Functions, f and g are given by f(x)= 3+ cos x and g(x) = 2x, x is a real number. Determine the value of c for which f(g(x))= g(f(x)) where 0[tex]\leq[/tex]x<2[tex]\pi[/tex]
Answers
The value x is equal to [tex]\pi[/tex] for which f(g(x))=g(f(x))
Given :
f(x)=3+cos(x)
g(x)=2x
To find : the value of x over the given interval [tex]0\leq x\leq 2\pi[/tex]
Apply composition of functions. Replace g(x) inside f(x) to find f(g(x))
[tex]f(g(x))=f(2x)=3+cos(2x)\\g(f(x))=g(3+cosx)=2(3+cosx)\\[/tex]
Now we set f(g(x))=g(f(x)) and solve for x
[tex]3+cos(2x)=2(3+cosx)\\3+cos(2x)=6+2cos(x)\\\cos \left(2x\right)-2\cos \left(x\right)-3=0\\\\we \; know:\ cos(2x)=2cos^2(x)-1\\-4-2\cos \left(x\right)+2\cos ^2\left(x\right)=0\\2cos^2(x)-2cos(x)-4=0\\\\divide \; by \; 2 \; and \; Factor \; left \; hand \; side\\\\cos^2(x)-cos(x)-2=0\\\\(cosx-2)(cosx+1)=0\\\cos \left(x\right)=2,\:\cos \left(x\right)=-1[/tex]
cos(x)=2 cannot be solved , so no solution
[tex]cos(x)=-1\\cos is -1 at x=180 degree\\So , x=\pi[/tex]
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Related Questions
I WILL GIE BRAINLY AND 50 POINTS PLZ PLZ PLZ HELP ME
Select the correct scientific notation form of this numeral using only 2 significant figures.
8,421,032.9266
84 × 10 9
8.4 × 10 10
8.4 × 10 6
None of these
Answers
Answer:
8.4 × 10^6
Step-by-step explanation:
Use floating-point system in which numbers are expressed as products consisting of a number between 1 and 10 multiplied by an appropriate power of 10 (as in 1.591 × 10−20)
Hope this helps <3
simplify
3sin 0+ 2sin 0- 4sin0+ 5sin0
step by step
Answers
Answer:
0
Step-by-step explanation:
3x0+2x0-4x0+5x0
0
Find the area of the figure in the image attached. Round to the nearest tenth if necessary.
Answers
Plz Help me Asap. And explain
Answers
Answer:
n=(1/6) or n=-5/2
Step-by-step explanation:
|6n+7|=8
6n+7=8 or 6n+7=-8
6n=1 or 6n=-15
n=(1/6) or n=-5/2
which numbers round to 40 when rounding to 10s?
Answers
Answer:
35, 36, 37, 38, 39, 41, 42, 43 and 44
Step-by-step explanation:
Everything above 5 rounds upwards, and all numvers below 5 rounds down. So 34 and down will be rounded to 30, and that's what happens with 44, 43, 42, and 41.
A waitress earned $73 for 6 hours of work. The total included $46 in tips. What was her hourly wage?
Answers
Answer: $4.5/hour
Step-by-step explanation:
Total earned in 6 hours subtracted tips equals wage over 6 hours.
Divide by 6 hours to find individual hourly wage.
Answer: $4.50 per hour
Step-by-step explanation:
First, find how much she earned, excluding the tips.
73-46= 27
She earned $27 in the 6 hours, without tips
To find her hourly wage, you divide 27 by six because, since she worked 6 hours to earn $27, we need to find the unit rate.
27/6 = 4 dollars 50 cents.
I need help plz sorry
Answers
Answer:
a)
[tex](4.3 \times {10}^{5} )(1.6 \times {10}^{4} ) = 6.88 \times {10}^{9} [/tex]
b)
[tex](2.25 \times {10}^{3} )(5.8 \times {10}^{6} ) = 13.05 \times {10}^{9} = 1.305 \times {10}^{10} [/tex]
I hope I helped you ^_^
The answers plzzz I need help
Answers
One bag of peanuts costs $ 1.52. How many bags can you buy with $34.96?
Answers
Si a cero se le resta cualquier número entero el resultado siempre es el
mismo número, pero con signo positivo.
Answers
Please comment this in english.
three fewer than four times a number is five more than twice the number. What is the number
A. 1
B. 2
C. 4
D. -1/3
Answers
Answer:
C.4
4x-3=2x+5
x=4
Step-by-step explanation:
The number which is "three fewer than four times a number is five more than twice the number" is 4.
Linear EquationThe equation having the highest power of its variables as 1 is known as a linear equation.
How do we find the number?Let the required number be x.
The given condition is - "Three fewer than four times a number is five more than twice the number."
Based on the given condition we will form an equation and solve it for x to find the required number.
The resulting linear equation is,
4x-3 = 2x+5
4x-2x = 5+3
2x = 8
x = 4
Hence, the required number is 4.
