The simplified value is 8*cos^4(x) = 3+ 4 cos2x + cos 4x.
What is power reduction identity?The trigonometric power reduction identities allow us to rewrite expressions involving trigonometric terms with trigonometric terms of smaller powers. This becomes important in several applications such as integrating powers of trigonometric expressions in calculus.
Given:
Using the power reduction identity, we have that:
cos² x= 1/2( 1+ cos 2x)
cos^4(x) = (cos² x)²= (1/2( 1+ cos 2x))²
cos^4(x) = 1/4( 1+ cos² 2x+ 2 cos (2x))
Again, cos² 2x= 1/2( 1+ cos 4x)
cos^4(x) = 1/4( 1+ 1/2( 1+ cos 4x)+ 2 cos (2x))
cos^4(x) = 1/4( 1+ 1/2 +1/2 cos 4x+ 2 cos (2x))
cos^4(x) = 1/4( 3/2 + 2 cos2x + 1/2 cos 4x)
8*cos^4(x) = 8*1/4( 3/2 + 2 cos2x + 1/2 cos 4x)
8*cos^4(x) = 2( 3/2 + 2 cos2x + 1/2 cos 4x)
8*cos^4(x) = 3+ 4 cos2x + cos 4x
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find the coordinates of D' after a Glide reflection of the triangle: translation 1 unit up and 5 units left and reflection across y= 3. Write your answer in (a,b). Part 2a
Answer:
D' = (-2, 1)
Step-by-step explanation:
Translating the point D one unit up and five units left moves it to (-2, 5)
Reflecting it across y=3 moves it from (-2, 5), to (-2, 1)
Answer:
D = (-2, 1)
This answer is 100% right hope it helps
The equation __ describes the relationship
Answer:
y= 1/3x
Step-by-step explanation:
points on the graph
(0,0), (3,1)
function as per above two points:
y= 1/3x
A box of 120 crayons contains variations of three colors: blue, red, and purple. The ratio of blue crayons to red crayons is 11:2, and the ratio of the number of red crayons to purple crayons is 2:7. If all of the purple crayons were removed, how many crayons would be left in the box?
Answer: there would be 106,am not sure
Step-by-step explanation:
1. Uma escada possui comprimento igual a 30m. Sabe-se que ela se encontra encostada em um muro, formando com este um ângulo de 60º. Podemos afirmar que a altura da escada, em m. é igual am:
Answer:
The height of the ladder is 15 meters.
Step-by-step explanation:
To find the height of the ladder, we just need to use the cosine relation of the 60 degrees angle.
The adjacent side to the angle is the height of the ladder, and the hypotenuse of the triangle created is the length of the ladder. So, we have that:
cos(60) = height / length
0.5 = height / 30
height = 30 * 0.5 = 15 meters
The height of the ladder is 15 meters.
Here is a map of a town.
The map shows a centimetre ruler.
5 km is represented by 1 cm.
Find the real-life distance between the ice rink and the museum.
Answer:
10km
Step-by-step explanation:
2x5=10km
Pleaseee help meee struggling currently
Answer: 2908.92435 inches.
Step-by-step explanation for shape 1: A = 2(wl + hl + hw) = 2 · (30 · 13 + 13 · 13 + 13 · 30) = 1,898 inches.
Step-by-step explanation for shape 2:
Using the formulas:
A=2AB+(a+b+c)h
AB=s(s﹣a)(s﹣b)(s﹣c)
s=a+b+c
2
Solving for A:
A=ah+bh+ch+1
2﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4=9·30+13·30+9·30+1
2·﹣94+2·(9·13)2+2·(9·9)2﹣134+2·(13·9)2﹣94≈1010.92435
Step-by-step explanation for total volume: 2908.92435 inches.
Answer: 6825 in^3
Step-by-step explanation:
First divided the whole shape into two shapes.
The first shape will be a rectangular prism and the second shape will be a triangular prism.
The rectangular prism will have a length of 13, a width of 30 and the height of 13.
