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Dmitry [639]
2 years ago
12

High school math question

Mathematics
1 answer:
Sloan [31]2 years ago
7 0

Answer: Choice C. x = \pm\frac{\pi}{6}

=========================================================

Explanation:

Recall that

\tan(x) = \frac{\sin(x)}{\cos(x)}\\\\

So we can say

\tan(3x) = \frac{\sin(3x)}{\cos(3x)}\\\\

The vertical asymptotes occur when the denominator is zero.

If we were to plug in x = \frac{\pi}{6}, then we'd have,

\tan(3x) = \frac{\sin(3x)}{\cos(3x)}\\\\\tan(3*\frac{\pi}{6}) = \frac{\sin(3*\frac{\pi}{6})}{\cos(3*\frac{\pi}{6})}\\\\\tan(\frac{\pi}{2}) = \frac{\sin(\frac{\pi}{2})}{\cos(\frac{\pi}{2})}\\\\\tan(\frac{\pi}{2}) = \frac{1}{0}\\\\\tan(\frac{\pi}{2}) = \text{und}\text{efined}\\\\

This shows that one vertical asymptote is at x = \frac{\pi}{6}

Through similar steps, you should find that another vertical asymptote is at x = -\frac{\pi}{6}

We can condense those two equations into x = \pm\frac{\pi}{6}

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I forgot to label the triangle below! I just know that the cos A = 0.48. Based on this information, which angle should be marked
lianna [129]

Answer:

angle 1

Step-by-step explanation:

Using the trigonometric mnemonic SOH CAH TOA, we know that cos or cosine is the ratio between the adjacent side and hypotenuse side.

This means that if cos A = 0.48, A is the measure of the angle which it's relative adjacent side divided by the hypotenuse of the triangle will be around 0.48.

Let's try angle 2, cos (angle 2) = adjacent / hypotenuse = 7.8 / 8.9 = 0.876404494382 ≈ 0.87 ≠ 0.48. Since the proportions are not equal, this angle cannot be the one marked as A.

Since angle 3 is a right angle, the adjacent could be either side so it cannot be correct. Thus angle 1 is correct.

5 0
3 years ago
In triangle abc, angle A is the right angle. What is the value of y?
Natalka [10]

Answer:

A

Step-by-step explanation:

In a right triangle, the side opposite to the 90 degree angle (here, side opposite to angle A) is known as the hypotenuse.

Also, the side that is "opposite" to the angle given (here side opposite is y to angle given 30 degrees) is the opposite side.

Since we want to find "opposite" and have "hypotenuse" , recalling trig ratios, we can say opposite/hypotenuse is the ratio SINE, so we can write:

Sin(30)=\frac{y}{7}

We solve for y:

Sin(30)=\frac{y}{7}\\y = 7 Sin(30)

Since the answer choice has angles in radians, we recall 30 degrees is \frac{\pi}{6} radians.

Thus, the correct answer is  7Sin(\frac{\pi}{6}), or option A

3 0
3 years ago
Read 2 more answers
What is the recursive formula for this geometric sequence?<br> -2, -16, -128, -1024,
FinnZ [79.3K]
<h3>Answer: Choice A</h3>

The first line shown in choice A is a_1 = -2 which means "the first term is -2"

The next line in choice A means "the nth term (a_n) is found by multiplying the prior term (a_{n-1}) by 8". Put another way: multiply each term by 8 to get the next term.

first term = -2

second term = 8*(first term) = 8*(-2) = -16

third term = 8*(second term) = 8*(-16) = -128

fourth term = 8*(third term) = 8*(-128) = -1024

and so on.

3 0
3 years ago
Read 2 more answers
Mary has 40% fewer marbles than Jolie. If they combine all their marbles in a single bag, what percent of the marbles in the bag
dedylja [7]
The easiest way to do this would be to imagine that Jolie has 100 marbles. If Mary has 40% fewer, that means she has 60 marbles. Then if they combine all their marbles into a single bag, they will have 160 marbles, of which 100 are Jolie's. So the % that is Jolie's is 100/160 = 0.625 = 62.5%.
4 0
3 years ago
7(1 - 76) - 2b = -197
noname [10]

Answer:

b= -164

Step-by-step explanation:

calculate the difference

7x(-75)-2b= -197

multiply the numbers

-525-2b= -197

move the constant to the right- hand side and change the sign

-2b= -197+525

add

-2b=328

divide

b= -164

4 0
3 years ago
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