The outcome variable is also called the response or dependent variable, and the risk factors and confounders are called the predictors, or explanatory or independent variables. In regression analysis, the dependent variable is denoted "Y" and the independent variables are denoted by "X".
The domine of definition of the function
[tex]f(x) = \frac{1}{ \sqrt{ |\cos(x)| + \cos(x) }} \: is \\ [/tex]
[tex]\large\underline{\sf{Solution-}}[/tex]
Given function is
[tex]\rm \longmapsto\:f(x) = \dfrac{1}{ \sqrt{ |cosx| + cosx} } [/tex]
Now,
[tex]\rm \longmapsto\:f(x) \: is \: defined \: if \: |cosx| + cosx > 0[/tex]
We know,
[tex]\begin{gathered}\begin{gathered}\bf\: \rm \longmapsto\: |x| = \begin{cases} &\sf{ - x \: \: when \: x < 0} \\ \\ &\sf{ \: \: x \: \: when \: x \geqslant 0} \end{cases}\end{gathered}\end{gathered}[/tex]
So,
[tex]\begin{gathered}\begin{gathered}\bf\: \rm \longmapsto\: |cosx| + cosx = \begin{cases} &\sf{ \: \: 0 \: \: when \: cosx \leqslant 0} \\ \\ &\sf{ \: \: 2 \: cosx \: \: when \: cosx > 0} \end{cases}\end{gathered}\end{gathered}[/tex]
So,
[tex]\rm\implies \:f(x) \: is \: defined \: when \: cosx > 0[/tex]
So, from graph we concluded that cosx > 0 in the following intervals.
[tex]\begin{gathered}\boxed{\begin{array}{c|c} \bf cosx & \bf \: x \: \in \: \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf + ve & \sf \bigg( - \dfrac{\pi}{2} ,\dfrac{\pi}{2} \bigg) \\ \\ \sf + ve & \sf \bigg(\dfrac{3\pi}{2} ,\dfrac{5\pi}{2} \bigg) \\ \\ \sf + ve & \sf \bigg(\dfrac{7\pi}{2} ,\dfrac{9\pi}{2} \bigg) \end{array}} \\ \end{gathered}[/tex]
So, if we generalized this we get
[tex]\rm\implies \:cosx > 0 \: when \: x \: \in \: \bigg(\dfrac{(4n - 1)\pi}{2} ,\dfrac{(4n + 1)\pi}{2} \bigg) \: \forall \: n \in \: Z[/tex]
Hence,
Domain of the function is
[tex]\red{\rm\implies \boxed{\tt{ \: x \in \: \bigg(\dfrac{(4n - 1)\pi}{2} ,\dfrac{(4n + 1)\pi}{2} \bigg) \: \forall \: n \in \: Z}}}[/tex]
[tex]\textsf{More to know :-} \\[/tex]
[tex]\begin{gathered}\begin{gathered}\boxed{\begin{array}{c|c} \bf T-eq & \bf Solution \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf sinx = 0 & \sf x = n\pi \: \forall \: n \in \: Z\\ \\ \sf cosx = 0 & \sf x = (2n + 1)\dfrac{\pi}{2}\: \forall \: n \in \: Z\\ \\ \sf tanx = 0 & \sf x = n\pi\: \forall \: n \in \: Z\\ \\ \sf sinx = siny & \sf x = n\pi + {( - 1)}^{n}y \: \forall \: n \in \: Z\\ \\ \sf cosx = cosy & \sf x = 2n\pi \pm \: y\: \forall \: n \in \: Z\\ \\ \sf tanx = tany & \sf x = n\pi + y \: \forall \: n \in \: Z\end{array}} \\ \end{gathered}\end{gathered}[/tex]
In triangle RST, mZR>m2S +mZT. Which must be true of triangle RST? Check all that apply.
OmZR > 90°
mZS + mZT< 90°
0 m2S = mZT
OmZR>mZT
OmZR>mZS
OmZS> mZT
Answer:
Step-by-step explanation:
1,2,4,5
The correct statements are,
m∠R > 90°
m∠S + m∠T < 90°
m∠R > m∠T
m∠R > m∠S
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
Here, RST is a triangle,
Therefore,
m∠R + m∠S + m∠T = 180°
⇒ m∠S+m∠T = 180° - m∠R
Since, m∠R > m∠S + m∠T
⇒ - m∠R < - (m∠S + m∠T) (by multiplying-1 on both sides)
⇒ 180°- m∠R < 180° - (m∠S + m∠T) (by adding 180° on both sides)
⇒ m∠S+m∠T < 180° - (m∠S + m∠T)
⇒ m∠S+m∠T+ m∠S+m∠T < 180° ( by adding m∠S + m∠T on both sides)
⇒ 2(m∠S+m∠T) < 180°
⇒ m∠S+m∠T < 90°
⇒ m∠R > 90° ( because m∠R+m∠S+m∠T = 180° )
Again, m∠R > m∠S + m∠T
⇒ m∠R > m∠S and m∠R > m∠T
Thus, Option first second fourth and fifth are correct.