Now find the volume of the rectangular prism by multiplying the length by the width then by the height.
V= 13 * 30 * 13
V = 5070
This means the volume of the rectangular prism is 5070 cubic inches.
Now will will need to find the volume of the triangular prism.
The triangular prism has a triangle at the base, with a base of 9 and a height of 13. If you multiply the the area of the base by the whole height of the triangular prism which is 30 then you will get the volume.
Find the area of the base.
The area is base time height times 1/2.
A = 9 * 13 * 1/2
A = 58.5
Now multiply the area by 30.
58.5 * 30 = 1775
Finally, add both volumes to find the full volume of the figure.
5070 + 1775 = 6825
Please answer correctly !!!! Will mark brainliest !!!!!!!!!
Answer:
[tex]=\left(x-4\right)^2[/tex]
Step-by-step explanation:
[tex]x^2-8x+16\\\mathrm{Rewrite\:}x^2-8x+16\mathrm{\:as\:}x^2-2x\cdot \:4+4^2\\x^2-8x+16\\\mathrm{Rewrite\:}16\mathrm{\:as\:}4^2\\=x^2-8x+4^2\\\mathrm{Rewrite\:}8x\mathrm{\:as\:}2x\cdot \:4\\=x^2-2x\cdot \:4+4^2\\\mathrm{Apply\:Perfect\:Square\:Formula}:\quad \left(a-b\right)^2=a^2-2ab+b^2\\a=x,\:b=4\\=\left(x-4\right)^2[/tex]
Answer:
0
Step-by-step explanation:
Since it is asking you to factor out the quadratic, you need to make it equal zero first. -4 times -4 is both 16 and -8. So that means (x-4)^2
can someone do my ixl its 6th grade math!! only 3 and you have to get 85 and higher i will give 25 points!! and mark as brainlist
Answer:
Okkk I will answer
Answer:
what question do you have?
Step-by-step explanation:
Find the sum of the first eight terms of the geometric series 1 + 2 + 4 + ...
Answer:
The sum of all of the terms would be 255
Step-by-step explanation:You would continue to multiply all of the answers by 2 until you hit 128. Then you would add all of them together 128+64+32+16+8+4+2+1=255
Need help ASAP!! Thank youu!
Answer:
The answer is 7.
Step-by-step explanation:
If you want to find what FE is, you have subtract GF from GE (GE - GF = FE).
Since GE = 13 and GF = 6, you have to subtract 6 from 13 which equals 7.
(13 - 6 = 7)
Which expression has a value of 15 when n=7 ?
19-28/n
n=7
19-28/7
19-4
=15
Answer:
d for the lazy people like me :D PROPS TO THE PERSON ON TOP OF ME
Step-by-step explanation:
2. A hemispherical water tank with a volume of 2094 m will have a radius of which
length?
?
a. 5 m
b. 25 m
c. 2.5 m
d. 10 m
You need to solve a system of equations. You decide to use the elimination
method. Which of these is not allowed?
3x-2y = 7 Equation 1
3x+4y= 17 Equation 2
A. Subtract equation 2 from equation 1.
B. Subtract the left side of equation 2 from the left side of equation
1.
C. Multiply equation 1 by 2. Then add the new equation to equation
2.
Answer:
Step-by-step explanation:
Both B and C would be using e
Option (B) Subtracting the left side of equation 2 from the left side of equation 1 would be the correct choice.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have two linear equations or systems of equations:
3x-2y = 7 Equation 1
3x+4y= 17 Equation 2
As we know, in the elimination method:
We try to eliminate the variables at a time by making a similar coefficient of the x or y.
In option (B) Subtract the left side of equation 2 from the left side of equation 1.
It is not allowed to perform because first, we have to make the coefficient of y similar.
Thus, option (B) Subtracting the left side of equation 2 from the left side of equation 1 would be the correct choice.
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describe fully the single transformation that maps triangle a onto triangle b
Answer:
Reflection about y=2
Step-by-step explanation:
Triangle A should be reflected about y=2 to map it onto Triangle B.
