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2 years ago

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Mathematics

1 answer:

Liula [17]2 years ago

4 0

The addition of the functions f(x) and g(x) will be ln (2x) + 3 sin(x) – 22. Then the correct option is C.

<h3>What is a function?</h3>

A function is a statement, rule, or law that establishes the connection between two variables. In mathematics, functions are everywhere and are necessary for constructing physical connections.

The functions are given below.

f(x) = ln (2x) – 15

g(x) = 3 sin(x) – 7

Then the addition of the function will be

(f + g)(x) = f(x) + g(x)

(f + g)(x) = ln (2x) – 15 + 3 sin(x) – 7

(f + g)(x) = ln (2x) + 3 sin(x) – 22

Then the correct option is C.

More about the function link is given below.

brainly.com/question/5245372

#SPJ1

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3 years ago

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3 years ago

A student is given that point P(a, b) lies on the terminal ray of angle Theta, which is between StartFraction 3 pi Over 2 EndFra

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Answer:

<em>The student made an error in step 3 because a is positive in Quadrant IV; therefore, </em>

<em /> $cos\theta = \frac{a\sqrt{a^2 + b^2}}{a^2 + b^2}$

Step-by-step explanation:

Given

$P\ (a,b)$

$r = \± \sqrt{(a)^2 + (b)^2}$

$cos\theta = \frac{-a}{\sqrt{a^2 + b^2}} = -\frac{\sqrt{a^2 + b^2}}{a^2 + b^2}$

Required

Where and which error did the student make

Given that the angle is in the 4th quadrant;

The value of r is positive, a is positive but b is negative;

Hence;

$r = \sqrt{(a)^2 + (b)^2}$

Since a belongs to the x axis and b belongs to the y axis;

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$cos\theta = \frac{a}{r}$

Substitute $r = \sqrt{(a)^2 + (b)^2}$

$cos\theta = \frac{a}{\sqrt{(a)^2 + (b)^2}}$

$cos\theta = \frac{a}{\sqrt{a^2 + b^2}}$

Rationalize the denominator

$cos\theta = \frac{a}{\sqrt{a^2 + b^2}} * \frac{\sqrt{a^2 + b^2}}{\sqrt{a^2 + b^2}}$

$cos\theta = \frac{a\sqrt{a^2 + b^2}}{a^2 + b^2}$

So, from the list of given options;

<em>The student's mistake is that a is positive in quadrant iv and his error is in step 3</em>

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