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Dmitry [639]
2 years ago
7

The diagram shows a 3 cm x 5 cm x 4 cm cuboid

Mathematics
1 answer:
Rainbow [258]2 years ago
4 0

Answer:

a) The length of segment AC is approximately 5.83 centimeters.

b) The angle ACD is approximately 34.5º.

Step-by-step explanation:

a) Since AB \perp BC, the length of segment AC is determined by Pythagorean Theorem, that is:

AC = \sqrt{(5\,cm)^{2}+(3\,cm)^{2}}

AC \approx 5.831\,cm

The length of segment AC is approximately 5.831 centimeters.

b) Since AB \perp BC \perp AD, the length of segment AD is determined by this Pythagorean identity:

AD = \sqrt{(3\,cm)^{2}+(5\,cm)^{2}+(4\,cm)^{2}}

AD \approx 7.071\,cm

The angle ACD is determined by the following trigonometric expression:

\cos C = \frac{AC}{CD}

\cos C = \frac{5.831\,cm}{7.071\,cm}

\cos C = 0.825

C = \cos^{-1} 0.825

C \approx 34.448^{\circ}

The angle ACD is approximately 34.448º.

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Simplify expression x8y-26/x14y-5 × x-39y-21
koban [17]

The simplified form of the expression is x^{-45} y^{-42}

<h3>Simplifying an expression</h3>

From the question, we are to simplify the given expression

The given expression is

\frac{x^{8}y^{-26}  }{x^{14}y^{-5}  } \times x^{-39} y^{-21}

The expression can be simplified as shown below

\frac{x^{8}y^{-26}  }{x^{14}y^{-5}  } \times x^{-39} y^{-21}

\frac{x^{8} \times x^{-39} \times  y^{-26} \times  y^{-21}  }{x^{14} \times y^{-5}  }

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\frac{x^{8-39} \times  y^{-26-21}  }{x^{14} \times y^{-5}  }

\frac{x^{-31} \times  y^{-47}  }{x^{14} \times y^{-5}  }

Then,

\frac{x^{-31} }{x^{14} } \times \frac{ y^{-47} }{ y^{-5} }

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x^{-31-14} \times y^{-47+5}

x^{-45} \times y^{-42}

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Hence, the simplified form of the expression is x^{-45} y^{-42}

Learn more on Simplifying an expression here: brainly.com/question/2320607

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MissTica

Answer:

These types of questions are not daunting if you break it down. First look at  "Five less than twice the value of a number."

"Twice the value of a number" is simply 2x.

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Checking the right side, 3(4+(34/2)) = 3(4+17) = 3(21) = 63.

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