The proof of d^2y/dx^2 - 2 cot x dy/dx +3y = 0 is determined as 6cos²xsinx - 3sin³x - 6cos²xsinx + 3sin³x = 0
Equation of the derivativesThe equation is given as;
[tex]\frac{d^2y}{dx^2} - 2\ cotx \ \frac{dy}{dx} \ + 3y = 0 \ \ ---(1)[/tex]
y = sin³x
First derivative of yy = sin³x
let u = sinx (du/dx = cosx)
y = u³
dy/du = 3u²
[tex]\frac{dy}{dx} = \frac{dy}{du} \ .\ \frac{du}{dx} \\\\[/tex]
dy/dx = 3u² x cosx
dy/dy = 3sin²xcosx
y' = 3sin²xcosx
Second derivative of yy' = 3sin²xcosx
let u = sin²x (du/dx = 2sinxcosx)
v = cosx (dv/dx = -sinx)
[tex]y'' = \frac{d^2y}{dx^2} = V\frac{du}{dx} + U\frac{dv}{dx}[/tex]
y'' = 3[cosx(2sinxcosx) + sin²x(-sinx)]
y'' = 6cos²xsinx - 3sin³x
Substitute first derivative and second derivative of y in equation (1)
[tex]\frac{d^2y}{dx^2} - 2\ cotx \ \frac{dy}{dx} \ + 3y \\\\(6cos^2xsinx \ - \ 3sin^3x) \ - \ 2(\frac{cosx}{sinx} )(3sin^2xcosx) \ + 3(sin^3x) \\\\6cos^2xsinx \ - \ 3sin^3x \ - 6cos^2xsinx \ + \ 3sin^3x = 0 \ \ proved[/tex]
Learn more about differentiation here: https://brainly.com/question/25081524
Integrate the expression below
[tex]\displaystyle\int~4t(5t^2-1)^6 dt \\\\[-0.35em] ~\dotfill\\\\ u=5t^2-1\implies \cfrac{du}{dt}=10t~\hspace{10em} \cfrac{du}{10t}=dt \\\\[-0.35em] ~\dotfill\\\\ \displaystyle\int~4t~u^6\cdot \cfrac{du}{10t}\implies \int~\cfrac{4t~u^6}{10t}\cdot du\implies \int~\cfrac{2~u^6}{5}du\implies \cfrac{2}{5}\int~u^6\cdot du \\\\\\ \cfrac{2}{5}\cdot \cfrac{u^7}{7}\implies \cfrac{2(5t^2-1)^7}{35}[/tex]
Counting techniques
1. A high school basketball has 15 players. In how many different ways can the coach choose the starting line-up?
Answer:
How many players in the starting line up ???
If 1 then its 15 ways
If 2 then its 15 × 14 = ___
If 3 then its 15 × 14 × 13 = ___
I WILL GIVE YOU 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
78°
Step-by-step explanation:
the whole measure of a triangle =180° =3angles plus together
the 1st + 2nd angle = 90°+12°=102°
the 3rd angle = 180°-102°=78°
Find the point on the line -5x + 7y - 4 = 0 which is closest to the point (2,3).
Answer:
(x, y) = (2 35/74, 2 25/74)
Step-by-step explanation:
The closest point on the line to the given point will be the point of intersection of the given line and a perpendicular through the given point.
__
A line perpendicular to ax+by+c=0 that goes through point (h, k) can be written as ...
b(x-h) -a(y-k) = 0
For the given line and point, the perpendicular line will be ...
7(x -2) +5(y -3) = 0
7x +5y -29 = 0
Using the cross-multiplication method, we can find the solutions to the system of equations consisting of these two lines. It will be ...
-5x +7y -4 = 07x +5y -29 = 0Δ = (-5)(5) -(7)(7) = -74
Δx = (7)(-29) -(5)(-4) = -183
Δy = (-4)(7) -(-29)(-5) = -173
x = Δx/Δ = -183/-74 = 2 35/74 ≈ 2.4730
y = Δy/Δ = -173/-74 = 2 25/74 ≈ 2.3378
__
For more on the cross multiplication method, you can read ...
https://brainly.com/question/26397343
5. A video game console at Games Galore
normally costs $399.50, but all consoles are
marked down by 20% this week. What is the
price of a video game console this week?
