[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]
Helppppppp!!!!!!!!!!
Answer:
c and d are monomial because they have only one term
37. Construct Arguments Luis and Raul are
riding their bicycles to the beach from their
respective homes. Luis proposes that they leave
their respective homes at the same time and
plan to arrive at the beach at the same time.
The diagram shows Luis's position at two points
during his ride to the beach.
Write an equation in slope-intercept form
to represent Luis's ride from his house to the
beach. If Raul lives 5 miles closer to the beach
than Luis, at what speed must Raul ride for the
plan to work?
Using the slope - intercept relation, the required equation which models the scenario and Raul's speed are ;
y = - 7.5x + 15 4 miles per hourTime difference, Δt = 1.2 hours - 0.5 hours = 0.7 hours
Change in distance, Δd = 11.25 - 6 = 5.25 miles
Assuming a constant speed :
Speed = (Δd ÷ Δt) = (5.25 ÷ 0.7) = 7.5 mi/hrUsing the general form :
y = bx + cAt, x = 1.2 hours ;
Miles left, y = 6 miles
End point decreases by 7.5 mi/hr (-7.5 mi/hr)
Inputting the data into the equation :
6 = - 7.5(1.2) + c
6 = - 9 + c
c = 6 + 9 = 15 miles
The expression in slope intercept form becomes ;
y = -7.5x + 15If Raul lives 5 miles closer to the beach ;
Time it will take Luis to get to the beach :
Time taken = (15 ÷ 7.5) = 2.5 hoursDistance Raul has to cover = 15 - 5 = 10 miles
To reach the beach after 2.5 hours ;
Speed required = (10 ÷ 2.5) = 4 mi/hrTherefore, Raul has to ride at 4 miles per hour for the plan to work.
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PLEASE HELP!!
Josh works for MooMoo Milkshakes. The company wants to know what milkshake flavor is the most popular. Today, he surveyed
every third female customer on their favorite milkshake flavor. Eighteen customers
(out of 60 total) were surveyed, and 7 customers
prefer MooChooChocolate, 5 customers prefer VeryStrawberry, and 6 customers prefer BananaBoBanna.
What type of sampling is demonstrated in the situation above?
A. census
B. random sampling
C. negative sampling
D.convenience sampling
Answer: random sampling
Step-by-step explanation: Random sampling is where each member of the sample is randomly selected from the population. Since Josh chose every third female customer, he randomly chose the sample.
Answer: B random sampling .
Step-by-step explanation:
Two-thirds of the sum of a number squared and 5 is fourteen
Answer:
2/3( x^2 + 5 ) = 14 or 2/3x^2 - 32/3
Step-by-step explanation:
Part 1:
Two-thirds ( 2/3 )
of the ( (---) )
sum ( + )
of a number squared ( x^2 ) and 5 ( + 5 )
is fourteen ( = 14 )
Part 2 (Not super confident about):
2/3( x^2 + 5 ) = 14
2/3x^2 + 10/3 = 14
2/3x^2 - 32/3
Hopefully this helps!
Brainliest please?
6. What might be the opportunity cost of a large portion of your income going toward credit
card payments each month?
Sarah's Volleyball team won 12 out of 14 games if this rate continues, how many games will they win if they play a total of 21 games
Answer:
18 games
Step-by-step explanation:
If Sarah's Volleyball team won 12 out of 14 games, then their win rate is 12/14. You can simplify this fraction down to 6/7 to make it easier, but you don't have to.
If they keep the same rate of 6/7 (6 wins for every 7 games they win), you multiply the rate by the total games to get the number of wins. wins/games (rate) x total games = total wins, so 6/7 x 21 = 18.
3y-6 = y+4 solve HELLLLKPPP
Help pleaseeeeeeeeeeeeeeeeeeeeeee
Answer:
I have to say this problem is poorly worded.
the answer they're looking for is 8, I believe.
they defined t(x) twice!
STEP BY STEP what is 8-11
Answer:
-3
Step-by-step explanation:
You might find it easier to write -(11 - 8), which is -(3), or -3.
Answer:
8-11
Infront of 8 there will be+
so +8-11
- + = - so 8-11=-3
-3 is the answer of 8-11
A movie theater uses a cone-shaped container to serve popcorn. The cone has a height of 12 inches and a volume of 16 π in2. What is the radius of the cone?
Volume can be defined as the capacity of a given container or a certain object.
The radius of the cone is 2 inches.
From the question, we are given the following parameters:
The height of the cone = 12 inches
The volume of the cone = 16 π in³
The formula to find the radius of the cone is given as:
√3V/πh
= √ 3 x 16π / π x 12
= 2 inches
Therefore, the radius of the cone is 2 inches.
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13. A bakery is having a buy 4, get 1 free sale on cakes. This sale is eguivalent to what percentage off the regular price of all 5 cakes? A. 196 B. 10%% C. 20 D. 25%6 E. 40%
Answer: 20
Step-by-step explanation:
Convert 47/16 to a decimal using long division.
2.9375 is the answer
3 is the rounded up answer
i cant show steps cuz :p
sorry
anyway hope tis helps
Answer:
47/16
is basically dividing
47÷16
Long Division for 47 divided by 16
=2.9375
Eva
Evaluate each expression
1/5
(252)
-5
COMPLETE
27
27
DONE
Answer:
9
Step-by-step explanation:
Reduce the expression, if possible, by cancelling the common factors.