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5/10+8/100
I NEED HELP PLSSSS
Answers
Answer:
1 58/100 or 1 29/50 (simplified)
Step-by-step explanation:
you can turn them into decimals
5/10 = 0.5
8/100 = 0.08
0.5 + 0.08 = 0.58
0.58 = 58/100 = 29/50
Please help answer all these questions. I will give brainliest questions aint in order
Answers
Answer:
please send the questions again
Please help with this.
Answers
Answer:
g(1)=-72; g(n)=g(n-1)*(1/6)
Step-by-step explanation:
g(1)= -72*(1/6)^(1-1)=-72*(1/6)^0=-72*1=-72
g(2)=-72*(1/6)^(2-1)=-72*(1/6)^1=-72*(1/6)=-12
g(2)=g(1)*(1/6)
g(n)=g(n-1)*(1/6)
In two or more complete sentences, explain how to find the average rate of change of a function
Answers
when given the value of a function at different points, calculate the average rate of change of a function for the interval between two values. calculate the difference between y2-y1 and x2-x1. then divide y/x to find the ratio.
The graph of a sinusoidal function intersects its midline at (0, -7) and then has a minimum point at (pi/4, -9)
Answers
Answer:
I don't know if you have any questions or need any further information please contact me at the sun with the sun with the sun with the sun
A map is drawn to a scale of 1 : 240 000.
(i) If a seawater lake has an area of 3.8 cm² on the map, find its actual area in square kilometres.
(ii) If the actual area of a plot of land is 2 908 800 m², calculate its area on the map.
Answers
Step-by-step explanation:
Above are the explanations
A map is drawn on a scale of 1: 240 000.
(i) Actual area [tex]$=21.888 \mathrm{~km}^{2}$[/tex]
(ii) Area on the map = [tex]$0.505 \mathrm{~cm}^{2}$[/tex].
How to estimate the area on the map?(i) 1 cm: 240000 cm = 1 cm: 2.4km
Area scale [tex]$=1^{2} \mathrm{~cm}^{2}: 2.4^{2} \mathrm{~km}^{2}$[/tex]
[tex]$=1 \mathrm{cm}^{2}: 5.76 \mathrm{~km}^{2}$[/tex]
[tex]$1 \mathrm{~cm}^{2}: 5.76 \mathrm{~km}^{2}$[/tex]
[tex]$3.8 \mathrm{~cm}^{2}: 21.888 \mathrm{~km}^{2}$[/tex]
Actual area [tex]$=21.888 \mathrm{~km}^{2}$[/tex]
[tex]$=21.9 \mathrm{~km}^{2}[/tex]
(ii) 1 cm: 240000 cm = 1 cm: 2400 m
Area scale [tex]$=1^{2} \mathrm{~cm}^{2}: 2400^{2} \mathrm{~m}^{2}$[/tex]
[tex]$=1 \mathrm{~cm}^{2}: 5760000 \mathrm{~m}^{2}$[/tex]
[tex]$1cm}^{2}: 5760000 \mathrm{~m}^{2}$[/tex]
[tex]$0.505 \mathrm{~cm}^{2} ; 2108800 \mathrm{~m}^{2}$[/tex]
The area on the map = [tex]$0.505 \mathrm{~cm}^{2}$[/tex].
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Choose a number line to model the following situation:
After a gain of 25 yards, the football team lost 25 yards on the next play. (4 points)
a
A horizontal number line is shown with labels at 0 and 25. A purple arrow (labeled gain 25 yds) begins at 0 and ends at 25. A red arrow (labeled lose 25 yds) begins at 25 and ends at 0.
b
A horizontal number line is shown with labels at negative 25, 0, and 25. A purple arrow (labeled gain 25 yds )begins at 0 and ends at 25. A red arrow (labeled lose 25 yds) begins at 0 and ends at negative 25.
c
A horizontal number line is shown with labels at 0, 25, and 50. A purple arrow (labeled gain 25 yds) begins at 0 and ends at 25. A red arrow (labeled lose 25 yds) begins at 50 and ends at 25.
d
A horizontal number line is shown with labels at 0, 25, and 50. A purple arrow (labeled gain 25 yds) begins at 0 and ends at 25. A red arrow (labeled lose 25 yds) begins at 25 and ends at 50.
Answers
Answer: A
Step-by-step explanation: because the number line shows a gain of 25 then a loss of 25, it represents the question showing +25 then -25. so the answer is A
Hope this helps
Find the area of each figure. Round to the nearest tenth if necessary.
Answers
Shape 1: TRIANGLE
Formula: A = 1/2 x bh
1/2 x (10)(5) = 25
AREA: 25 square yards
Shape 2: RECTANGLE
Formula: A = lw
(12)(10) = 120
AREA: 120 square yards
Sum (ADD)
25 yd^2 + 120 yd^2 = 145 yd^2
The area of the composite figure is 145 yd^2
the formula for triangles is a =1/2 x bh
5x10 = 50
50 x 1/2= 25
So the area for shape 1 is 25.
Shape two / rectangle :
the formula for quadrilaterals is a = bh
12 x 10 = 120
so the area of shape 2 is 120
Determine whether each sequence is an arithmetic sequence. If yes, then state the common difference.
-6, -5, -3, -1,...
