x+a\right)^2 \\ \\ x^2-8x+\left(-4\right)^2=\left(x-4\right)^2$

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3 years ago

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alexandr402 [8]

Answer:

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Step-by-step explanation:

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Where d is the distance between the cars, d1 is the distance traveled by the first car and d2 is the distance traveled by the second car.

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