Since, m∠S = m∠T is only possible when m∠R=90° (but it is not given)
That is why m∠S = m∠T is not correct.
And, there are not enough information to prove m∠S > m∠T
That is why m∠S > m∠T is also incorrect.
Learn more about the triangle visit;
brainly.com/question/1058720
#SPJ7
Please help me
Please
What is an advantage of debt consolidation?
A. You will pay a higher interest rate.
B. You will have one monthly payment to manage.
C. You will have less time to make payments.
D. You will need to meet with a debt counselor.
An advantage of debt consolidation is: B. You will have one monthly payment to manage.
What is Debt consolidation?Debt consolidation can be defined as the way in which a person borrow or collect a loan so as to payoff their old debt or liabilities.
One of the advantage of debt consolidation loan is that you will have one monthly payment to manage or one bill to pay per month instead of several bill.
Therefore the correct option is B.
Learn more about debt consolidation here:https://brainly.com/question/11199005
#SPJ1
Identify two segments that are marked parallel to each other on the diagram below.(diagram is not to scale)
Answer:
DC and EF are parallel
Step-by-step explanation:
Parallel lines are indicated by arrow heads on the segments that are parallel.
In this case DC and EF
Que. 19. In the equation x = 2y + 9, if x = 1, than y =
Answer: y = -4
Step-by-step explanation:
If x = 1
1 = 2y + 9
1 - 9 = 2y
-8 = 2y
y = -8/2
y = -4
please give me a brainliest answer
Answer:
[tex]y = ( - 4)[/tex]
Step-by-step explanation:
Given that,
[tex]x = 1[/tex]
Question :
[tex]x = 2y + 9[/tex]
You have to find the value of y. So, make the y as the Subject
[tex]x = 2y + 9 \\ x - 9 = 2y \\ \frac{x - 9}{2} = \frac{2y}{2} \\ \frac{x - 9}{2} = y[/tex]
Now replace 1 instead of x
[tex]y = \frac{x - 9}{2} \\ y = \frac{1 - 9}{2} \\ y = \frac{ - 8}{2} \\ y = - 4[/tex]
Hope this helps you.
Let me know if you have any other questions :-)
A grocery store orders 3 large cartons of eggs for every 7 small cartons of eggs. Which ratio could represent the number of large cartons of eggs to small cartons of eggs in an order from the grocery store?
Answer:
3:7
Step-by-step explanation:
-
Hope that helps
Can somebody please help me?
Which number best represents a positive charge of 1,640 volts? A.
-1,540
B.
-1,640
C.
1,640
D.
1,540
Answer:
Hello there! I think the answer to your question
C
Because a "A positive voltage is a voltage that pushes electrons out of a battery."
How do you solve for x and y. Thanks!!
Kinda urgent sorry..
Answer:
x= 17.5
y= 35
Step-by-step explanation:
Steps are in attachment.
Answer:
• For x (Acute angle property)
[tex]{ \rm{(2x + 10) \degree + 30 \degree + 6x=180 \degree}} \\ \\ { \rm{8x + 40=180}} \\ \\ { \rm{8x = 140}} \\ \\ { \boxed{ \underline{ \rm{ \: \: x =17.5 \: \: }}}}[/tex]
• For y ( Interior angle sum of triangles )
[tex]{ \rm{(y + 10) \degree + 6x \degree + 30 \degree = 180 \degree}} \\ \\ { \rm{y + 10 + 30 + (6 \times 17.5) = 180}} \\ \\ { \rm{y +145 = 180 }} \\ \\ { \boxed{ \underline{ \rm{ \: \: y = 35 \: \: }}}}[/tex]
The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 7 to 5. If there were 11,724 total votes, how many no
votes were there?
Solve the math problem
Answer:iqual like 12
Step-by-step explanation:xD i think :/
At the movie theatre, child admission is $6.40 and adult admission is $9.60. On Tuesday, four times as many adult tickets as child tickets were sold, for a total sales of $896.00. How many child tickets were sold that day?
Answer:
893
Step-by-step explanation:
you take away from the number and you can get your answer or you can do it different like add the number and get the number of children tickets were sold
Find the sum of the first twelve terms of the sequences 3, -6, 12, -24,..
Show your work.
Answer:
3, -6, 12, -24, 48, -96, 192, -384, 768, -1536, 3072, -6144...
×-2
Geometric sequence
Convert to slope-intercept form to graph 3x+5y=10
find the product binomial expression of;
(x-5) (8-5)
Answer:
3x-15
Step-by-step explanation:
(x-5)(8-5)
(x-5)(3)
re-order
(x-5)×3
3(x-5)
Distribute
3(x-5)
3x-15
please explain how to solve this
(12+5i) - (9-2i)
i have answers but dont understand
Answer: 3 + 7i
Step-by-step explanation:
Equation expanded: 12 + 5i - 9 + 2i // now simplfy
12 - 9 = 3
5i + 2i = 7i
// together, we get
3 + 7i
Answer:
10i
Step-by-step explanation:
(12+5i) - (9-2i)
(17i) - (7i)
10i
A teacher wants to buy the same number of colored markers and pencils. Markers come in packs of 12, and pens come in packs of 16. What is the fewest number of markers and pens the teacher needs to buy?
