Step-by-step explanation:
Derivation using Product rule : -
To find the derivative of f(x) = sin 2x by the product rule, we have to express sin 2x as the product of two functions. Using the double angle formula of sin, sin 2x = 2 sin x cos x. Let us assume that u = 2 sin x and v = cos x. Then u' = 2 cos x and v' = -sin x. By product rule,
f '(x) = uv' + vu'
= (2 sin x) (- sin x) + (cos x) (2 cos x)
= 2 (cos2x - sin2x)
= 2 cos 2x
This is because, by the double angle formula of cos, cos 2x = cos2x - sin2x.
Thus, derivation of sin 2x has been found by using the product rule.
Answer:
2cos2x
Step-by-step explanation:
Using the Chain rule
[tex]\frac{d}{dx}[/tex] (sin2x)
= cos2x × [tex]\frac{d}{dx}[/tex] (2x)
= cos2x × 2
= 2cos2x
Mean of 72, 75, 78, 72, 73
to find the mean you add all the numbers together
72 + 75 + 78 + 72 + 73 = 370
then you divide by the number of numbers there are
370/5= 74
74
72+75+78+72+73 = 370
370/5 = 74
Find the value of x
Answer:
x = 17
Step-by-step explanation:
The hash marks indicate that the segment marked x+2 connects the midpoints of the sides of the triangle. Therefore, it is a "midline" and has half the length of the parallel base.
x +2 = 1/2(38)
x = 19 -2 . . . . . subtract 2
x = 17
What is an equation of the line that passes through the points (-6, -4)(−6,−4) and (3, 8)(3,8)?
Answer:
y = 4/3x + 4
Step-by-step explanation:
-4 - 8 / -6 - 3
-12 / -9
4/3 is slope
y = 4/3 x + b so we need to find b
Put one of the points in for y and x.
-4 = 4/3 (-6) + b
-4 = -8 + b
4 = b
y = 4/3x + 4
If f(x) = -3x - 5 and g(x) = 4x - 2, find (f - g)(x).
A. (f- g)(x) = -7x - 3
B. (f- g)(x) = x - 3
C. (f - g)(x) = -7x + 3
D. (f- g)(x) = x - 7
Answer:
A. (f-g)(x) = -7x -3
Step-by-step explanation:
(f -g)(x) = f(x) -g(x) = (-3x -5) -(4x -2)
= -3x -5 -4x +2
= -3x -4x -5 +2
(f -g)(x) = -7x -3
my Christmas present to you
Answer:
i can help u if u need help
Step-by-step explanation:
Answer:
it's not Christmas but OK.
Step-by-step explanation:
btw thx!!
slopes of a quadrilateral please hurry before a bot attacks me ive been attacked all day. Multippe choice.
Answer: 3rd one got it right on mine
Step-by-step explanation:
Select the correct answer.
Why do the hands on the clock form an angle?
OA.
The hands lie in the same circle.
OB.
The hands are two line segments that share the same endpoint.
Oc.
The hands are two line segments that are perpendicular to one another.
OD.
The hands lie in the same plane.
Answer:
Step-by-step explanation:
The hands are two line segments that share the same endpoint.
Lucia brought 13 2/5 pitchers of juice to a volleyball game, and the players drank 5 4/5
pitchers of it. How much juice is left?
Write your answer as a fraction or as a whole or mixed number.
Answer:
7 3/5 or 38/5
Step-by-step explanation:
13 2/5 - 5 4/5 = 38/5 = 7 3/5
Rotate the following triangle 90 degrees.
A(4, -3) B(-12, 8) C(6, -4)
Answer:
given vertices of triangle ABC
A(4, -3) B(-12, 8) C(6, -4)
Rotating through 90°
P (x , y) -----> P' (y , -x)
A(4, -3) ------> A' ( -3 , -4 )
B(-12, 8) -----> B' (8 , 12 )
C(6, -4) ------> C' (-4 , -6)
Find the fourth degree polynomial function with zeros 6,-6,6i
Answer:
See below
Step-by-step explanation:
6 is a solution to x-6=0, -6 is a solution to x+6=0, and 6i is a solution to x^2+36=0. So, we can do (x-6)(x+6)(x^2+36) to get (x^2-36)(x^2+36) which gets us x^4-1296. Therefore, the fourth degree polynomial with zeroes 6, -6, 6i is x^4-1296
Simplify this expression
9xy ^4 x 3x^3y
Answer: 27x by the power of 4 y by the power of5
Step-by-step explanation:
Answer:
Refers to attachment
Step-by-step explanation:
a grandmother 2 mothers and 2 daughters went to the cafe. they ordered one cup of coffee each. what was the total number of cups they ordered.
Answer:
5 cups of coffee
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
1 grandmother = 1 cups
2 mothers = 2 cups
2 daughters = 2 cups
2 + 2 + 1 = 5
-3(-3x-7)=48 please show work
Answer:
x = 3Step-by-step explanation:
-3(-3x - 7) = 48=> 9x + 21 = 48=> 9x = 48 - 21=> 9x = 27=> x = 3Conclusion:
Therefore, the answer is 'x = 3'.