Answer:
$319.60
Step-by-step explanation:
Normal Game console cost : $399.50
Discount: %20 (0.20)
$399.50×0.20= $79.90
Total cost of discount $79.90
$399.50-$79.90= $319.60
New cost after Discount= $319.60
*NEED HELP I WILL GIVE BRAINLIEST FOR BEST ANSWER PLEASE HELP ME*
A cylinder has a height of 9 meters and a diameter of 36 meters. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.
______cubic meters
Answer:
0.15 cubic meters
Step-by-step explanation:
Formula volume = π x radius² x height
Answer
πr2h
Step-by-step explanation:
What do 12y and 8y represent? You can look up the formula for the volume of a cylinder pir^2h and plug in your dimensions.
Find the number of real number solutions for the equation.
x2 + 26 = 0
2
1
0
Answer:
0
Step-by-step explanation:
x² + 26 = 0 ( subtract 26 from both sides )
x² = - 26 ( take square root of both sides )
x = ± [tex]\sqrt{-26}[/tex]
[tex]\sqrt{-26}[/tex] ← has no real solutions
Answer:
0
Step-by-step explanation:
Look above goofy, have a good day!
Determine whether the following is a statistical question.
How many boogers does Karissa the ogre have in her left nostril?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Statistical
(Choice B)
B
Not statistical
Answer:
It is Statistical. Karissa would have to count how many boogers she has in her left nostril.
Step-by-step explanation:
.
The given question is not a statistical question. So, option (B) is correct. Since this is not related to any other data and there is no variation with the previous data, this is not a statistical question.
What is a statistical question?The statistical question is a question that can be answered by collecting data and there will be a variation in the data used for calculating.
Given question:Given that " How many boogers does Karissa the orge have in her left nostril?"
This question does not need any collection of data. So, this is not a statistical question.
Therefore, option B is correct.
Learn more about the statistical question here:
https://brainly.com/question/12150562
#SPJ2
Help help math math math
[tex]y=-6x+12\\\\\text{When}~ x = -1\\\\y=-6(-1)+12 = 6+12 = 18[/tex]
Shaniqua has 12 apples to divide into "eating" and "using" in apple pie. If she puts at least 3 apples in each group, how many different ways can she divide the apples
Answer:
the answer is 4 i hoped this helped
Step-by-step explanation:
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
x=11 and t=6
Step-by-step explanation:
If ABC and KLM are approximately equal, 44 degrees=4x and 18 inches=3t.
44/4=11
18/3=6
Marissa drew and labeled 4 triangles on grid paper as shown below. Which triangle appears to be an obtuse triangle
The triangle that must appear to be obtuse mmust have one of its angle to be greater than 90 but less than 180 degrees:
What are obtuse triangles?Obtuse triangles are triangles that has one of theor angles to greater than 90 degrees.
Most obtuse triangles has two acute angles (angles less than 90 degrees) and a obtuse angle (angles between 90 and 180 degrees)
Hence the triangle that must appear to be obtuse mmust have one of its angle to be greater than 90 but less than 180 degrees:
Learn more on obtuse triangle here: https://brainly.com/question/3250447
Two methods to measure one's heart rate are:
A. Palpitation and monitor
B. Monitor and EKG
C. Palpitation and pulse rate
Can you find the area and explain how you got the area
Answer:
102cm^2 - hope this helps
Step-by-step explanation:
find the area of the rectangle first in the middle
which equals 6 x 13 = 78cm^2
then find the traingles on the side
(6 x 4) / 2 = 12
there are 2 traingles so it would be 12 + 12 = 24
so all together the area would be 78 + 24 = 102cm ^2
Calculate the mean and median of the data set below:
8, 9, 2, 4, 5, 11, 7, 9, 10, 9
Answer:
Mean - 7.4
Median - 8.5
Mode - 9
Step-by-step explanation:
Mean - add up all of the numbers = 74
then divided by the numbers of numbers (10 numbers) (74/10) = 7.4
Median - the middle number of the data set
Mode - the number most frequent
Can someone help me please
Answer:
59.55555555555556
Step-by-step explanation:
If rectangle ABCD were rotated 90° clockwise about the origin to create rectangle A'B'C'D', which set of sides would be parallel in the resulting image?
