cos(4x + π/5) - sin(2x) = 0
Since cos(x + π/2) = -sin(x), we can write
cos(4x + π/5) = cos(4x + π/2 - 3π/10) = -sin(4x - 3π/10)
Then we can absorb the negative signs into either sin expression, using the fact that sin(-x) = -sin(x):
-sin(4x - 3π/10) - sin(2x) = 0
sin(3π/10 - 4x) + sin(-2x) = 0
Recall that
• sin(a + b) = sin(a) cos(b) + cos(a) sin(b)
• sin(a - b) = sin(a) cos(b) - cos(a) sin(b)
==> • 2 sin(a) cos(b) = sin(a + b) + sin(a - b)
We can further condense the left side in our equation if there exists a solution to
{ 3π/10 - 4x = a + b
{ -2x = a - b
We have
(a + b) + (a - b) = (3π/10 - 4x) + (-2x)
==> 2a = 3π/10 - 6x
==> a = 3π/20 - 3x
(a + b) - (a - b) = (3π/10 - 4x) - (-2x)
==> 2b = 3π/10 - 2x
==> b = 3π/20 - x
So in our equation, we have
sin(3π/10 - 4x) + sin(-2x) = 0
2 sin(3π/20 - 3x) cos(3π/20 - x) = 0
sin(3π/20 - 3x) cos(3π/20 - x) = 0
Solve for x :
sin(3π/20 - 3x) = 0 or cos(3π/20 - x) = 0
[3π/20 - 3x = arcsin(0) + nπ or 3π/20 - 3x = π - arcsin(0) + nπ]
or [3π/20 - x = arccos(0) + nπ or 3π/20 - x = -arccos(0) + nπ]
[3π/20 - 3x = nπ or 3π/20 - 3x = π + nπ]
or [3π/20 - x = π/2 + nπ or 3π/20 - x = -π/2 + nπ]
[3x = 3π/20 - nπ or 3x = -17π/20 - nπ]
or [x = -7π/20 - nπ or x = 13π/20 - nπ]
[x = π/20 - nπ/3 or x = -17π/60 - nπ/3]
or [x = -7π/20 - nπ or x = 13π/20 - nπ]
(where n is any integer)
Exercise 1
4x...X4 =
7 times
The first three terms of a sequence are given. Round to the nearest thousandth (if
necessary).
6,2,2/3….
Find the 8th term.
Answer:
Just divide 2/3 by 3 (or multiply by 1/3), 6 times to get the answer.
solve the following equations 6÷x=18
[tex]\boxed{\underline{\bf \: ANS WER}}[/tex]
[tex] \sf \frac{6}{x} = 18 \\ [/tex]
Variable x cannot be equal to 0 as division by zero is not defined. Multiply both sides of the equation by x.
[tex] \sf \: 6=18x [/tex]
Swap sides so that all variable terms are on the left-hand side.
[tex] \sf \: 18x=6 [/tex]
Divide both sides by 18.
[tex] \sf \: x=\frac{6}{18} \\ [/tex]
Reduce the fraction [tex] \sf\frac{6}{18}[/tex] to its lowest terms by extracting and cancelling out 6.
[tex] \sf \: x=\frac{1}{3} \\ [/tex]
[tex] \sf \: x=\frac{1}{3}\approx \boxed{\underline{0.33... }}\\ [/tex]
______
Hope it helps.
ᏒᎯᎨᏁᏰᎾᏯᏕᎯᏝᎿ2222
f(x) = x − 7 and g(x) = x2 find f(g(−1))
Answer:
g (-1) = (-1)² = 1
f(g(-1)) = f(1)
f(1) = 1 - 7 = -6
The cost of a jacket increased from $50.00 to $59.00. What is the percentage increase of the cost of the jacket?
Answer:
18%
Step-by-step explanation:
I know this because i am a smoot person l o l. Hope this helps!
What is the value of -2/3 x (-1/4)x(-24/4)
Answer:
-1
Step-by-step explanation:
In Ellens Math class, there are 2 boys for every 3 girls. if there are 21 girls in the class, how many boys are in the classroom.
Answer:
14 boysStep-by-step explanation:
Given,
There are 3 girls for every 2 boys
So,
For every 1 girl
[tex] = \frac{2}{3} \: boys [/tex]
Therefore,
For every 21 girls,
[tex] = \frac{2}{3} \times 21 \: boys[/tex]
= 14 boys (Ans)
4.
