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
I don’t understand how to solve this
Answer:
42.1
Step-by-step explanation:
The height of the main triangle is,
h = 47√3/2 (since it's an 30-60-90 triangle)
so to find x,
tan(44) = h/x
x = h/tan(44)
x = 42.1 (rounded to the nearest tenth)
Answered by GAUTHMATH
simplify (-216mtn square)/(8mn)
Answer:
-27tn
Step-by-step explanation:
Use KIO (keep, inverse, opposite) then divide.
Select the false statement
A. Vertical angles are always congruent
B.Vertical angles are sometimes complimentary
C.Two right angles are always supplementary
D. Angles that form a linear pair are sometimes supplementary. Plz answer ASAP
Answer: D. Angles that form a linear pair are sometimes supplementary.
That is not true, linear pairs are always supplementary.
Answer:
D. Angles that form a linear pair are sometimes supplementary.
~OAmalOHopeO
PLZ HELP!! ASAP PLZ!! NO FILES.
Answer:
Slope is (1/4)
Step-by-step explanation:
The slope is calculated by (6-5)/(5-1)=1/4
Answer? Which one is it? 1 2 3 or 4
It's bottom left
It says let C represent the cost of a one-year membership.
C is 80 in order to represent the day you must divide it by 10.
which gives one box for day and 10 boxes for year
Please help me solve this guys
Answer:
Factored Form: y=(x+1) ( x+3)y=(x+1)(x+3)
X-intercepts: (-1,0), (-3,0)(−1,0),(−3,0)
Axis of Symmetry: x= -2x=−2
Vertex: (-2,-1)(−2,−1)
Domain: (\begin{gathered}(-\infty , \infty ), ( x | x ER)\\\end{gathered}
(−∞,∞),(x∣xER)
Range: y > =-1y>=−1
The sum of 2 consecutive integers 117 what are the integers
Answer:
58,59
Step-by-step explanation:
Let x be the first integer
x+1 be the next consecutive integer
x + x+1 = 117
2x+1 = 117
2x +1-1 =117-1
2x = 116
2x/2 = 116/2
x = 58
x+1 = 59
Helpppppp pleaseeee anyoneeeee!!!!!
Answer:
Create a function representing number of published articles per month:
[tex]a=12m+60[/tex]
Where:
a = total number of articles publishedm = number of months12 = slope = number of articles published per month60 = y-intercept = number of published articles at the start (month 0)Now substitute in the values of m to get the a-value:
m = 1 → a = 12(1) + 60 = 72m = 3 → a = 12(3) + 60 = 36 + 60 = 96m = 4 → a = 12(4) + 60 = 48 + 60 = 108m = 9 → a = 12(9) + 60 = 108 + 60 = 168Joanna bakes a cake in the shape of a
cylinder. The cake is 10 inches in
diameter and 4.5 inches tall. She
wants to put frosting on the entire
cake that is not resting on the tray.
How many square inches of frosting
will she need? im confused on how to do the work. please answer quickly
Answer:
total surface area = 298.45105 m2
lateral surface area = 141.37155 m2
top surface area = 78.53975 m2
bottom surface area = 78.53975 m2
Step-by-step explanation:
Joanna will need approximately 298.3 square inches of frosting to cover the entire cake.
To calculate the amount of frosting Joanna will need for the entire cake, we first need to find the surface area of the cylindrical cake.
The formula for the surface area of a cylinder is given by:
Surface Area = 2πr² + 2πrh
Where r is the radius of the base and h is the height of the cylinder.
Given that the diameter of the cake is 10 inches, we can find the radius by dividing it by 2: r = 10/2 = 5 inches.
Plugging in the values, we have:
Surface Area = 2π(5)² + 2π(5)(4.5)
Simplifying the equation:
Surface Area = 2π(25) + 2π(22.5)
Surface Area = 50π + 45π
Surface Area = 95π
To find the actual numerical value, we can approximate π as 3.14:
Surface Area ≈ 95 * 3.14
Surface Area ≈ 298.3 square inches
To learn more about cylinder click on,
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5 + 8n = 7(-7 + 4n) -6
Answer:
n = 3
Step-by-step explanation:
Given
5 + 8n = 7(- 7 + 4n) - 6 ← distribute parenthesis on right side
5 + 8n = - 49 + 28n - 6 ( subtract 28n from both sides )
5 - 20n = - 55 ( subtract 5 from both sides )
- 20n = - 60 ( divide both sides by - 20 )
n = [tex]\frac{-60}{-20}[/tex] = 3
PLEASE ILL MAKE BRAINIEST!!!