Answer:
if the teacher buys 4 packa of markers and 3 packs of pens she would have the same amount
Find the slope, m, and y-intercept, b, for the graph of the linear equation represented by the table below.
Answer:
y = -3x - 2
Step-by-step explanation:
M: -3
B: -2
Can someone explain how the following Matrix can be multiplied? I thought the column of the first matrix had to match the row of the second and the row of the first had to match the column of the second. I how the matrices listed below as (1x3) and (3x3) respectively. Yet my online Pre-cal course says it's possible. Please explain why this is so.
You are correct in thinking that the columns of the first matrix must match with the rows of the second matrix.
So for example, we can multiply a 1 x 5 matrix with a 5 x 7 matrix. The two matching '5's are directly what make multiplication possible in this case. For your problem, the first two '3's match and multiplication is possible.
The rows of the first matrix don't need to match with the columns of the second matrix.
Find the value of y that will make these two triangles congruent:
Answer:
5
Step-by-step explanation:
if the triangles are congruent then the side lengths must be equal:
JL=PM
PN=LK
NM=JK and
4y + 12 = 32 subtract 12 from both sides
4y = 20 divide both sides by 4
y = 5
what is the slope of a line parallel to the line whose equation is 2x + y = 3?
Step-by-step explanation:
Here is the answer to the question
Answer:
-2/1
Step-by-step explanation:
Rewrite equation in point-slope form
y=-2x+3
in y=mx+b, m= the slope
The slope of the line is -2/1
Any lines parallel to this line will have the same slope
12. The function t = 19m + 65 represents the temperature t (in degrees Fahrenheit)
of an oven after preheating for m minutes.
The temperature in Fahrenheit after preheating for 2 minutes is 103⁰F
The question looks incomplete but we can as well find the temperature in Fahrenheit after preheating for 2 minutes
Give the function t = 19m + 65 that represents the temperature t (in degrees Fahrenheit) of an oven after preheating for m minutes.
If t = 2,
t = 19(2) + 65
t = 38 + 65
t = 103⁰F
Hence the temperature in Fahrenheit after preheating for 2 minutes is 103⁰F
Learn more here:https://brainly.com/question/16510024
Sage needs 2 boards to make a shelf. One board is 260 cm long and the other is 1 1/4 m long. What is the total length of the shelf?
Answer:
385
Step-by-step explanation:
1 1/4 meters = 125 cm
125+260 = 385
Answer:
sum = 260 + 270 = 535 cm or = 5,35 m
Step-by-step explanation: take 11/4m = 2,75m * 100 = 275 cm
What is the equation for the line that is parallel to the x-axis and passes through the point (5, -2)?
Answer:
y = -2
Step-by-step explanation:
What is 268 divided by 6 with a remainder
Answer:
264 with a remainder of 4
Step-by-step explanation:
The solution is: 44 is 268 divided by 6 with a remainder 4.
Here, we have,
given that,
268 divided by 6
Given the following mathematical expression;
268 / 6
We would apply the law of division for fractions.
268 / 6
= 268 ÷ 6
= 44 + 4
the remainder is 4
Hence, The solution is: 44 is 268 divided by 6 with a remainder 4.
To learn more on division click:
brainly.com/question/21416852
#SPJ6
Is this righttt????
Huh
Answer:
Should be!!! i remember taking that quiz but i dont really remember
Step-by-step explanation:
Emmanuel went to Circuit City to buy a refrigerator for $3,652. This week at Circuit City, all kitchen appliances have a discount of 35%. If Emmanuel goes to Circuit City this week, how much will he pay for the refrigerator?
Answer:
2373.8 dollars
Step-by-step explanation:
3652 times 35% equals 1272.2 so 3652 - 1272.2 = 2372.8
THE HECK IS THIS‽ IF SB CAN answer+EXPLain YOU SHALL RECEIVE BRAINLIEST+50 POINTS
bro what am i sposed to do?
thanks xx)
Step-by-step explanation:
here is your answer
hope it will be helpful for you
thanks ☺
Answer:
I have come to claim these points as my own...again, thank you friend.
Step-by-step explanation:
⏁⊑⏃⋏☍ ⊬⍜⎍ ⎎⍜⍀ ⏁⊑⟒ ⌿⍜⟟⋏⏁⌇ ⎅⟒⏃⍀ ⎎⍀⟟⟒⋏⎅, ⟟ ⏃⋔ ⎎⍜⍀⟒⎐⟒⍀ ⟟⋏ ⊬⍜⎍⍀ ⎅⟒⏚⏁.
anyone know what to do no bot answer please they are annoying very annoying..
Answer:
5
Step-by-step explanation:
Hope it helps. :D
Answer:
144 I think have a good day
From the graph, write the linear equation in slope-intercept form
Answer:
1.y=1/2+2
2.y=-2+1
3.y=3/2+3
4.y=-2/3-2
Step-by-step explanation: