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Citrus2011 [14]
3 years ago
10

Evaluate each logarithm. Do not use a calculator. ln ^3 square root e^4

Mathematics
1 answer:
Alona [7]3 years ago
6 0

Answer:

\large\boxed{\ln\sqrt[3]{e^4}=\dfrac{4}{3}}

Step-by-step explanation:

\text{Use}\\\\\sqrt[n]{a^m}=a^\frac{m}{n}\\\\\ln a^n=n\ln a\\\\\ln e=1\\-----------\\\\\ln\sqrt[3]{e^4}=\ln e^\frac{4}{3}=\dfrac{4}{3}\ln e=\dfrac{4}{3}\cdot1=\dfrac{4}{3}

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A

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Neko [114]

Dilation is the process in which the dimensions of a given shape is increased or decreased by a scale factor. Therefore the answers to the questions are:

A. Since the dilation of triangle XYZ do not affect the measure of its internal angles, then the trigonometric ratios of respective internal angles are the same.

B. segment CB = 10

ii. segment AB = 11.18

From the given information in the question, triangle XYZ is an image of triangle ACB. In triangle XYZ, given that Sin X = ; it implies that its hypotenuse is 5.59, and the opposite side as 5. So that;

Sin X =

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X  =

Thus,

<X + <Y + <Z =

+  + <Z =

<Z =  -

   =

<Z =

So then, the third side can be determined by applying the Pythagoras theorem.

=  +

=  +

=  -

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x =

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x = 2.5

Thus,

Cos X =

          =

Cos X =

Tan X =

         =

Tan X =

Therefore:

A. Considering triangles XYZ and ACB, the measure of their respective internal angles are the same.

i.e <X ≅ <A

   <B ≅ <Z

   <C ≅ <Y

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B. Given that triangle XYZ was dilated by a scale factor of 2, then the respective length of each sides of triangle ACB is twice that of XYZ.

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i. segment CB = 2 x segment YZ

                    = 2 x 5

segment CB = 10

ii. segment AB = 2 x segment XZ

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segment AB = 11.18

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Answer:

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