If the dimensions of a rectangle ABCD are 15 x 12, what is the area of rectangle BEFD?
Answer:
The area of rectangle BEFD is 180 square units.
Step-by-step explanation:
After checking the figure given, we have the following information:
[tex]AD = 15[/tex], [tex]AB = 12[/tex], [tex]BC = 15[/tex], [tex]CD = 12[/tex]
By Pythagorean Theorem, we determine the length of the line segment BD:
[tex]BD = \sqrt{AB^{2}+AD^{2}}[/tex] (1)
[tex]BD = \sqrt{12^{2}+15^{2}}[/tex]
[tex]BD = 3\sqrt{41}[/tex]
In addition, we know the following characteristics of the rectangle BEFD:
[tex]BD = EF[/tex], [tex]EF = EC + CF[/tex], [tex]BE = FD[/tex] (2), (3), (4)
By Pythagorean Theorem:
[tex]BC^{2} = BE^{2}+EC^{2}[/tex] (5)
[tex]CD^{2} = CF^{2}+DF^{2}[/tex] (6)
By (3), (4), (5) and (6):
[tex]BC^{2} = BE^{2} + EC^{2}[/tex] (7)
[tex]CD^{2} = (EF-EC)^{2} + BE^{2}[/tex] (8)
By (7) in (8):
[tex]CD^{2} = (EF-EC)^{2}+ (BC^{2}-EC^{2})[/tex]
[tex]CD^{2} = EF^{2}-2\cdot EF\cdot EC + EC^{2}+BC^{2}-EC^{2}[/tex]
[tex]CD^{2} = EF^{2}-2\cdot EF\cdot EC +BC^{2}[/tex]
Then, we clear [tex]EC[/tex]:
[tex]2\cdot EF\cdot EC = EF^{2} + BC^{2} - CD^{2}[/tex]
[tex]EC = \frac{EF^{2}+BC^{2}-CD^{2}}{2\cdot EF}[/tex]
If we know that [tex]EF = 3\sqrt{41}[/tex], [tex]BC = 15[/tex] and [tex]CD = 12[/tex], then the length of the segment [tex]EC[/tex] is:
[tex]EC = \frac{75\sqrt{41}}{41}[/tex]
And the length of the line segment [tex]CF[/tex] is:
[tex]CF = EF - EC[/tex]
[tex]CF = 3\sqrt{41}-\frac{75\sqrt{41}}{41}[/tex]
[tex]CF = \frac{48\sqrt{41}}{41}[/tex]
And the length of the line segment [tex]DF[/tex] is determined by Pythagorean Theorem:
[tex]FD = \sqrt{CD^{2}-CF^{2}}[/tex]
[tex]FD = \sqrt{12^{2}-\left(\frac{48\sqrt{41}}{41} \right)^{2}}[/tex]
[tex]FD = \frac{60\sqrt{41}}{41}[/tex]
And the area of the rectangle is determined by the following formula:
[tex]A = FD\cdot EF[/tex]
[tex]A = \left(\frac{60\sqrt{41}}{41} \right)\cdot (3\sqrt{41})[/tex]
[tex]A = 180[/tex]
The area of rectangle BEFD is 180 square units.
Decide!!!!!!!!!!!!!!!!
Answer:
6 + 5 = 11Step-by-step explanation:
6 + 2 = 4, given
2 → 5, move two matchsticks, #10 and #124 → 11, move one matchstick, #186 + 5 = 11, correct
Also with explanation
helppppppppppppppppppp helppppppppppppp
HOPE ITS HELPFUL ^_^
•RHONAfind the area of triangle
i. b=6cm ,h=4cm
ii. b=5cm ,h=7cm
iii. b=8.4 cm ,h=5cm
answer
[tex]i.12cm {}^{2} [/tex]
[tex]ii.17.5cm {}^{2} [/tex]
[tex]iii.21cm {}^{2} [/tex]
Answer:
Step-by-step explanation:
What are we supposed to do? You already have the answers and they’re all correct if that’s what you wanted to know
Does Anybody Know The Answer?
