It looks like your equation (it's not an identity) is
2 cos(5x) cos(3x) + sin(x) = cos(8x)
Recall that
cos(x + y) = cos(x) cos(y) - sin(x) sin(y)
cos(x - y) = cos(x) cos(y) + sin(x) sin(y)
==> 2 cos(x) cos(y) = cos(x + y) + cos(x - y)
so that
2 cos(5x) cos(3x) = cos(8x) + cos(2x)
Then the equation simplifies to
cos(8x) + cos(2x) + sin(x) = cos(8x)
cos(2x) + sin(x) = 0
Also recall that
cos(2x) = 1 - 2 sin²(x)
so the equation is quadratic in sin(x) and can be factorized:
1 - 2 sin²(x) + sin(x) = 0
2 sin²(x) - sin(x) - 1 = 0
(2 sin(x) + 1) (sin(x) - 1) = 0
Solve for x :
2 sin(x) + 1 = 0 or sin(x) - 1 = 0
sin(x) = -1/2 or sin(x) = 1
[x = arcsin(-1/2) + 2nπ or x = π - arcsin(-1/2) + 2nπ] or x = arcsin(1) + 2nπ
(where n is any integer)
x = -π/6 + 2nπ or x = -5π/6 + 2nπ or x = π/2 + 2nπ
please help me with this problem !
Use the drawing tools to form the correct answer on the graph.
Every day the ocean has two low tides and two high tides. Function grepresents the height, in feet, of the water level in a cove relative to the
average sea level. Let trepresent the number of hours elapsed since the water height was equal to the average sea level after a low tide.
g(t) = 4sin(t)
Plot the points where g(t) is equal to the average sea level.
Answer:
The sinusoidal function that represent the height of the water level, is presented as follows;
[tex]g(t) = 4 \cdot sin \left(\dfrac{\pi}{6} \cdot t \right)[/tex]
Where;
t = The number of hours since the water height was the average sea level height
The graph of g(t) showing the points where g(t) = The average see level, created with MS Excel is attached
Step-by-step explanation:
Answer:
put a dot on points
(0,0)
(0,6)
(0,12)
Step-by-step explanation:
help asap answer ----------------
Answer:
[tex]f^-^1(f(3.14))=3.14[/tex]
[tex]f(f(-7))=5[/tex]
Step-by-step explanation:
Hi there!
[tex]f^-^1(f(x))=x[/tex]
Therefore, [tex]f^-^1(f(3.14))=3.14[/tex]
[tex]f(f(-7))[/tex]
The table tells us that f(-7) is equal to -12.
[tex]f(-12)[/tex]
The table also tells us that f(-12) is equal to 5.
[tex]5[/tex]
I hope this helps!
Can someone help me please like please I need to turn it in like in 10 minutes
Use linear combination to solve for x and y.
2x+4y=-4
3x+5y=-3
Dautienbanchuyenvexophuongtrinhthu1saudothevaophuontrinhthu2,thuchiencacbuoc
chuyenvedoidaularaketquanhe
Samantha found a great deal on sweatshirts at the mall and bought 5 sweatshirts at the
Super Duper sale price. Allison went the next day, but the sale was over, so she only bought
2 sweatshirts and paid $30 more per sweatshirt than Samantha. If the total cost of all 7
sweatshirts was $340, how much did one sweatshirt cost at the Super Duper sale price?
Answer:
$40
Step-by-step explanation:
You have two sweatshirts that cost $30 more the day after.
First, you do [tex]340 -(2*30)[/tex]
Second, you divide what you got above ($280), by 7 and voila, you have $40 per sweatshirt.
SOMEONE HELP ME PLEASE
Answer:
3/5 * 3/5 = 9/25 = .36 = 36%
Step-by-step explanation:
Use elimination to solve the system 4x + 7y = –14 and 8x + 5y = 8 for x. Round to the nearest tenth.
Answer:
x = 3.5
y = - 4
Step-by-step explanation:
2(4x + 7y = -14)
8x + 14y = -28
8x + 5y = 8
- (8x + 14y = -28)
--------------------------
- 9y = 36
y = 36/-9
y = - 4
4x + 7y = - 14
4x + 7(- 4) = - 14
4x -28 = - 14
4x = 14
x = 14/4
x = 3.5
Suppose a normal distribution has a mean of 98 and a standard deviation of 6. What is P(x < 104)?