Hoped this helped
[tex]BrainiacUser1357[/tex]
Answer:
−3(−3x−7)=48
Divide both sides by −3.
−3x−7= 48
Divide 48 by −3 to get −16.
−3x−7=−16
Add 7 to both sides.
−3x=−16+7
Add −16 and 7 to get −9.
−3x=−9
Divide both sides by −3.
x= −3 −9
Divide −9 by −3 to get 3.
x=3
Step-by-step explanation:
4/5=x/100 solve please
Answer:
x = 80
Step-by-step explanation:
4/5 = x/100
100 · 4/5 = 100 · x/100
100 · 4/5= x
80 = x
x = 80
Hence, The Answer is 80.
Solve |6x + 3| = 27.
A. x = 4 and x = -5
B. x = -4 and x = -5
C. x = -4 and x = 5
D. x = 4 and x = -4.
Answer:
it's d
.
hope I helped! I need to write more words so I can send this
Answer:
The answer is A
Step-by-step explanation:
|6x + 3| = 27
Use the definition of absolute value6x + 3 = 27
6x + 3 = -27
Subtract three from both sides of the equation.6x = 24
6x = -30
Divide both sides by 6.x = 4
x = -5
So:
x = 4, -5
A can contains 48 cups of fruit juice. How many gallons of fruit juice does the can contain?
Answer:
3
Step-by-step explanation:
In 2013, a State Library received a three-year grant to add 69,678 books to their
collection. During a used book sale, the library sold 430 books. If the collection
now is five times more than the original number of books, how many books did
the library hold before it received the grant?
The number of books the library holds before it received the grant is 17,312 books
Let the original number of books in the library be x
If the State Library received a three-year grant to add 69,678 books to their collection, the total number of books will be x + 69,678If during a used book sale, the library sold 430 books, the remaining books will be (x+69,678) - 430 = x + 69,248If the collection now is five times more than the original number of books, then;
x + 69,248 = 5x
5x - x = 69,248
4x = 69,248
x = 69,248 /4
x = 17,312
Hence the number of books the library holds before it received the grant is 17,312 books
Learn more on equations here: https://brainly.com/question/25678139
solve each equation by factoring 12p^2+78p-151= -7
Answer:
Ok so im not to sure but I think its 40.62 but i could be wrong since it was worded odd
Step-by-step explanation
Write and solve an equation for the following:
Answer:
x = 12
Step-by-step explanation:
The measures of ∠XYW and ∠WYZ would equal m∠XYZ.
[tex]3x + 2 + 72 = 110\\\rule{150}{0.5}\\3x + 74 = 110\\\\3x + 74 - 74 = 110 - 74\\\\3x = 36\\\\\boxed{x = 12}[/tex]
Hope this helps.
Determine whether the relation is a function. (8, 5), (6, "-2)," (4,-9), (2, "-6)," (4,7)
Yes Or No
Answer: No
Step-by-step explanation:
Because 4 is used 2 times in the x coordinates it is NOT a function
I need a step by step explanation please on this please so I can understand it better
Answer:
P = 29 units
Step-by-step explanation:
Let h represent the height of the triangle. Then 2h is the length of the base. The area is given by ...
A = 1/2bh
36 = 1/2(2h)(h) = h²
h = √36 = 6
base = 2h = 12
The base of the isosceles triangle is 12 units, and its height is 6 units.
__
The altitude line makes a right angle with the base, dividing it into two right triangles with sides of length 6. The hypotenuse (s) of each of those is given by the Pythagorean theorem as ...
s = √(6² +6²) = 6√2
Then the perimeter of the triangle is ...
P = base +2s = 12 +2(6√2) = 12(1 +√2) ≈ 28.97 ≈ 29
The perimeter of the triangle is about 29 units.
_____
Additional comment
The Pythagorean theorem tells you the square of the hypotenuse is the sum of the squares of the other two sides.
For an isosceles right triangle, this means the hypotenuse is √2 times the side length. (This is a useful relationship to remember, as it is used a lot in algebra and geometry problems.) The acute angles in such a triangle are 45°.
AtQ
[tex]\\ \rm\hookrightarrow \dfrac{1}{2}(2x)(x)=36[/tex]
[tex]\\ \rm\hookrightarrow x^2=36[/tex]
[tex]\\ \rm\hookrightarrow x=6[/tex]
Base=12Apply Pythagorean theorem
[tex]\\ \rm\hookrightarrow H^2=6^2+6^2=36+36=72\implies H=8.5[/tex]
Perimeter
2(8.5)+12=17+12=29unitsHow to find a and b in the equation below.
3(a+b)=28
Answer:
a equals and b equals 7
Step-by-step explanation
divide both side by 3 getting a+b=(28/3)
subtract b from both sides getting a=(28/3)-b
to solve for b its the same way so b=(28/3)-a
you can then substitute
[tex]\sf -8(6x+3)[/tex]
Answer:
[tex] - 8(6x + 3) = - 8 \times 6x + - 8 \times 3 \\ = - 48x - 24[/tex]
The expression 3.5d + 5 represents the number of miles Erin ran last week when she ran 5 miles on sunday and 3.5 miles each day after Sunday. The expression 2.5d+ 3 represents the number of miles Luis ran last week when he ran 3 miles on Sunday and 2.5 each day after Sunday what expression can be used to determine the total amount erin and Luis ran last week
Answer: 14 miles
Step-by-step explanation: 3.5d+5+2.5d+3
What is the common ratio for the geometric sequence below, written as a fraction? 768, 480, 300, 187. 5, … /.
The common ratio for the given geometric sequence, written as a fraction is [tex]\frac{5}{8}[/tex]
Given the following geometric sequence:
768, 480, 300, 187. 5To determine the common ratio for the given geometric sequence:
The common ratio of a geometric sequence refers to the ratio or constant factor between two (2) consecutive numbers in the sequence.
Mathematically, the common ratio of a geometric sequence is given by the formula:
[tex]C=\frac{T_{n+1}}{T_n}[/tex]
Substituting the given parameters into the formula, we have;
[tex]C = \frac{300}{480} \\\\C=\frac{30}{48} \\\\C=\frac{5}{8}[/tex]
Read more: https://brainly.com/question/13162487
The midpoint of \overline{\text{AB}} AB is M(0, -3)M(0,−3). If the coordinates of AA are (2, -5)(2,−5), what are the coordinates of BB?
The formating kinda screwed up
Using the mid-point concept, it is found that the coordinates of B are (-2, -1).
The mid-point of two points is the mean of the coordinates of each point.In this problem:
The points are: A(2, -5) and B(x,y).The mid-point is (0, -3).Applying the concept for both the x and y-coordinates, we have that:
[tex]\frac{x + 2}{2} = 0[/tex]
[tex]x + 2 = 0[/tex]
[tex]x = -2[/tex]
[tex]\frac{-5 + y}{2} = -3[/tex]
[tex]-5 + y = -6[/tex]
[tex]y = -1[/tex]
The coordinates of B are (-2, -1).
To learn more about the mid-point concept, you can take a look at https://brainly.com/question/10956693
Can someone plz help me? I really don’t get this
Answer:
D.
Step-by-step explanation:
The question is asking which expressions are the same. To find the answer, or rather confirm it, you should simplify each expression.
A. 8+(3*y) and (8+3)*y
8+3y and 11y
This cannot be the answer, when simplified they are not equal
B. (7-3)*y and 7-(3*y)
4y and 7-3y
This cannot be the answer, when simplified they are not equal
C. (6/y)+13 and 13+(y/6)
13+6/y and y/6+13
This cannot be the answer, when simplified they are not equal
D. 7+(y*5) and 7+(5*y)
7+5y and 7+5y
This is the answer, when simplified they are equal
I hoped this helped and made it easier to understand! :)
For which of the following geometric series can the infinite sum be determined? a1 = –0.25, r = –3 a1 = 0.75, r = 4 a1 = 3, r = 2 a1 = 5, r = –0.5
So, the infinite sum can be determined in the geometric series a₁ = 5, r = -0.5.
For a geometric series the infinite sum is given by s = a/(1 - r) where a = first term, r = common ratio and |r| < 1.
For each of the geometic series given below, we need to determine if |r| < 1.
For a₁ = -0.25, r = - 3, |r| = |-3| = 3 > 1
For a₁ = 0.75, r = 4, |r| = |4| = 4 > 1
For a₁ = 3, r = 2, |r| = |2| = 2 > 1
For a₁ = 5, r = -0.5, |r| = |-0.5| = 0.5 < 1
Since we require |r| < 1 to find the infinite sum and |r| in the last geometric series |r| = 0.5 < 1, the infinite sum can be found in the geometric series a₁ = 5, r = -0.5..
So, the infinite sum can be determined in the geometric series a₁ = 5, r = -0.5.
Learn more about infinite sum of geometric series here:
https://brainly.com/question/16037289
Help with geometry question
Answer:
see explanation
Step-by-step explanation:
On each median the distance from the vertex to the centroid is twice the distance from the centroid to the midpoint, or
the distance from the centroid to the midpoint is one third of the median
23
LF = 2 × HL = 2 × 30 = 60
HF = HL + LF = 30 + 60 = 90
24
KL = [tex]\frac{1}{3}[/tex] KE = [tex]\frac{1}{3}[/tex] × 15 = 5
LE = 2 × KL = 2 × 5 = 10
25
LJ = [tex]\frac{1}{2}[/tex] DL = [tex]\frac{1}{2}[/tex] × 24 = 12
DJ = DL + LJ = 24 + 12 = 36
what is 5,272 divided by 8 give the answer step by step
Answer: 659
Step by step solution:
Answer:
659
Step-by-step explanation:
0659
8 5272
0
52
48
47
40
72
72
0
Dividend:
5272
Divisor:
8
Quotient:
659
Remainder:
0
You may have to write this on paper because it might be hard for you to understand. I'm sorry if this isn't helping and it is very confusing, this is the only way that I could explain it. Thank you for the question and I hope you enjoy your answer :)