Yes. When a graph has more than one line it is a piece wise graph.
The following house is called an A-frame house because it looks like the letter A from the front.
Suppose that all edges of this A-frame house measure 6.5 yards, and the height of the house is 5.6 yards.
What is the area covered by the roof? [Type your answer as a number. Do not round.]
__ square yards
The area covered by the roof would be 84.5 square yards.
How to calculate the area covered by the roof of the house?To calculate the area covered by the roof the formula that should be used would be the formula for the area of a square;
That is ;
Area = 2(length×width)
= 2(6.5×6.5)
= 2(42.25)
= 84.5 yards²
Learn more about area here:
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In a right triangle, two sides are 12 and 13. Find the measure of the third side. Consider all cases.
Answer: Approximately 17.69
Step-by-step explanation:
The formula needed to find the third side of this equation is the Pythagorean theorem. Which is as follows:
[tex]a^2+b^2=c^2\\c=\sqrt{a^2+b^2}[/tex]
The difference between the two is that the first one after you do [tex]a^2+b^2[/tex] you still need to square root the answer you get to get the third side, aka. the hypotenuse. If you do the second method, you get the answer after you do the calculation which is a lot easier.
Below are the calculations needed to be made in both ways:
[tex]12^2+13^2=313\\\sqrt{313}= 17.69[/tex] 17.69 was rounded to the hundredths place.
[tex]\sqrt{12^2+13^2}=17.69[/tex] once again this answer was rounded to the hundredths place.
[tex]a^2+b^2[/tex] are respectively for the sides of the triangles.
[tex]c^2[/tex] is respectively for the hypothenuse, which is the longest side, and across from the right angle (located by a box).
Answer:
5 or 17.69
Step-by-step explanation:
1st case senario:
c^2=a^2+b^2
c^2=12^2+13^2
c^2=144+169
c^2=313
c^2=[tex]\sqrt{313}[/tex]
c=17.69
2nd case senario:
144+b^2=169
b^2=169-144
b^2=25
b^2=[tex]\sqrt{25}[/tex]
b+5
How would two billion, nine hundred seventy-six million, twelve thousand, eight be written
write the point-slope form of the equation of the line through the given points (0,4) and (-5,-4)
Answer:
y - 4 = 8/5 (x - 0)
Step-by-step explanation:
first, find the slope using the points given ((0,4) and (-5,-4))
use the following formula to find the slope:
m= y2 - y1/x2 - x1
using this formula you should get the following:
m= -4-4/-5-0 = -8/-5 = 8/5
using the point (0,4) and the slope, it into the slope-point form (y-y1=m(x-x1)
the answer should be: y - 4 = 8/5(x - 0)
an expression that equals to 6/5
Answer:
(3+3) / (2+3) = 6/5
:)))
..........
Please help me solve this quickly!
Answer:
33.80
Step-by-step explanation:
AB = BC = AD√2
AB = BC = 7√2
AD = DC
AC = 2AD
perimeter = AC + AB + BC
= 2AD + 2AB
= 2(7) + 2(7√2)
= 14 + 14√2
≈ 33.80
Answer:
33.8
Step-by-step explanation:
45-45-90 degree triangle rules states that the sides that are opposite the angles measure 45 degrees have the same value. That means that BD has the same value as AD, which is 7. Since triangle BDC is also a 45-45-90 degree triangle, DC is equal to BD, which is 7. We have the value of AC, which is 7+7=14. Now, we can use the Pythagorean theorem to figure out BC and AB. We know that [tex]DC^2+BD^2=BC^2[/tex]. We know that DC and BD is equal to 7, so we can simplify that to [tex]49+49=BC^2[/tex], and we can further simplify that to [tex]BC=\sqrt{98}[/tex]. This is also equal to [tex]7\sqrt{2}[/tex]. Since BC is also equal to AB because of 45-45-90 degree triangle rules, we have the perimeter of the triangle as
[tex]7\sqrt{2} + 7\sqrt{2}+14[/tex], which is equal to [tex]14\sqrt{2} + 14[/tex]. We can simplify 14 times the square root of 2 as 19.8 (rounded to 2 decimal places). We have the answer as 19.8 + 14, which is 33.8.