A. 0.16
B. 0.975
C. 0.84
D. 0.025
Answer:
Step-by-step explanation:
If the mean is 98, then 104 is only standard deviation away. If we are looking for the values less than this, we have the areas under the normal curve of 34%, 34%, 13.5%, 2.35%, .15% which add to 84%, or as a decimal, .84, choice C.
The z-score of the normal distribution P ( x ≤ 104 ) = 0.84
What is a z-score?The relationship between a value and the mean of a set of values is expressed numerically by a Z-score. The Z-score is computed using the standard deviations from the mean. A Z-score of zero indicates that the data point's score and the mean score are identical.
The Z-score is calculated using the formula:
z = (x - μ)/σ
where z: standard score
x: observed value
μ: mean of the sample
σ: standard deviation of the sample
Given data ,
Let the z-score of the distribution be z
And , the mean be μ = 98
And , the standard deviation be σ = 6
where z = (x - μ)/σ
So , P ( x ≤ 104 ) = [ P ( x - 98/6 ) ≤ 104 - 98 / 6 ) ]
On further simplification , we get
P ( x ≤ 104 ) = P ( x ≤ 1 )
Using a standard normal distribution table or calculator, we can find that the probability of a z-score less than 1 is approximately 0.8413. Therefore, the probability of x being less than 104 is approximately:
P(x < 104) = P(z < 1) ≈ 0.8413
So there is approximately an 84.13% chance that a value selected at random from this normal distribution will be less than 104
Hence , the probability is 0.84
To learn more about z-score click :
https://brainly.com/question/25638875
#SPJ7
Help Now Please!!!
Find The Volume Of This Cylinder
Answer:
502.4 m³.
Step-by-step explanation:
Formula: πr²h
4² = 16 x 10 = 160
160 x 3.14 (about π) ≈ 502.4 m³.
Hope this helps.
If there is something wrong, please let me know.
Answer:
160[tex]\pi[/tex] or
500[tex]m^{3}[/tex]
Step-by-step explanation:
[tex]\pi[/tex] x [tex]4^{2}[/tex] x 10 = 160[tex]\pi[/tex] or 500[tex]m^{3}[/tex]
To the nearest degree, find the measure of angle A?
Answer:
I would say 26 or 42 but i would o with 26
Step-by-step explanation:
Answer:
26
Step-by-step explanation:
[tex]arccos\left(\frac{18}{20}\right)[/tex] = 25.8
Anyone know the answer? Pls help
10 times what equals 2204622621.8488?
Answer:
220462262.18488
Step-by-step explanation:
1. 2204622621.8488/10 = 220462262.18488
Find x. PLEASE HELP ASAP
Answer:x=35.6
Step-by-step explanation:
look at the left triangle. I hope you're familiar with SOH, CAH and TOA.
sin 60°=O/(11√7)
so O= (11√7)sin 60°
now look at the triangle on the right.
cos 45=adjacent/x
cos 45=[(11√7)sin60°]/x
therefore, using ur calculator, you'll get x= [(11√7)sin60°]/cos 45
x=35.64407384
Quadrilateral MNTU below is a parallelogram. If m2 M = 4x + 6 and m2N = 2x + 30, what is the value of x?
Answer:
x=12
Step-by-step explanation:
im not 100% but i think you would get the answer by setting the equations equal to one another.
4x+6=2x+30
2x=24
x=12
During a sale, Cindy found boxes of dog biscuits on sale for $0.69 that had previously cost $2.23. What percentage is the discount?
Answer:
The dog biscuits are approximately 69% off.
Step-by-step explanation:
(1 - 0.69/2.23) * 100
(223/223 - 69/223) * 100
154/223 * 100 = 69%
what is the solution to the system of equation below y=2/5x-3 and X=_10
Answer:
read explanation
Step-by-step explanation:
since y=2/5x-3 we substitute x=10 in making it y=2/5*10-3
following PAMDAS we do multiplication first so 2/5*10=4.
so y=4-3 and then we subtract and get y=1. Hope this helps:> if you need more explanation message me. If not give this a heart for helping. Good luck.
WILL GET BRAINLEST WILL HAVE TI ZOOM IN THI SHIW WORK TOO PLSSS ASAP
Answer:
sin = 1.333333
cos = 0.75
If triangle BCD was reflected over the x-axis, what would be the coordinates of the new triangle's vertices?