For which discriminant is the graph possible?
A. b2 – 4ac = 0
B. b2 – 4ac = 6
C. b2 – 4ac = –2
Answer:
A. b2 – 4ac = 0
Step-by-step explanation:
Hey user☺☺
Option a is correct
Because the graph has only one solution.
As the graph touches the x-axis at one point that means that it will have only one solution for x. But we know that a quadratic equation has two solutions. So the graph will have two equal solution and therefore the discriminant will be 0.
Hope this will help☺☺
In a sample of 600 college students, 87.2% said they graduated from high school. How many of the students graduated from high school?
Answer:
523.2 students
Step-by-step explanation:
87.2%×600=523.2 students
Answer:
523.2
Step-by-step explanation:
SEE THE IMAGE FOR SOLUTION
HOPE IT HELPS
HAVE A GREAT DAY
What is the sum of all positive intergers from √8 to √42
√8 < √9 = 3
and
√42 > √36 = 6
which means the positive integers between √8 and √42 are 3, 4, 5, and 6, and their sum is 18.
put in order , smallest to largest 0.13 ,0.7 , 0.6
Answer:
0.13, 0.6, 0.7
Step-by-step explanation:
Basically when comparing a decimal from least to greatest look at the tenths place. Whoever's is the smallest, is the smallest decimal. Then you look at the second smallest etc. If two tenths are the same then you would compare the hundredths place so on.
HELP HURRY I WILL GIVE BRAINLIEST
Is 1.304 rational or irrational?
Answer:
Rational numbers are those numbers that are integers and can be expressed in the form of x/y where both numerator and denominator are integers whereas irrational numbers are those numbers which cannot be expressed in a fraction. ... The denominator of a rational number is a natural number(a non-zero number).
Answer:
Rational
Step-by-step explanation:
A rational number can be expressed in the form
[tex]\frac{a}{b}[/tex] ← where a and b are integers
Given
1.304
= 1 + [tex]\frac{304}{1000}[/tex]
= [tex]\frac{1304}{1000}[/tex] ← as a rational number
janessa is playing a board game with two friends. using a single die, one friend rolled a four, and the other friend rolled a three. janessa needs to roll a number higher than both friends in order to win the game, and she wants to calculate her probability of winning. Is the probability of Janessa winning an independent event or dependent event
Answer:
It is a dependent event, because it depends of the number she'll get rolling the die
Help with geometry please
In which of the following pairs of numbers is -6 larger than the first number, but smaller than the second number?
Answer:
-7, -6, -5
Step-by-step explanation:
-7 < -6
-5 > -6
-7 < -6 < -5
Write two equivalent expressions that represent the situation. What is the difference in their elevations?
An airplane flies at an altitude of 26,000 feet. A submarine dives to a depth of 700 feet below sea level.
2. Shelby and her two friends have 2 pies left after the bake sale after
school. They divide the pies evenly among themselves. How much pie did each
student receive?
Answer:
.67
Step-by-step explanation:
There are three friends and two pies. You are splitting the pies not the people so you divide 2 by 3 to get 0.66666667. Meaning each girl got .67 or around 6/10 of a pie.
algebra hcf
10xyz and 15y²z²
Answer:
5yz
Step-by-step explanation:
1st expression=10xyz
=5*2*x*y*z
2nd expression=15(y)2 (z)2
=5*3*y*y*z*z
therefore H.C.F=5yz
underlines are taking common.
Determine which ordered pair is a solution to the following equation x+y=8
Answer:
(8,0)
and infinite number of ordered pairs make the equation
true 4,4 ... 5,3 ... 9,-1 ....
the solution can be said to be the loation where the graph crosses the x axis that point is (8,0)
Step-by-step explanation:
pq + 4; use p=4, and q = 4
Answer:
20
Step-by-step explanation:
pq + 4
Given:
p = 4
q = 4
We plug the numbers in:
pq + 4
4(4) + 4
16 + 4
20
The answer you are looking for is 20.
Since p=4 and q=4,
Therefore,
pq+4
Substitute each of the given values of the variables,
(4)(4)+4
16+4
20
Which equation represents a line which is parallel to the y-axis?
x = 6
O y = -1
Submit Answer
O x = 4y
Oy= 2 +1
PLS HELP ASAP
Answer:
x=6
Step-by-step explanation:
when there is no 'y' in equation, the line is always
parallel to y-axis
What is the prime factorization of 81?