Hii, please help me with this question I keep getting an option that isn't there.
A cylindrical piece of iron pipe is shown below. The wall of the pipe is 1.25 inch thick:
The figure shows a cylinder of height 16 inches and diameter 6 inches.
What is the approximate inside volume of the pipe?
a. 88 cubic inches
b. 49 cubic inches
c. 142 cubic inches
d. 154 cubic inches
The volume of this pipe considering the thickness of the pipe is 154 cubic inches.
How do you calculate the volume of the pipe?The general formula to calculate the volume of a cylindric object such as a pipe is:
V = πd^2h/4In this formula, d represents the diameter and h represents the height.
What is the diameter?The external diameter is 6 inches; however, the pipe is 1.25 inches thick, which implies the real internal diameter is 3.5.
6 inches - 2.5 (1.25 x 2) = 3.5Now, let's calculate the volume:
V = πd^2h/4V= π (12.25 x 16)/4V= π (196)/4V= 615.713 / 4 = 153.93 which can be rounded as 154 cubic inches.Learn more about cylindric in: https://brainly.com/question/14965384
Answer:
D. 154 cubic inches
Step-by-step explanation:
Please help! Thank you.
Answer:
B
Step-by-step explanation:
x((7/2)-(7/3))=y+x
x(7/6)=y+x
7x=6y+6x, x=6y. y/x=1/6
Need help ASAP rocky ! Help needed
Answer:
x/x∈R,x≤5 1/6
Step-by-step explanation:
if 7/12 has the same value as a fraction x/60.say what number is x?
4. Find the center and radius of the circle given by this equation: x2 – 8x + y2 + 4y - 16 = 0
Answer:
Center ( 4 , -2) and r = 6
Step-by-step explanation:
x² - 8x + y² + 4y - 16 = 0
x² - 8x + y² + 4 y = 16
x²- 2*4x + y² + 2 *2y = 16
(x² - 2*4x + 16 ) - 16 + (y² + 2*2y + 4) -4 = 16
(x - 4)² + (y + 2)² = 16 + 16 + 4
(x - 4)² + (y -[-2])² = 36
(x- 4)² + ( y - [-2] )² = 6²
Compare with (x - h)²+ (y - k)² = r²
Center ( 4 , -2) and r = 6
The length of a rectangle is six times its width. If the area of the rectangle is 384^2, find its perimeter.
Answer:
Perimeter, P = 112 meters
Step-by-step explanation:
Let the length of the rectangle be L.Let the width of the rectangle be W.Translating the word problem into an algebraic expression, we have;
L = 6W ...... equation 1
Given the following data;
Area of rectangle = 384 m²To find the perimeter of the rectangle;
First of all, we would determine the dimensions of the rectangle using its area.
Mathematically, the area of a rectangle is given by the formula;
Area of rectangle = LW ..... equation 2
Substituting eqn 1 into eqn 2, we have;
384 = 6W(W)
384 = 6W²
Dividing both sides by 6, we have;
W² = 384/6
W² = 64
Taking the square root of both sides, we have;
W = √64
Width, W = 8 meters
Next, we would find the length;
L = 6W
L = 6 * 8
Length, L = 48 meters
Lastly, we would determine the perimeter of the rectangle using the above dimensions;
Mathematically, the perimeter of a rectangle is given by the formula;
Perimeter = 2(L + W)
Substituting the values into the formula, we have;
Perimeter, P = 2(48 + 8)
Perimeter, P = 2(56)
Perimeter, P = 112 meters
Which function has a double root of 3 and a double root of -2
can someone help me with this one ....
Answer:
-5, - 2, 3
Step-by-step explanation:
y=2x+3, y=-7, x=-5; y=-1, x=-2, y=9, x=3
