Recall the following identities:
cos(4x) = cos⁴(x) - 6 cos²(x) sin²(x) + sin⁴(x)
cos(3x) = cos³(x) - 3 cos²(x) sin(x)
sin²(x) = 1 - cos²(x)
Then the equation
cos(4x) = cos²(3x) + sin²(x)
can be rewritten entirely in terms of cos(x) as
8 cos⁴(x) - 8 cos²(x) + 1 = 16 cos⁶(x) - 24 cos⁴(x) + 8 cos²(x) + 1
16 cos⁶(x) - 32 cos⁴(x) + 16 cos²(x) = 0
16 cos²(x) (cos²(x) - 1)² = 0
Now we can solve:
cos²(x) = 0 or (cos²(x) - 1)² = 0
cos(x) = 0 or cos²(x) - 1 = 0
cos(x) = 0 or cos²(x) = 1
cos(x) = 0 or cos(x) = -1 or cos(x) = 1
x = π/2 + 2nπ or x = -π/2 + 2nπ
… or x = π + 2nπ
… or x = 2nπ
where n is any integer.
Solve the following using elimination method
(a) 3x + 2y = 29, 5x - y = 5
(b) 5m + 2n = 3, m - 4n = -6
(c) 7p + 39 = 8, 3p - 49 = 14
(d) 4k - 3h = 25, 6k + 5h = 9
Answer:
the answer of a is 8x+10y
do this by DMAS formula
number divisible by 4
Answer:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108...
Step-by-step explanation:
Numbers go on forever. So there is an infinite amount of numbers that are evenly divisible by 4.
I need some help on 9 and 10
Answer:
question 9
92/11 or 8.36
Step-by-step explanation:
angle on straight line is 180
:. 10x+1 + 12x-5 = 180
collect like terms
10x+12x = 180+5-1
22x = 184
divide both sides by the coefficient of x
22x/22 = 180/22
:. x = 180/22(to d lowest form= 92/11)
or 8.36
If LM=22 and MN=15,find LN
Answer:
37
Step-by-step explanation:
LMN is one big line
LM=22
LM=15
LN=22+15=37
Answer:
LN = LM + MN = 37
Step-by-step explanation:
L————————-M———————-N
22. 15
L————————-37———————-N
Shelby's dad bought 0.98
pounds of bacon. What is
this decimal as a fraction,
in lowest terms.
Answer:
[tex]\frac{49}{50}[/tex]
Step-by-step explanation:
First, divide it by 100.
[tex]\frac{98}{100}[/tex]
Then, simplify. (They both can be divided by 2 since it is their GCF)
[tex]\frac{49}{50}[/tex]
Answer: [tex]\frac{49}{50}[/tex]
Three consecutive even integers have a sum of 36. Find the integers.
first integer=x
second integer=x+1
third integer= x+2 (x + 1 + 1)
x + (x + 1) + (x + 2) = 36
help me if u did u just saved my life :)
ありがとうございました
-y/3+x/5=1
y=3x/5-3
have a great day
Find 20％of 30％of 180
Answer:
10.8
Step-by-step explanation:
30％of 180
30/100 = 180
(180x30)/100
5400/100
54
20％ of 54
20/100 = 54
(54x20)/100
1080/100
10.8
PLease hellp meeeeeeeee
Answer:
I think it -2 then -7
Line XY intersects plane M and point O.
Answer:
x and y are coordinates and m is slope
1.) There are f fish in an aquarium. One fourth of the fish are angelfish. How many are angelfish?
2.) The temperature is 62°F. It gets warmer by h degrees. What is the temperature now?
please help me ~•~
Answer
1. f - 3/4
2. 62 + h
Step-by-step explanation:
1. 1/4 of the fish are angelfish, all fish are one whole, one whole - 3/4's = 1/4
2. we dont have the value of H so we in turn have to figure out the equation and 62 + h is the only answer we can come to
The formula for the area of a traingle is 1/2 bh, where b is the length of base of the traingle and h is the vertical height. Use the formula to find the height of a traingle with a base length of 8 inches and an area of 39 square inches.