I. A'B' and D'C'
II. A'D' and D'C'
III. A'B' and A'D'
IV. A'D' and B'C'
A.
I and II only
B.
I and IV only
C.
II and III only
D.
I, II, III, and IV
answers is B
Answer: B. I and IV only
Step-by-step explanation:
We can look at the rectangle already graphed. Since it is being rotated, parallel sets of sides will be parallel in ABCD and A'B'C'D'
I. A'B' and D'C'
-> True
II. A'D' and D'C'
-> False
III. A'B' and A'D'
-> False
IV. A'D' and B'C'
-> True
This means your answer is option B.
I and IV only
ABC has side lengths that are each equal to
1 unit. Is there another triangle with the
same side lengths but different angles?
Explain.
Answer:
there are cannot be another triangle with same side lengths but different angles. since all the sides are same thus all the angles will also be same.
What is the slope of the line described by the equation below?
y-5= -3(x - 17)
hos
A. -3
B. -5
C. 3
O D. 5
SUBMIT
Answer:
A. -3
Step-by-step explanation:
We recognize the given equation as being in point-slope form:
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
__
Comparing that to the given equation ...
y -5 = -3(x -17)
we see that m = -3.
The slope of the line is -3.
Our competitor struggled to sell 350 products & we sold 46% more than they did
Answer:
The quantity we sold more than the competitors is 161.
What are percentages?
Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred.
How much more did we sell?
Quantity sold more = percentage sold more x number sold by competitors
46% x 350
0.46 x 350=161.
please help giving branliest
Answer:
7
Step-by-step explanation:
since it's a right triangle we can use the pythagorean theorem.
hence, sqrt(25^2 - 24^2) = the answer = 7
make sure to ask if you need any further guidance.
I neef way more help! Only a few more questions then you will have helped me pass my class!
Answer:
[tex]\boxed{\sf{705.3cm^3}}[/tex]Step-by-step explanation:
To solve this problem, you need to determine the volume of the prism.
Volume of the prism formula:
[tex]\Longrightarrow: \sf{V=L*W*H}[/tex]
L (length): 8 cmW (width): 15.2 cmH (height): 5.8 cmMultiply them all together.
[tex]\sf{8*15.2*5.8=\boxed{\sf{705.3}}[/tex]
Therefore, the volume of the prism is "D. 705.3 cm³", which is our answer.I hope this helps. Let me know if you have any questions.
Answer:
Option D, [tex]705.3\ cm^3[/tex]
Step-by-step explanation:
Step 1: Determine the volume of a rectangular prism
[tex]V = l * w * h[/tex]
[tex]V = (15.2\ cm) * (8\ cm) * (5.8\ cm)[/tex]
[tex]V = 705.28\ cm^3[/tex]
Answer: Option D, [tex]705.3\ cm^3[/tex]
A number is selected at random from the set (2, 3, 4, . 10}. Which event, by definition, covers the entire sample space of this experiment?
OA. The number Is greater than 2.
O B. The number Is not divisible by 5.
O C. The number Is even or less than 12.
O D. The number is nelther prime nor composite.
O E. The square root of the number Is less than 3.
Reset
Next
s reserved.
This is the list of choices that accompany that question:
A) The number is greater than 2. ---> FALSE BECAUSE IT INCLUDES GREATER THAN 10, AND 10 IS THE LAST NUMBER OF THE SET.
B) The number is not divisible by 5. ----> FALSE BECAUSE 10 IS DIVISIBLE BY 5.
C) The number is even or less than 12. ---> THIS CAN BE RIGHT BECAUSE 1) ALL THE NUMBERS SHOWN ARE EITHER EVEN OR LESS THAN 12 AND THE DEFINITION, AND 2) THE DEFINITION DOES NOT INCLUDE A NUMBER OUT OF THE NUMBERS SHOWN.
D) The number is neither prime nor composite. ---> FALSE BECAUSE ANY NUMBER IS EITHER PRIME OR COMPOSITE.
E) The square root of the number is less than 3. ---> FALSE BECAUSE THE SQUARE ROOT OF 10 IS GREATER THAN 2.
How many, Inch cubes fit into a rectangular prism that measures 4 Inches long, 5 Inches wide, and
Inches high?
C. 780
A. 130
D. 1,040
B. 260
Help help help help math math
In a 51-inch television, the length of the screen's diagonal is 51 inches. If the screen's height is 25 inches,
what is the width? Round your answer to the nearest tenth of an inch.
Answer:
44.452
Step-by-step explanation:
Using the Pythagorean theorem you can use:
51^2 = 25^2 + w^2
2601 = 625 +w^2
w^2 = 1976
w = 44.452
Answer:
The width is 44.5in.
Step-by-step explanation:
25^2 + b^2 = 51^2
625 + b^2 =2601
b^2= 2601-625=1976
Square root it (1976)
=44.45= 44.5
What is the value of the expression 3(x+19)-25/5 if x=15
Hey there!
3(x + 19) - 25/5
= 3(15 + 19) - 25/5
= 3(15) + 3(19) - 25/5
= 45 + 57 - 25/5
= 45 + 57 - 5
= 102 - 5
= 97
OR
3(x + 19) - 25/5
= 3(15 + 19) - 25/5
= 3(34) - 25/5
= 102 - 25/5
= 102 - 5
= 97
97 = 97 ☑️
Therefore, your answer is: 97
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Answer:
Value of expression = 97Step-by-step explanation:
In the question we have given an expression that is 3 ( x + 19 ) - 25/5 and value of x is equal to 15 .
And we are asked to find the value expression when value of x is 15 .
Solution : -
[tex] \longmapsto \: 3( x+ 19) - \cancel{\frac{25}{5} }[/tex]
Step 1 : Substituting value of x in given expression and cancelling 25 by 5 :
[tex] \longmapsto \: 3(15 + 19) - 5[/tex]
Step 2 : Solving parenthesis by adding 15 and 19 :
[tex] \longmapsto \: 3(34) - 5[/tex]
Step 3 : By multiplying 3 with 34, we get :
[tex] \longmapsto \: 102 - 5[/tex]
Step 4 : Subtracting 5 from 102 :
[tex] \longmapsto \: \red{ \boxed{ \frak{97}}}[/tex]
Henceforth , value of expression is 97 .#Keep LearningWhat is the complex conjugate of 12i ?
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
The conjugate of given complex number is ~
[tex]\qquad \tt \dashrightarrow \: \overline{z} = - 12i[/tex]
Conjugate of a complex number is the same number with its imaginary part having opposite sign.
Eg. if z = a + i b
Then it's Conjugate = a - i b
Based on the supply graph and the demand graph shown above, what is the price at the point of equilibrium? a. 20 b. 30 c. 40 d. There is not enough information given to determine the point of equilibrium. Please select the best answer from the choices provided A B C D
Answer:
ITS (B) 30
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
edge
The rectangle of the rectangle is shown 44m squared. Find out the missing length of x
Answer:
12 m
Step-by-step explanation:
3 ⅔
= 3 + 2/3
= 9/3 + 2/3 { LCM = 3 }
= ( 9 + 2 ) / 3
= 11/3
In the diagram,
Length ( l )= x m
Breadth ( b ) = 3 ⅔ m = 11/3 m
Given that area of the rectangle = 44 m²
Formula : -
Area of the rectangle = lb
lb = 44
x * 11/3 = 44
x = ( 44 * 3 ) / 11
x = 4 * 3
x = 12 m
Therefore,
the missing length = 12 m