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Neporo4naja [7]
2 years ago
15

PLEASE HELP!!!!!!!!!!!!!!

Mathematics
1 answer:
Alex17521 [72]2 years ago
3 0

Answer:

angle = 50.8° (to the nearest tenth of a degree)

Step-by-step explanation:

In a right triangle:

  • The angle between the shorter leg and the hypotenuse is the larger acute angle of the triangle.
  • The angle between the longer leg and the hypotenuse is the smaller acute angle of the triangle.

We have been given the measures of the <u>shorter leg</u> and the <u>hypotenuse</u>, so the angle between them is the <u>larger acute angle</u> (which we need to find).

shorter leg = 3√6 cm

hypotenuse = 3√15 cm

So to find the angle, we need to use the trig ratio: cos(\theta)=\frac{adjacent}{hypotenuse}

If \theta is the angle, then the short leg is the "adjacent" side to the angle and the "hypotenuse" is the hypotenuse.

Substituting the given values:

cos(\theta)=\frac{3\sqrt{6} }{3\sqrt{15} }

⇒ \theta=arccos(\frac{3\sqrt{6} }{3\sqrt{15} })=50.76847952..

Therefore, the angle = 50.8° (to the nearest tenth of a degree)

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Answer:

Step-by-step explanation:

8 0
3 years ago
Which is equivalent to V180x11 after it has been simplified completely?
inna [77]

Question:

Which is equivalent to \sqrt{180x^{11}} after it has been simplified completely?

Answer:

\sqrt{180x^{11}} = 6x^{5}\sqrt{5x}

Step-by-step explanation:

Given

\sqrt{180x^{11}}

Required

Simplify

We start by splitting the square root

\sqrt{180x^{11}} = \sqrt{180} * \sqrt{x^{11}}

Replace 180 with 36 * 5

\sqrt{180x^{11}} = \sqrt{36 * 5} *  \sqrt{x^{11}}

Further split the square roots

\sqrt{180x^{11}} = \sqrt{36} *\sqrt{5} *  \sqrt{x^{11}}

\sqrt{180x^{11}} = 6*\sqrt{5} *  \sqrt{x^{11}}

Replace power of x; 11 with 10 + 1

\sqrt{180x^{11}} = 6*\sqrt{5} *  \sqrt{x^{10 + 1}}

From laws of indices; a^{m+n} = a^m * a^n

So, we have

\sqrt{180x^{11}} = 6*\sqrt{5} *  \sqrt{x^{10} * x^1}

\sqrt{180x^{11}} = 6*\sqrt{5} *  \sqrt{x^{10} * x}

Further split the square roots

\sqrt{180x^{11}} = 6*\sqrt{5} *  \sqrt{x^{10}} * \sqrt{x}

From laws of indices; \sqrt{a} = a^{\frac{1}{2}}

So, we have

\sqrt{180x^{11}} = 6*\sqrt{5} *  x^{10*\frac{1}{2}} * \sqrt{x}

\sqrt{180x^{11}} = 6*\sqrt{5} *  x^{\frac{10}{2}} * \sqrt{x}

\sqrt{180x^{11}} = 6*\sqrt{5} *  x^{5} * \sqrt{x}

Rearrange Expression

\sqrt{180x^{11}} = 6 *  x^{5} * \sqrt{5} * \sqrt{x}

\sqrt{180x^{11}} = 6x^{5} * \sqrt{5} * \sqrt{x}

From laws of indices; \sqrt{a} *\sqrt{b} = \sqrt{a*b} = \sqrt{ab}

So, we have

\sqrt{180x^{11}} = 6x^{5} * \sqrt{5*x}

\sqrt{180x^{11}} = 6x^{5} * \sqrt{5x}

\sqrt{180x^{11}} = 6x^{5}\sqrt{5x}

<em>The expression can no longer be simplified</em>

Hence, \sqrt{180x^{11}} is equivalent to 6x^{5}\sqrt{5x}

7 0
3 years ago
Read 2 more answers
a boutique handmade umbrella factory currently sells 22500 umbrellas per year at a cost of 9 dollars each. in the previous year
sergij07 [2.7K]

Answer:

The maximum revenue of the two years is $ 394,500 .

Step-by-step explanation:

Given as :

The current number of selling of umbrellas = 22500

The price of each umbrellas = $ 9

So, The Total price of 22500 umbrellas at $ 9 per umbrellas = $ 9 × 22500

I.e The Total price of 22500 umbrellas at $ 9 per umbrellas = $ 202,500

Again ,

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The price of umbrellas = $ 16

So, The Total price of 12000 umbrellas at $ 16 per umbrellas = $ 16 × 12000

I.e The Total price of 12000 umbrellas at $ 16 per umbrellas = $ 192,000

So, The maximum revenue of the two years = $ 202,500 + $ 192,000

I.e The maximum revenue of the two years = $ 394,500

Hence The maximum revenue of the two years is $ 394,500 . Answer

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Answer:

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Step-by-step explanation:

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