Answers
Answer:
No
Step-by-step explanation:
it need to have a common difference
Answer:
The sequence is not arithmetic because it is not consistent.
Step-by-step explanation:
Please help these are the last ones I need I will mark you as brainliest if you answer them correctly! Ty
Answers
i need help with this question.
Answers
Find the area of the figure in the image attached. Round to the nearest tenth if necessary.
Answers
Work:
First you split the shape into a rectangle and a triangle. So now you have a triangle with the sides 4 x 3.6 and a triangle with the sides 4 x 2.7.
Side note: 2.7 comes from subtracting 3.6 off of 6.3.
Rectangle:
A = lw
A = 4 (3.6)
A = 14.4m²
Triangle:
A = 1/2lw
A = 1/2 (4) (2.7)
A = 5.4m²
Then you add the areas of both the rectangle and the triangle together.
14.4 + 5.4 = 19.8m²
Is it illegal in california to eat raw oranges in bathroom?
Answers
Answer:
nah it's illegal in cali to eat raw oranges in the bathtub, but im not sure if that's a real law
so i guess if ur on the toilet or smth you can eat it...but like why would you? like in the bathroom?
Answer:
No, it's not.
Step-by-step explanation:
It's not even a real law. People used to think that the citric acid coming from the orange would mix with bath oils and create an explosion. As it turns out, citric acid, obviously, does not cause any explosions when mixed with bath oils. It's just gossip.
A trader has purchased ball pens at the rate of Rs. 42 per dozen. If he sells each ball
pen for Rs. 5, he gets
(A) profit of Rs. 8 (B) profit of Rs. 18 (C) loss of Rs. 18 (D) loss of Rs.8
Answers
Answer:
im confused
Step-by-step explanation:
Answer:
(B)
Step-by-step explanation:
The total would be Rs. 60, so a profit of Rs. 18. Also, please mark brainliest.
this is 6th grade
Which of the following would be the best equation for the function of the values for Frankie’s reading?
A. p = 6h
B. p = 35h
C. h =35p
D. 35 + p = h
Answers
Answer:
B would be the answer.
Step-by-step explanation:
Because 1 x 35 is 35. 35 x 2 is 70. 35 x 3 is 105. And so on. :> Good luckk
HEEEEELLLLLLPPPPPPPPOP
Answers
4(x-8) = 4x-4*8
= 4x - 32
Answer:
4(x-8) = 4x-4*8
= 4x - 32
Step-by-step explanation:
Club members wrote a program together, with several people working on each of 4 parts. If the first part of the program required 1/3 of the total time, the second part needed 1/2 of the remaining time, the third part took 30 minutes, and the fourth part took 60 minutes, how many hours did the program take to write?
Answers
Answer:
Step-by-step explanation:
4 parts: 1/3 + 1/2 + 30min + 60min
1/3 of an hour is = 20 minutes
1/2 of an hour is 30 minutes
20 + 30 + 30 + 60(1h)= 140 minutes = 2 hours and 20 minutes
The total time did the program take to write is 2 hours and 20 minutes.
It is required to find total time.
What is arithmetic?The branch of mathematics dealing with the properties and manipulation of numbers. a science that deals with the addition, subtraction, multiplication, and division of numbers. Fractions, decimals, percentages, fractions, square root, exponents, and other arithmetic operations are used to achieve mathematical simplifications.
Given that:
several people working on each of 4 parts.
First part = 1/3 of the total time,
The second part = 1/2 of the remaining time,
The third part =30 minutes,
Fourth part= 60 minutes,
So, the total time in hour.
4 parts:
1/3 of an hour is = 20 minutes
1/2 of an hour is 30 minutes
Total time=1/3 + 1/2 + 30min + 60min
=20 + 30 + 30 + 60(1h)
= 140 minutes
= 2 hours and 20 minutes.
So, the total time did the program take to write is 2 hours and 20 minutes.
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Help a girl out?
17 - 12m = -11(m-2)
Answers
Answer:
-5 = m
Step-by-step explanation:
17 - 12m = -11(m-2)
Distribute
17 -12m = -11m +22
Add 12m to each side
17 -12m+12m = -11m+22+12m
17 = m+22
Subtract 22 from each side
17 -22 = m+22-22
-5 = m
[tex]\underline{\sf \: 17 - 12m = -11(m-2)}[/tex]
Use the distributive property to multiply -11 by m-2.
17 - 12m = - 11m + 22
Add 11m to both sides.
17 - 12m + 11m = 22
Combine -12m and 11m to get -m.
17 - m = 22
Subtract 17 from both sides.
- m = 22 - 17
Subtract 17 from 22 to get 5.
- m = 5
Multiply both sides by -1.
[tex]\large\boxed{\underline{\bf \: m = -5}}[/tex]
Hope it helps.
RainbowSalt2222
Write a ratio and a percent for the shaded figure.
Answers
Total Squares = 10 × 10
= 100
Shaded Squares = 100 - (6×6)
= 64
Non Shaded = 6 × 6
= 36
Now Ratio of shaded portion is 64:100
= 16:25
Percentage = 64/100 × 100
= 64%
Answered by Gauthmath must click thanks and mark brainliest