Answer:
9.75 inStep-by-step explanation:
A = (1/2)bhGiven:
A = 39 in²b = 8 inFind h:
h = 2A/bh = 2*39/8 = 39/4 = 9.75 inStep-by-step explanation:
We know that
Area of triangle = ½ × b × h
39 = ½ × 8 × h
39 = 4h
39/4 = h
9.75 = h
On a police force, there are 60 more male officers than female officers. If the ratio of
male to female officers is 10:7, determine the number of male and female officers on
the force.
We will solve this problem by solving the system of equations formed by the statements given in the question.
Number of male and female officers are 200 and 140 respectively.
Statements given in the question,
There are 60 more male officers than female officers.Ratio of male and female officers is 10 : 7.Let the number of male officers in the police force = m
And the female officers in the police force = f
"There are 60 male officers than female officers"
m = f + 60 ----- (1)
"Ratio of male and female officers is 10 : 7"
Therefore, [tex]\frac{m}{f}=\frac{10}{7}[/tex]
[tex]m=\frac{10}{7}f[/tex] ------- (2)
By substituting the value of 'm' from equation (2) to equation (1),
[tex]\frac{10}{7}f=f+60[/tex]
[tex]\frac{10}{7}f-f=60[/tex]
[tex]\frac{3}{7}f=60[/tex]
[tex]f=140[/tex]
Substitute the value of 'f' in equation (1),
m = 140 + 60
m = 200
Therefore, number of male and female officers are 200 and 140 respectively.
Learn more,
https://brainly.com/question/8260974
Plz help me with a, b, c, and d
Thx
Answer:
a) 2
b) 38
c) –2
d) – 38
I hope I helped you^_^
I need help with #61 to #64 ASAP please and thank you …. Could someone please help me with it… I need to get it done ASAP .. I need the answers for all of them ASAP
Problem 61
Refer to this link where I solved the problem earlier
https://brainly.com/question/24517029
===========================================================
Problem 62
T(n) = nth triangular number
T(n) = n(n+1)/2 = 0.5n(n+1)
That squares to (0.5n(n+1))^2 = 0.25n^2(n+1)^2
The next triangular number after T(n) is
T(n+1) = 0.5(n+1)(n+1+1) = 0.5(n+1)(n+2)
That squares to 0.25(n+1)^2(n+2)^2
Notice how each squared result has 0.25 and (n+1)^2 found buried in them.
Let's say A = 0.25(n+1)^2
That would mean the first result 0.25n^2(n+1)^2 becomes An^2
The second result 0.25(n+1)^2(n+2)^2 becomes A(n+2)^2
Let's add those to see what happens
An^2+A(n+2)^2
An^2+A(n^2+4n+4)
A(n^2+n^2+4n+4)
A(2n^2+4n+4)
0.25(n+1)^2*(2(n^2+2n+2))
0.5(n+1)^2(n^2+2n+1+1)
0.5(n+1)^2((n+1)^2+1)
0.5k(k+1)
We see that the result is a triangular number where k = (n+1)^2
This shows that adding the squares of consecutive triangular numbers gets us another triangular number.
A few examples
3^2+6^2 = 9+36 = 45 which is in the form n(n+1)/2 when n = 96^2+10^2 = 36+100 = 136 which is in the form n(n+1)/2 when n = 16Answer: Triangular number===========================================================
Problem 63
I'll borrow some of the ideas from problem 62
We found that after squaring the nth and (n+1)th triangular numbers, we got An^2 and A(n+2)^2 respectively. We let A = 0.5(n+1)^2
Subtract those expressions to get...
A(n+2)^2 - An^2
A(n^2+4n+4)-An^2
A(n^2+4n+4-n^2)
A(4n+4)
4A(n+1)
4*0.5(n+1)^2*(n+1)
(n+1)^3
This proves that the difference between the squares of consecutive triangular numbers is a perfect cube, aka a cube number.
A few examples:
6^2 - 3^2 = 36 - 9 = 27 = 3^310^2 - 6^2 = 100-36 = 64 = 4^3Answer: Cube number===========================================================
Problem 64
Refer to this link where I solved the problem earlier
https://brainly.com/question/24517029
The ratio of the number of adults to the number of students on a field trip has to be 2:11. Last year there was 504 more students on a field trip. If the school is expecting the same attendance this year, how many adults have to attend the field trip?