A. (-1, 0), (-1, -2), (-4, 1)
B. (-1, 0), (-1, 2), (-4, 1)
C. (-1, 0), (-1, 2), (4, -1)
D. (1, 0), (-1, 2), (-4, 1)
on time 4 learning
Answer:
b the answer is B because
For the following right triangle, find the side length x
Answer:
x = 25
Step-by-step explanation:
b² + h² = x²
24² + 7² = x²
576 + 49 = x²
625 = x²
√625 = √x²
25 = x
Step-by-step explanation:
x² = 7² + 24²
x² = 49 + 576
x² = 625
x = 25
yea...we most def ain't learn this in class
Answer:
F. 300,000
Step-by-step explanation:
logically, it is decreasing by 1.
What is the multiplicative rate of change of the
exponential function shown on the graph?
81
2,
4
0
16
1
A
12
4
AN
8
1.
NI
-2.
2
-1.
9
x
(0,1)
1
-3 -2
-1
N
3
Answer:
The answer for thue would happened to be 2
-1.
Answer:
9/2
Step-by-step explanation:
Which of the following statement is false?
a. all real numbers are complex numbers.
b. all irrational numbers are real numbers.
c. all complex numbers are pure imaginary numbers.
d. all whole numbers are rational numbers
Answer:
c not all complex are imaginary
but all imaginary are complex
please brainlist
Answer:
C is False
Step-by-step explanation:
A complex number is represented by
[tex]z = a + bi[/tex]
A imaginary number is represented by
[tex]z = bi[/tex]
A complex number could include a real number so it cant be a pure imaginary number so C is False.
56 out of the 56 employees at the sports shop are part-time employees. What percentage of the employees at the sports shop work part-time?
Answer:
100%
Step-by-step explanation:
Since 56/56 employees at the sports shop work part time, that means 100% of them do, or all of them.
Which one of the following sets is real numbers?
A. |x| = -1
B. |x| < -1
C. |x| > -1
the area of a rectangle is given by 6x²+19x+15. if x represents 4m, what are the dimensions of the length and width of the rectangle?
Answer:
Length = 17m
Width = 11m
Step-by-step explanation:
Expression for the area of the rectangle = 6x² + 19x + 15
Factorising the quadratic expression
6x² + 19x + 15 = (6x² + 9x) + (10x + 15) = 3x(2x + 3) +5(2x + 3) = (3x + 5)(2x + 3)
x = 4m
Length = 3x + 5 = 3(4) + 5 = 12 + 5 = 17m
Width = 2x + 3 = 2(4) + 3 = 8 + 3 = 11m
didn't pay attention and now im stuck :/
Answer:
A (First One)
Step-by-step explanation:
Side AC Is Congruent By Side DF
Side CB Is Congruent By Side FE
Side AB Is Congruent By Side DE
(There's no angles shown so it can't be the second option.)
The diagram has lines on the sides, if it we're SAS then the triangle would have an angle.
Answer:
ΔABC≅ΔDEF by SSS Postulate
Step-by-step explanation:
Hi there!
We are given 2 triangles
And we want to prove them congruent
You may notice that AC and FD have the same tick markings, AB and ED have the same tick markings, and CB and FE have the same tick markings
This means that those sides are congruent
In other words,
AC≅FD
AB≅DE
CB≅FE
If we have 3 pairs of congruent sides, that is enough for one concurrency postulate called side-side-side (SSS), which states that if 3 sides of a triangle are congruent to 3 sides in another triangle, then those triangles are congruent
So the triangles are congruent, but we need to put their vertices in the correct order
So if we make the name of the first triangle ABC, then we need to find the corresponding vertices in the second triangle
So let's find those vertices
D is corresponding to A, as they are both in between line segments that have 1 and 2 tick markings on them
E is corresponding to B, as they are both between line segments that have 2 and 3 tick markings on them
And finally, F is corresponding to C, as they are both between line segments that have 1 and 3 tick markings on them
So the name of the second triangle is DEF
ΔABC≅ΔDEF by SSS Posulate
Hope this helps!
write the point-slope form of an equation of the line through the points (6,-1) and (5,7)
Answer:
y - 7 = -8 (x - 5)
Step-by-step explanation:
y2 - y1 / x2 - x1 7 - (-1) / 5 - 6 = -8
y - 7 = -8 (x - 5)
can someone help with this, and explain it as well
Answer:
WRS and VRT are vertical angles
Step-by-step explanation:
Vertical angles are formed by the same lines and share a vertex
WRS and VRT are vertical angles
Use the parabola tool to graph the quadratic function f(x)=−(x−2)2+4.
Answer:Use demos it could give you the answer
Step-by-step explanation:
