Get the answers you've been searching for with IDNLearn.com. Get step-by-step guidance for all your technical questions from our knowledgeable community members.
Sagot :
Sure! Let's solve each problem step-by-step.
### Question 11
"Which one of the following is an exponential function?"
An exponential function is typically in the form [tex]\( f(x) = a b^x \)[/tex], where [tex]\(a\)[/tex] and [tex]\(b\)[/tex] are constants and [tex]\(b > 0\)[/tex].
Reviewing the provided options:
A. [tex]\( O = 2 B \cdot h \bigcirc^\prime = 3 \)[/tex] (not in an understandable form)
C. [tex]\( 0 = \)[/tex] (seems incomplete)
D. [tex]\( 0 = 2 \)[/tex] (not a valid equation)
None of these options clearly represent an exponential function, so the correct choice based on typical exponential form [tex]\(y = a e^{bx}\)[/tex] doesn't explicitly match. However, we may be dealing with a misprint or a non-traditional setup here.
### Question 12
"Which of the following is the radian measure of an angle [tex]\(330^\circ\)[/tex]?"
To convert degrees to radians:
[tex]\[ \text{radians} = \text{degrees} \times \frac{\pi}{180} \][/tex]
So for [tex]\(330^\circ\)[/tex]:
[tex]\[ 330^\circ \times \frac{\pi}{180} = \frac{330}{180} \pi = \frac{11}{6} \pi \][/tex]
Therefore, the radian measure of [tex]\(330^\circ\)[/tex] is:
[tex]\[ \boxed{\frac{11}{6} \text{ rad}} \][/tex]
### Question 13
"If an acute angle satisfies [tex]\(4 \sin x = 3 \cos x\)[/tex], then [tex]\(\sin x\)[/tex] is equal to:"
Given:
[tex]\[ 4 \sin x = 3 \cos x \][/tex]
Dividing both sides by [tex]\(\cos x\)[/tex]:
[tex]\[ 4 \tan x = 3 \Rightarrow \tan x = \frac{3}{4} \][/tex]
We need to find [tex]\(\sin x\)[/tex]. Recall the identity:
[tex]\[ \sin^2 x + \cos^2 x = 1 \][/tex]
We start by using [tex]\(\tan x = \frac{\sin x}{\cos x}\)[/tex]:
[tex]\[ \sin x = \cos x \cdot \tan x = \cos x \cdot \frac{3}{4} \][/tex]
Let's denote [tex]\(\cos x = \cos x = \cos x\)[/tex]. Using a 3-4-5 right triangle, where:
[tex]\[ \sin x = 3/5 \quad \text{and} \quad \cos x = 4/5 \][/tex]
Therefore:
[tex]\[ \sin x = \boxed{\frac{3}{5}} \][/tex]
### Question 14
"A function is said to be a logarithmic function, where"
A standard logarithmic function is given as:
[tex]\[ \text{A. } f(x) = \log_b x, b > 0, b \neq 1 \text{ and } x > 0 \][/tex]
Hence, the correct answer is:
[tex]\[ \boxed{C} \][/tex]
### Question 15
"Which one of the following is not equal to [tex]\(\cos 72^\circ\)[/tex]?"
We need to check each option:
A. [tex]\(\cos(-648^\circ) = \cos(648^\circ) = \cos(360 \times 1 + 288^\circ) = \cos(288^\circ) = \cos(360^\circ - 72^\circ) = \cos(-72^\circ) = \cos(72^\circ)\)[/tex]
B. [tex]\(\sin(792^\circ) = \sin(792^\circ - 2 \times 360^\circ) = \sin(72^\circ)\)[/tex]
C. [tex]\(\sin(18^\circ)\)[/tex] – Not 72°; let's find out:
[tex]\(\sin(18^\circ)\)[/tex].
D. [tex]\(\cos(432^\circ) = \cos(360^\circ + 72^\circ) = \cos(72^\circ)\)[/tex]
Among these, [tex]\(\sin(18^\circ) = \cos(72^\circ)\)[/tex].
The answer here seems to revolve around precision, hence clear out options matching other than 18°.
Looking closely, based on identity checks:
[tex]\[ \boxed{\sin(18^\circ)} \][/tex] - double check for clear non-matching earlier checks.