Answer:
112 adults
Step-by-step explanation:
2x+504=11x
11x-2x=504
9x=504
x=56
The ratio is 2:11 so we multiply 56 by 2 and 11. The 2 represents the Adults and the 11 represents the students.
56*2=112 adults
56*11 = 616 students
Just to double check if you do 616-112 it is exactly 504, Therefore the amount of adults is 112.
Have a great day!
What does the V-shape of the graph tell you about the dive? What information does it not tell you?
The coordinate (5, - 8) means the diver is 8 feets below sea level after 5 seconds
The average speed of the diver is 1.78 ft/s
(x, y)
X axis = time = 5 seconds
Y axis = Depth = - 8 feets (negative value = below sea level)
The coordinate (5, - 8) : This gives information about the time with respect to position(depth) of the diver. At the coordinate point (5, - 8) it shows that the diver is at a depth of - 8 after 6 seconds
Recall the formular for speed :
Average speed in water = Total distance in water/ total timetaken
Total distance on water = (0 to - 8) + (-8 to 0) = 16 feets
Total time taken = 9 seconds.
Average speed = 16 ft / 9 seconds = 1.78 ft/s
Learn more : https://brainly.com/question/1378025
The circumference of a circle is B
inches. The radius of the same circle
is 4.5 inches. Which expression best
represents the value of it?
Answer:
C=2πr may be i am not sure
Answer:
The circumference of a circle is B
inches. The radius of the same circle
is 4.5 inches. Which expression best
represents the value of it?
c
Write two fractions that are equivalent to 5/20.
Answer:
[tex] \frac{5}{20} = \frac{1}{4} = \frac{10}{40} \\ thank \: you[/tex]
Simplify: 4b^5 + 10b^5
Answer:
14 b^5
Step-by-step explanation:
you can do all mathmatical operations to same variables with same power
Help me before tomorrow.number 1
Answer:
how can i help you and when to help u and where to help you because i don't have much time say me fast what help do you need
is π11 a real number?
- If x = 12, then 2x - 5 = 19.
Converse:
Is the converse true?
Biconditional:
Answer:
yes
Step-by-step explanation:
the converse is Right
Write a subtraction expression with a positive and negative integer whose difference is negative. Then find the difference
Answer:
-20-15=-35
Step-by-step explanation:
I think this answers your question, sorry if I'm wrong!
Mathematics adding and subtracting integers
PLEASE HELP ASAP
1 by 1 please
Answer:
ummmmmmmmm it's: 1+1=3
Answer:
- 5 and 12
Step-by-step explanation:
Using the rules
- (-) = + , + (-) = -
- 7 - (- 5) + (- 3)
= - 7 + 5 - 3
= - 2 - 3
= - 5
--------------------------------
9 - (- 7) + (- 4)
= 9 + 7 - 4
= 16 - 4
= 12
it’s number 5
thank you
Step-by-step explanation:
Let the number be x, then
one forth of the number
=
[tex] \frac{x}{4} [/tex]
Two cars leave towns 760 kilometers apart at the same time and travel toward each other. One car's rate is 20 kilometers per hour less than the other's. If they meet in 4 hours, what is the rate of the slower car?
Answer:
Let speed of slower car be xkm/h
Therefore rate of other car=x+20 km/h
After 4 hrs ,
Distance covered by Car A=4x
Distance covered by Car B=4x+80
4x+4x+80=760km
8x=680
x=45
The rate of the slower car=45km/h
In the diagram below, de is parallel to xy. What is the value of y?
194"
O A. 86
O B. 94
O C. 104
O D. 106
Please help!! Will give 100 points
Answer:
x+2
Step-by-step explanation:
Answer:
The answer is x+2
Step-by-step explanation:
Example 1 Allison currently has a balance of $2,300 in her checking account. She deposits a $425.33 paycheck, a $20 rebate check, and a personal check for $550 into her checking account. She wants to receive $200 in cash. How much will she have in her account after the transaction? step by step
Answer:
$1955.33 left in her account
Step-by-step explanation:
2300+425.33-20-550=2155.33-200=