Enter your answer as a product of prime numbers, like 2 x 3, or as a single prime number, like 17.
Answer:
[tex]3^{4}[/tex]
Step-by-step explanation:
81
27 3
9 3
3 3
3*3*3*3 = [tex]3^{4}[/tex]
Evaluate the function: f(n)=3n-1 ; f(-1)= ?
Answer:
A certain brand of laundry detergent is manufactured for $5.80 and then marked up 35% by the local store before selling. The store offers a 15% discount with the purchase of three or more bottles of the detergent. Showing all work, determine the total cost, before tax, of four bottles of detergent. (10 points)
Step-by-step explanation:
A certain brand of laundry detergent is manufactured for $5.80 and then marked up 35% by the local store before selling. The store offers a 15% discount with the purchase of three or more bottles of the detergent. Showing all work, determine the total cost, before tax, of four bottles of detergent. (10 points)
Evaluate 9ab, for a = 5 and b =
- 7
Answer:
-315
Step-by-step explanation:
Plug in 5 as a and -7 as b into the term:
9ab
9(5)(-7)
Multiply:
= -315
So, the answer is -315.
[tex]\huge\boxed{\textsf{Hey there!}}\\\\\\\huge\boxed{\mathsf{9ab}}\\\huge\boxed{\mathsf{= 9(5)(-7)}}\\\huge\boxed{\mathsf{= 45(-7)}}\\\huge\boxed{\mathsf{= -315}}\\\huge\boxed{\frak{Answer: -315}}\huge\checkmark\\\\\huge\boxed{\textsf{Good luck on your assignment \& enjoy your day!}}\\\\\huge\boxed{\frak{Amphitrite1040:)}}[/tex]
what are congruent triangles?
Answer:
triangles that have the same size and shape.
f(x) = (x + 1)(x - 5). What is the vertex?
(1,5)
(5.1)
(2.-9)
(-9,2)
Answer:
(2, -9)
Step-by-step explanation:
f(x) = (x + 1)(x - 5)
[tex] =f(x) = {x}^{2} - 5x + x - 5[/tex]
[tex] = f(x) = {x}^{2} - 4x - 5[/tex]
[tex] = f(x) = {1x}^{2} - 4x - 5[/tex]
[tex] = f(x) = {1x}^{2} + ( - 4x) - 5[/tex]
= a = 1, b = -4
[tex] = x = \frac{ - 4}{2 \times 1} [/tex]
[tex] = x = - \frac{ - 4}{2} [/tex]
[tex] = x - ( - 2)[/tex]
[tex] = x = 2[/tex]
= f(x) = (x + 1) x (x - 5); x = 2
= f(2) = -9
= (2, -9)
PLEASE HELP
Seven more than the quotient of a number and 5 is equal to 4.
Use the variable b for the unknown number.
Answer:
7 + b/5 = 4
OR
b/5 + 7 = 4
Step-by-step explanation:
also, b = -15
9. Tobias ran 3 miles. How many millimeters did he run? (1 mile = 1,610 meters)
Welcome to Brainly! I'm happy to help!
We see that there are 1,610 meters in a mile. However, we are looking for millimeters, not meters. But, knowing the meters will help us out.
A millimeter is a very small measurement. There are 1,000 millimeters in 1 meter. A meter is much larger. So, if we want to convert 1,610 meters to millimeters, there are going to be way more millimeters because they are so minute.
This means that we will have to multiply. We know that there are 1,000 millimeters in 1 meter, so if we multiply our meters by 1,000 (which is basically just adding 3 zeros), we will get the number of millimeters in one mile!
1,610×1,000=1,610,000 (one million six hundred and ten thousand!)
Don't forget that we are looking for 3 miles though, so we can take the number of millimeters in one mile and multiply by three.
1,610,000×3=4,830,000 (four million eight hundred and thirty thousand!)
So, Tobias ran 4,830,000 millimeters!
Have a wonderful day and keep on learning! :D
helppppppppppppppppppppppppppppppppppp pleaseeeeeeeeeeeeeeeeee
Answer:
answer is D
Step-by-step explanation:
i promise good luck
Answer:
d
Step-by-step explanation:
change the fractions into improper fractions
then multiply nominators by nominators
then same for denominators
then simplify
I need help on an assignment.
Answer:
i believe that answer would be D
Step-by-step explanation: