Simplify ^3_/125x^21y^33

1 answer:

7 0

$\sqrt[3]{125x^{21}y^{33}}=\sqrt[3]{125}\cdot\sqrt[3]{x^{21}}\cdot\sqrt[3]{y^{33}}=\sqrt[3]{5^3}\cdot\sqrt[3]{(x^7)^3}\cdot\sqrt[3]{(y^{11})^3}\\\\=\boxed{5x^7y^{11}}\\\\Used:\\\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\\sqrt[n]{a^n}=a\\\\(a^n)^m=a^{nm}$

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A fire ranger stands atop an observation tower 70 feet above the ground and sees a fire in the distance. She measures the angle

mrs_skeptik [129]

Answer:

$103.78\:\mathrm{ft}$

Step-by-step explanation:

We can form a right triangle where the distance between the ranger's current position and fire is the hypotenuse of the triangle. In a right triangle, the tangent of an angle is equal to its opposite side divided by the hypotenuse.

Therefore, we have:

$\tan 34^{\circ}=\frac{70}{x}$ , where $x$ is the distance between the base of the tower and the fire.