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3 years ago

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>1?

alex41 [277]

Answer:

The satisfied table of the given function $y = log_{b} (x)$

x 1/8 1/4 1/2 1 2

y -3 -2 -1 0 1

Step-by-step explanation:

Explanation :-

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

Given first table

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)

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

y = -3

ii)

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

$y = log_{2} (\frac{1}{4} )$

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

we will apply logarithmic formula

log x ⁿ = n log (x)

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

y = -2

iii)

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

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

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

we will apply logarithmic formula

log x ⁿ = n log (x)

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

y = -1

iv)

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

$y = log_{2} (1 )$ = 0

y = 0

v)

put x = $2$ given b > 1 so we can choose b = 2

$y = log_{2} (2 )$

y = 1

Final answer:-

The satisfied table of the given function

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