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mestny [16]
3 years ago
15

Find the exact value of the expression

Mathematics
1 answer:
Serhud [2]3 years ago
6 0

Answer:

The answer to your question is the letter C

Step-by-step explanation:

Data

sec Ф = 9/2

tan Ф = ?

To solve this problem use trigonometric functions.

1.- The first condition is that the angle must be in the fourth quadrangle

(270° < Ф < 360°).

2.- Write the trigonometric function sec.

           sec Ф = hypotenuse / adjacent side   and sec Ф = 9/2

then, hypotenuse = 9   adjacent side = 2

3.- Use the Pythagorean theorem to find the adjacent side.

           Hypotenuse² = Opposite side² + Adjacent side²

-Solve for Opposite side

            Opposite side² = Hypotenuse² - Adjacent side sie²

-Substitution

            Opposite side² = 9² - 2²

-Simplification

            Opposite side² = 81 - 4

            Opposite side² = 77

            Opposite side = √77

4.- Find the tan Ф

             tan Ф = Opposite side/Adjacent side

-Substitution

             tanФ = -√77 / 2    It is negative because in the fourth quadrangle

                                           tan is negative.

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Which table represents the graph of a logarithmic function in the form y=log3x when b&gt;1?
alex41 [277]

Answer:

<u><em>The satisfied table of the given function</em></u>y = log_{b} (x)<u><em></em></u>

<em>x                    1/8            1/4             1/2              1             2</em>

<em>y                    -3                 -2            -1               0               1</em>

<em></em>

Step-by-step explanation:

<u><em>Explanation</em></u> :-

Given logarithmic function y = log_{b} (x)   if b >1

Given first table

i)

put x = \frac{1}{8}     given b > 1 so we can choose b = 2

y = log_{2} (\frac{1}{8} )

y = log_{2} (2^{-3}  )

we will apply logarithmic formula

log x ⁿ = n log (x)

y = log_{2} (2^{-3}  ) = -3 log_{2} (2) = -3 (1) = -3

<em>y = -3</em>

<em>ii)</em>

<em>put x = </em>\frac{1}{4}<em>     given b > 1 so we can choose b = 2</em>

<em></em>y = log_{2} (\frac{1}{4} )<em></em>

<em></em>y = log_{2} (2^{-2}  )<em></em>

we will apply logarithmic formula

log x ⁿ = n log (x)

y = log_{2} (2^{-2}  ) = -2 log_{2} (2) = -2 (1) = -2

<em>y = -2</em>

<em>iii) </em>

<em>put x = </em>\frac{1}{2}<em>     given b > 1 so we can choose b = 2</em>

<em></em>y = log_{2} (\frac{1}{2} )<em></em>

y = log_{2} (2^{-1}  )

<em>we will apply logarithmic formula </em>

<em>log x ⁿ = n log (x)</em>

y = log_{2} (2^{-1}  ) = -1 log_{2} (2) = - (1) = -1

<em>y = -1</em>

<em>iv) </em>

<em>put x = 1     given b > 1 so we can choose b = 2</em>

<em></em>y = log_{2} (1 )<em> = 0</em>

<em>y = 0</em>

<em>v) </em>

<em>put x = </em>2<em>     given b > 1 so we can choose b = 2</em>

y = log_{2} (2 )

<em>y = 1</em>

<em></em>

<u><em>Final answer:-</em></u>

<u><em>The satisfied table of the given function</em></u>

<em>x                    1/8            1/4             1/2              1             2</em>

<em>y                    -3                 -2            -1               0               1</em>

<em></em>

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3 years ago
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