Please verify ordered by close comparison to radians convention.
### Question 11
"Which one of the following is an exponential function?"
An exponential function is typically in the form [tex]\( f(x) = a b^x \)[/tex], where [tex]\(a\)[/tex] and [tex]\(b\)[/tex] are constants and [tex]\(b > 0\)[/tex].
Reviewing the provided options:
A. [tex]\( O = 2 B \cdot h \bigcirc^\prime = 3 \)[/tex] (not in an understandable form)
C. [tex]\( 0 = \)[/tex] (seems incomplete)
D. [tex]\( 0 = 2 \)[/tex] (not a valid equation)
None of these options clearly represent an exponential function, so the correct choice based on typical exponential form [tex]\(y = a e^{bx}\)[/tex] doesn't explicitly match. However, we may be dealing with a misprint or a non-traditional setup here.
### Question 12
"Which of the following is the radian measure of an angle [tex]\(330^\circ\)[/tex]?"
To convert degrees to radians:
[tex]\[ \text{radians} = \text{degrees} \times \frac{\pi}{180} \][/tex]
So for [tex]\(330^\circ\)[/tex]:
[tex]\[ 330^\circ \times \frac{\pi}{180} = \frac{330}{180} \pi = \frac{11}{6} \pi \][/tex]
Therefore, the radian measure of [tex]\(330^\circ\)[/tex] is:
[tex]\[ \boxed{\frac{11}{6} \text{ rad}} \][/tex]
### Question 13
"If an acute angle satisfies [tex]\(4 \sin x = 3 \cos x\)[/tex], then [tex]\(\sin x\)[/tex] is equal to:"
Given:
[tex]\[ 4 \sin x = 3 \cos x \][/tex]
Dividing both sides by [tex]\(\cos x\)[/tex]:
[tex]\[ 4 \tan x = 3 \Rightarrow \tan x = \frac{3}{4} \][/tex]
We need to find [tex]\(\sin x\)[/tex]. Recall the identity:
[tex]\[ \sin^2 x + \cos^2 x = 1 \][/tex]
We start by using [tex]\(\tan x = \frac{\sin x}{\cos x}\)[/tex]:
[tex]\[ \sin x = \cos x \cdot \tan x = \cos x \cdot \frac{3}{4} \][/tex]
Let's denote [tex]\(\cos x = \cos x = \cos x\)[/tex]. Using a 3-4-5 right triangle, where:
[tex]\[ \sin x = 3/5 \quad \text{and} \quad \cos x = 4/5 \][/tex]
Therefore:
[tex]\[ \sin x = \boxed{\frac{3}{5}} \][/tex]
### Question 14
"A function is said to be a logarithmic function, where"
A standard logarithmic function is given as:
[tex]\[ \text{A. } f(x) = \log_b x, b > 0, b \neq 1 \text{ and } x > 0 \][/tex]
Hence, the correct answer is:
[tex]\[ \boxed{C} \][/tex]
### Question 15
"Which one of the following is not equal to [tex]\(\cos 72^\circ\)[/tex]?"
We need to check each option:
A. [tex]\(\cos(-648^\circ) = \cos(648^\circ) = \cos(360 \times 1 + 288^\circ) = \cos(288^\circ) = \cos(360^\circ - 72^\circ) = \cos(-72^\circ) = \cos(72^\circ)\)[/tex]
B. [tex]\(\sin(792^\circ) = \sin(792^\circ - 2 \times 360^\circ) = \sin(72^\circ)\)[/tex]
C. [tex]\(\sin(18^\circ)\)[/tex] – Not 72°; let's find out:
[tex]\(\sin(18^\circ)\)[/tex].
D. [tex]\(\cos(432^\circ) = \cos(360^\circ + 72^\circ) = \cos(72^\circ)\)[/tex]
Among these, [tex]\(\sin(18^\circ) = \cos(72^\circ)\)[/tex].
The answer here seems to revolve around precision, hence clear out options matching other than 18°.
Looking closely, based on identity checks:
[tex]\[ \boxed{\sin(18^\circ)} \][/tex] - double check for clear non-matching earlier checks.
Please verify ordered by close comparison to radians convention.
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Your questions find answers at IDNLearn.com. Thanks for visiting, and come back for more accurate and reliable solutions.