Answer:
reflection across y=2
Step-by-step explanation:
To number the apartments in a building, metal plates with digits were used: one digit on each plate. How many plates were used to number 136 apartments in the building?
Answer:
301 plates
Step-by-step explanation:
For numbers between 0 and 9, 1 plate was used each.
This means that 10 plates were used.
For numbers between 10 and 99, 2 plates were used for each.
This means that the number of plates used will be:
2 * 90 = 180 plates
For numbers between 100 and 136, 3 plates were used for each.
This means that the number of plates used is:
3 * 37 = 111 plates
The total number of plates used is therefore:
10 + 180 + 111 = 301 plates
301 plates were used in total.
whats the answer to 5^-2
Hey!!
Solution,
(5)^-2
=1/5^2
=1/25
The answer is 1/25
hope it helps
Good luck on your assignment
Ping lives at the corner of 3rd Street and 6th Avenue. Ari lives at the corner of 21st Street and 18th Avenue. There is a gym Two-thirds the distance from Ping's home to Ari's home.
x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1
y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1
Where is the gym?
Answer: (15th street, 14th Avenue)
Step-by-step explanation:
Given the following :
Ping's residence = (3rd street, 6th Avenue)
Ari's residence = (21st street, 18th Avenue)
Gym location = 2/3 the distance of Ping's residence to Ari's residence
So, distance between Ping's home to Ari's home
Distance = (21st street, 18th Avenue) - (3rd street, 6th Avenue)
Distance = (21 - 3) street, (18 - 6) avenue
Distance between ping and Ari = (18th , 12th )
Gym distance = 2/3 of distance between ping and Ari
Gym distance = 2/3 × (18), 2/3 ×(12)
Gym distance = (12, 8)
Gym location = Ping's location + gym distance
Gym location = (3rd street, 6th Avenue) + (12th street, 8th Avenue)
Gym location = (15th street, 14th Avenue)
Answer:
d) 15th Street and 14th Avenue
will mark brainliest!! factor the following equation: f(x)=3x²+7x+2
Answer:
(x + 2) (3x + 1)
Step-by-step explanation:
3x² + 7x + 2
3x² + 6x + x + 2
3x(x + 2) + 1(x + 2)
(x + 2) (3x + 1)
Which ordered pair comes from the table?
Can you pls help i really NEED IT
WANT BRAINIEST
Answer:
V =13/150 yd^3
Step-by-step explanation:
The volume of a rectangular prism is given by
V = l*w*h
V = 1/2*( 13/15)* 1/5
V =13/150 yd^3
Answer:
13\150 yd³
Step-by-step explanation:
V=height×weight×legth
1\2×13\15×1\5=13\150 yd³
This chart shows the growth of a maple tree. If the tree's height increases in this same pattern, what will be the height of the tree, in inches, after 8 months?
Months
Height of Tree
1
10 inches
2
13 inches
3
16 inches
4
19 inches
Answer:
31 inches
Step-by-step explanation:
you can get this answer by 2 ways. one is using number patterns.
find the difference between each of the heights.
13-10=3
16-13=3
19-16=3
therefore the common difference is 3
now create a number pattern.
first term + common difference× (n-1)= nth term
a+(n-1)d
let's check this with the 2nd month
10+ 3× (2-1)
10+3=13
in second month 13 inches
so this pattern works
let's find the height in 8th month
10+ 3(8-1)
10+ 21=31 inches
height in 8th month is 31 inches.
you can find this by just adding too. but forming an equation is always good and safe
Estimate the solution to the system of equations.
You can use the interactive graph below to find the solution.
