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Whitepunk [10]
3 years ago
12

Which function is odd? Check all that apply.

Mathematics
2 answers:
kvasek [131]3 years ago
6 0
<em></em>The\ function\ is\ odd\ if\ f(-x)=-f(x)\\\\We\ know:\\\sin x;\ \tan x\ and\ \cot x\ are\ odds.\\\cos x\ is\ even\ /\cos(-x)=\cos x/\\--------------------\\\\A.\ y=\sec x\\\\\sec(-x)=\dfrac{1}{\cos(-x)}=\dfrac{1}{\cos x}=\sec x-\fbox {NO}\\\\B.\ y=\sin x-\fbox{YES}\\\\C.\ y=\cot x\\\\\cot(-x)=\dfrac{\cos(-x)}{\sin(-x)}=\dfrac{\cos x}{-\sin x}=-\dfrac{\cos x}{\sin x}=-\cot x-\fbox{YES}\\\\D.\ y=\csc x\\\\\csc(-x)=\dfrac{1}{\sin(-x)}=\dfrac{1}{-\sin x}=-\dfrac{1}{\sin x}=-\csc x-\fbox{YES}
zalisa [80]3 years ago
5 0
An odd function is  a function which when x is substituted with -x, the function is equal to the negative counterpart of the original function. we use pi as x in the expressions

1.  y = sec x   <span> y = 1/ cos pi/3 = 2
   </span><span> y = 1/ cos -pi = 2
2. </span><span> y = sin pi/3 = sqrt 3 over 2
      </span><span>y = sin -pi/3 = -sqrt 3 over 2
3. </span><span>y = 1/ tan  pi /3 = sqrt 3 / 3 
    </span> y = 1/ tan  pi /3 = -<span>sqrt 3 / 3 
4. </span><span> y = csc x = 1/ sin pi/3 = 2/sqrt 3
</span><span>    y = csc x = 1/ sin -pi/3 = -2/sqrt 3
</span>
odd functions are B, C and D
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three bells ring at the intervals of 10 minutes and 20 minutes if they all ring together at 10 clock when will they ring togethe
mario62 [17]

Answer:The LCM of 10, 15, and 20 is 60. After 60 minutes, they ring together again.

Step-by-step explanation:

6 0
3 years ago
Molly was on a long 136 mile road trip. The first part of the trip there was lots of traffic, she only averaged 16 mph. The seco
Mazyrski [523]

Answer:

In traffic, she drove for 3 hours

and After the traffic cleared she drove for 2 hours.

Explanation:

Given that the road trip was 136 miles;

d=136

The first part of the trip there was lots of traffic, she only averaged 16 mph;

v_1=16

The second part of the trip there was no traffic so she could drive 44 mph;

v_2=44

She traveled for a total of 5 hours;

t=5

let x represent the time in traffic when she traveled at 16 mph

t_1=x

the time the traffic is clear would be;

t_2=t-t_1=5-x

Recall that distance equals speed multiply by time;

d=v_1t_1_{}_{}^{}+v_2t_2

substituting the values;

136=16x+44(5-x)

solving for x;

\begin{gathered} 136=16x+220-44x \\ 44x-16x=220-136 \\ 28x=84 \\ x=\frac{84}{28} \\ x=3 \end{gathered}

So;

\begin{gathered} t_1=3\text{ hours} \\ t_2=5-x=5-3=2 \\ t_2=2\text{ hours} \end{gathered}

Therefore, In traffic, she drove for 3 hours

and After the traffic cleared she drove for 2 hours.

7 0
1 year ago
Which of these numbers has the most factors? 6:<br> 17:<br> 25:<br> 36:
vovikov84 [41]

Answer:

36

Step-by-step explanation:

3 0
4 years ago
Read 2 more answers
Given the two functions, which statement is true?
tia_tia [17]

Answer:

Option D

Step-by-step explanation:

f(x) = \text{log}_{15}x

Transformed form of the function 'f' is 'g'.

g(x) = \frac{1}{2}\text{log}_{15}(x+4)

Property of vertical stretch or compression of a function,

k(x) = x

Transformed function → m(x) = kx

Here, k = scale factor

1). If k > 1, function is vertically stretched.

2). If 0 < k < 1, function is vertically compressed.

From the given functions, k = \frac{1}{2}

Since, k is between 0 and \frac{1}{2}, function f(x) is vertically compressed by a scale factor \frac{1}{2}.

g(x) = f(x + 4) represents a shift of function 'f' by 4 units left.

g(x) = f(x - 4) represents a shift of function 'f' by 4 units right.

g(x) = \frac{1}{2}\text{log}_{15}(x+4)

Therefore, function f(x) has been shifted by 4 units left to form image function g(x).

Option D is the answer.

8 0
3 years ago
Help please!!! AHAHSBHSBDR​
Degger [83]

Answer:

a = 8/29 thus: Step 1 is wrong!

Step-by-step explanation:

Solve for a:

8 - a/2 = 3 (4 - 5 a)

Hint: | Put the fractions in 8 - a/2 over a common denominator.

Put each term in 8 - a/2 over the common denominator 2: 8 - a/2 = 16/2 - a/2:

16/2 - a/2 = 3 (4 - 5 a)

Hint: | Combine 16/2 - a/2 into a single fraction.

16/2 - a/2 = (16 - a)/2:

(16 - a)/2 = 3 (4 - 5 a)

Hint: | Make (16 - a)/2 = 3 (4 - 5 a) simpler by multiplying both sides by a constant.

Multiply both sides by 2:

(2 (16 - a))/2 = 2×3 (4 - 5 a)

Hint: | Cancel common terms in the numerator and denominator of (2 (16 - a))/2.

(2 (16 - a))/2 = 2/2×(16 - a) = 16 - a:

16 - a = 2×3 (4 - 5 a)

Hint: | Multiply 2 and 3 together.

2×3 = 6:

16 - a = 6 (4 - 5 a)

Hint: | Write the linear polynomial on the left hand side in standard form.

Expand out terms of the right hand side:

16 - a = 24 - 30 a

Hint: | Move terms with a to the left hand side.

Add 30 a to both sides:

30 a - a + 16 = (30 a - 30 a) + 24

Hint: | Look for the difference of two identical terms.

30 a - 30 a = 0:

30 a - a + 16 = 24

Hint: | Group like terms in 30 a - a + 16.

Grouping like terms, 30 a - a + 16 = (-a + 30 a) + 16:

(-a + 30 a) + 16 = 24

Hint: | Combine like terms in 30 a - a.

30 a - a = 29 a:

29 a + 16 = 24

Hint: | Isolate terms with a to the left hand side.

Subtract 16 from both sides:

29 a + (16 - 16) = 24 - 16

Hint: | Look for the difference of two identical terms.

16 - 16 = 0:

29 a = 24 - 16

Hint: | Evaluate 24 - 16.

24 - 16 = 8:

29 a = 8

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides of 29 a = 8 by 29:

(29 a)/29 = 8/29

Hint: | Any nonzero number divided by itself is one.

29/29 = 1:

Answer: a = 8/29

5 0
3 years ago
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