Exact Form:
9
Only an answer please please
Answer: 41
Step-by-step explanation: r= 3c+ 5
3 (12) +5 36+5= 41
Answer:
B 35
Step-by-step explanation:
the value goes up by six in each box
What’s does 120$ plus 40% mean
Answer:
ur suppose to find how much it is after the discount so for example in question 1 the discount is 40% so subtract that from 100% to get 60% then multiply this 60% by the origanial vaule which is 120 so for the answer for question 1 would be 72. Also when multiplying 60% u dont multiply by 60 u multiply it by 0.6
Hope this help and sry for the bad grammar
Find the measures of the four angles below.
Answer:
x = 38.8
Step-by-step explanation:
Write the slope intercept form of the equation of the line through the given point with the given slope.
(0,-1), slope=3
Step-by-step explanation:
y=mx+c
-1=3(0)+c
c=-1
y=3x-1
Sharon called 4 friends on Friday. On Saturday, each of those 4 friends called 4 different friends. On Sunday, each person who was called on Saturday called 4 different people.
Answer:
it [tex]4^{3}[/tex]
Step-by-step explanation:
i took a test
Solve the quadratic equation
d²-5d+6=0
Answer:
BBC
Step-by-step explanation:
Answer:
d = 6 d = -1
Step-by-step explanation:
Use displacement to factor
d²-5d+6=0
d²+d-6d-6=0
d(d+1)-6(d+1)=0
(d-6)(d+1)=0
d-6=0 or d+1=0
d = 6 d = -1
Which graph represents the equation y – 4 = -1/3(x-2)
George is looking at stock market charts. He can buy a collection of stocks for 6 shares for $618. How much would it be for 11 shares?
Which of the following represents the equation of a line that is parallel to 2y-x=16 and passes through the
point (-6, 1)?
The equation of a line that is parallel to (2y - x = 16) and passes through the point (-6, 1) is [tex](y - 1)=0.5(x+6)[/tex] and this can be determined by using the slope-intercept form of the line.
Given :
Line Equation -- 2y - x = 16Point -- (-6,1)First, convert the given line in slope-intercept form that is in the form of (y = mx + c).
2y = x + 16
[tex]y = \dfrac{1}{2}x +16[/tex]
Comparing the above equation with slope-intercept form.
m = 0.5
c = 16
The line parallel to the line (y = 0.5x + 16) means the slope of that line is also equal to 0.5.
The equation of the line whose slope is m and passing through the point [tex](x_1,y_1)[/tex] is given by:
[tex](y-y_1) = m(x-x_1)[/tex]
Now, put the value of slope m and point [tex](x_1,y_1)[/tex] in the above equation.
[tex](y - 1)=0.5(x+6)[/tex]
So, the equation of a line that is parallel to (2y - x = 16) and passes through the point (-6, 1) is [tex](y - 1)=0.5(x+6)[/tex].
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There are 24 students in a math class and 20 students passed the last quiz. What was the ratio of the students who passed the quiz to those who did not pass the quiz?
Answer: 25% did not pass the quiz:)
Step-by-step explanation:
Suppose Felipe has 9.24 pounds of seed if it takes 6.6 pounds of seed to plant on acre of grass how many acres of grass can be planted?
Answer:
1.4 acres of grass can be planted.
Step-by-step explanation:
He has 9.24 pounds of seeds.
If one acre of grass needs 6.6 pounds of seeds we can divide 9.24 pounds by 6.6 pounds to find how many acres of grass he can plant.
9.24 lbs × [tex]\frac{1acre}{6.6 lbs}[/tex] = 1.4 acres
What is the slope of the line shown?
Answer:
m=-2/-1 or m=-2
Step-by-step explanation:
Find two points on the line, then use this formula: m=rise/run or m=y2-y1/x2-x1
m=0- 2/-3-(-2)
m=-2/-1 or m=-2
A woman places a laser pointer on the ground and shines it at the top of a lamp post. She then
stands between the laser and the lamp post so the laser just barely touches the top of her head.
The woman, the lamppost, the laser, and the ground combine to form two similar right triangles.
She is standing 2.4 meters away from the lamppost and 2.1 meters from the laser. If the woman
is 1.8 meters tall, how tall is the lamppost?
estimate 1.75 * 12.5
Answer:
21.875, round as needed.
Step-by-step explanation:
1.75 * 12.5
21.875
You can also round to:
21.88
21.9
22
Just depends on what your teacher is asking
FEAR OF CLOWNS When you see a clown, what do you feel? You feel happy and ready to laugha, right? That's because we know that clowns make jokes, do funny antics and perform tricks to make us laugh. But did you know that there are people who tremble with fear when they see a clown?
These people have an unnatural fear of clowns. To know what this phobia is called:
Directions: Encircle the CORRECT LETTER. Then write the correct letter on the blank below. Determine the equation of a line passing through the following points. Use another sheet of paper for the solution.
Answer:
Coulrophobia
Step-by-step explanation:
Coulrophobia
8. There are 3 cows for every 4 chickens on a farm. If there are 154
animals, how many are cows?
Pls help me
Answer:
12 po
Step-by-step explanation:
I try my best I don't know if right
Solve for x step by step
Answer:
n=11
Step-by-step explanation:
n+5/-16=-1, multiply both sides by -16
n+5=16, subtract 5 from both sides
n=11