-3x + 3y = 9
2x – 7y = -14
Answer:
x= -7/5 y=8/5
Step-by-step explanation:
1. choose a variable to eliminate (i chose 6)
2. multiply the first equation by 2 and the second equation by 3
3. now you have
-6x+6y=18
6x-21y=-42
and the x's can now cancel out when you add the equations together
4. after adding the equations, you get
-15y=-24
5. solve for y (y= 8/5)
6. now plug in 8/5 for the y in one of the original equations to solve for x. (i chose the first one)
7. -3x+3(8/5)=9
-3x+24/5=9
-3x=21/5
x= -7/5
What segment is a reflection of segment ab over the line x=1
Answer:
The correct answer is: (Line segment E F)
what is 9x=4.5 if u can solve this u are very smart
Answer:
x = 1/2
Step-by-step explanation:
9x=4.5
Divide each side by 9
9x/9 = 4.5/9
x = 45/90
x = 1/2
Answer:
x = 1/2 or x = 0.5
Step-by-step explanation:
9x = 4.5/9
= 45/90
= 1/2 or 0.5
Hope this helps, and please mark me brainliest if it does!
Simplify the following expression (x-8y)-(2x-4y)
Answer:
-x - 12y
Step-by-step explanation:
(x-8y)-(2x-4y)=
x-8y-2x-4y=
x-2x-8y-4y=
-x - 12y
Answer: -x - 4y
Step-by-step explanation:
(x-8y)-(2x-4y)
x-8y-2x+4y
-x-4y
21) Natalie kicked a soccer ball. The equation ℎ=−162+50 describes the height of the ball t seconds after it was kicked. Approximately how many seconds went by before the ball hit the ground?
To find the time until the ball hits the ground, you need to solve the quadratic as the height equals zero.
0 = -16t^2+50t
This gives us a classing quadratic that you can factor or use the quadratic formula to solve.
x = 0, x = 25/8
If you graph this, think of y = 0 as the ground, so when the parabola intersects the x-axis on the right that represents how much time would have passed.
Hope this helps you out! Good luck with your homework! Stay safe and stay healthy.
Please answer correctly !!!!! Will mark brainliest !!!!!!!!
Answer:
k(-7) = = -89
Step-by-step explanation:
k(t) = 10t -19
Let t = -7
k(-7) = 10*-7 -19
= -70-19
= -89
Answer:
-89
Step-by-step explanation:
K(t) = K(-7)
10 is being multiplied by t. t = -7
so:
10(-7) = -70
-70 - 19 = -89
Hope this helps!
If 48 % of students in a certain college are female and there are 1,440 female students, what is the total number of students in the college? Please show work
Answer:
The total number of students in the college is 3,000.
Step-by-step explanation:
[tex]\frac{48}{100}=\frac{1,440}{x}[/tex] Set up a proportion.
[tex]48x=144,000[/tex] Cross-multiply.
[tex]x=3,000[/tex] Divide both sides by 48.
damian rides his bike 38 miles each week for 15 weeks how many total miles did he ride in 15 weeks
Answer:
570 miles
Step-by-step explanation:
If Damian rides 38 each week and we want to know how much it was for 15 weeks, then we just multiply the two to get 570 miles in a 15 week period.
Answer:570
Step-by-step explanation:
38 times 15= 570
Alegbra 4 questions giving brainlist!
Answer:
1) 4
2) 1
3) -7
4) 13
Step-by-step explanation:
Instructions:
a) Subtract or add the slope from each side
( it doesn't matter which one you pick )
b) Subtract or add the # next to the slope from each side
( it doesn't matter which one you pick )
c) Divide Each number by the slope
d You have you answer
____________________________________________
1) 9x - 35 = - 7x + 29
+7x + 7x
_____________________
16x - 35 = 29
+ 35 +35
_____________________
16x = 64
_____________________
16 16
x = 4
2). - 2x - 2 = 9x - 13
+2x +2x
_____________________
- 2 = 11x - 13
+ 13 + 13
_____________________
11 = 11x
_____________________
11 11
1 = x
3). 3x + 29 = - 5x - 27
+5x + 5x
_____________________
8x + 29 = - 27
-29 -29
_____________________
8x = -56
_____________________
8 8
x = -7
4). x - 11 = 3x - 37
- x - x
______________________
-11 = 2x - 37
+37 +37
______________________
26 = 2x
_______________________
2 2
13 = x
Hope this helps! (:
