Answer:
6x-3
Step-by-step explanation:
If y=sin^3 x,prove that d^2y/dx^2 - 2 cot x dy/dx +3y=0
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
A set of books sits on a shelf at a store. This line plot shows the thickness of each book. Jessica buys one of the second thinnest books on the shelf. Jada buys the second thickest book on the shelf.
How much thicker is Jada's book than Jessica's book?
Enter your answer in the Box as a mixed number in simplest form.
Please help.
Answer:
2 inches
Step-by-step explanation:
if there are 2 books that are 1 1/2 thick, the second thinnest book would be 1/12... the second thickest book im guessing would be 3 1/2, so you'd have 2 inches in between
Answer: the answer is, 2 and one half
Step-by-step explanation: I took the test. Please give brainliest
Use the vectors v = (3,-4) and w =(1,2) to answer the following questions:
a. Find v. w
b. Find the angle between v and w. Round to the nearest degree.
We will see that for the given vectors:
a) v.w = -5b) The angle between the vectors is 116.57°How to find the dot product?
Remember that the dot product between two vectors:
a = (x₁, y₁) and b = (x₂, y₂) the dot product is:
a.b = x₁*x₂ + y₁*y₂ = |a|*|b|*cos(θ).
a) We have:
v = (3,-4) and w = (1,2)
The dot product will give:
v.w = 3*1 + (-4)*2 = 3 - 8 = -5
b) We will have:
|v|*|w|*cos(θ) = -5
Where:
|v| = √(3^2 + (-4)^2) = 5|w| = √(1^2 + 2^2) = √5Then we have:
5*√5*cos(θ) = -5
cos(θ) = -1/√5
θ = Acos(-1/√5) = 116.57°
The angle between the two vectors is 116.57°.
If you want to learn more about vectors, you can read:
https://brainly.com/question/3184914
A square has side length 3.4 cm. The side length of the enlargement is 17 cm. Determine the scale factor.
Answer:
The scale factor is 5
Step-by-step explanation:
To find the scale factor, we divide 17 by 3.4 to find how much it was enlarged by.
17/3.4 = 5
We do this becuase when finding the scale factor, we take the dilated shape/side length and divide it by the original shape/side length.
Pls help word problem how many hours?
This answer was deemed incorrect, so sorry for posting this!
What is the slope of
the line?
Give your answer as
a fraction in simplest
form.
Answer:
3/4
Step-by-step explanation:
two points are
(8,6) and (12,9)
formula :
(y2-y1)/(x2-x1)
(9-6)/(12-8) =
3/4
slope often means rate of change
in this graph
price changes as the number of lemon changes
in economics this graph is called the
supply curve
its called the law of supply
increases in price causes increase in the quantity supplied
if something is worth more, it will cause an increase in price which will cause people who want to make money to try supply more of it
quizlet
help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
D
Step-by-step explanation:
This is because of the slope and amount of earnings Tatiana has.
Tatiana gets 26 dollars added to her earnings every 2 hours
Sample: 16 + 26 = 42
The 16 represents the number of earnings that Tatiana gets/earns for hour 0.
If we were to graph the earnings of Tatiana meaning her time represents X and the earnings represent Y. We could clearly see that Tatiana earns more money than Darryl.
Express as a sum of logarithms.
[tex] log_{2}(16 \times 24) [/tex]
please help (due tomorrow)
7:obtuse angle
8:right angle
9:FDE, AFB
Find the distance between A(3, 2) and B(8,2) a. 2 units b. √5 units c. 3 units d. 5 units
Answer:
[tex]\boxed{\sf{5 \quad units}}[/tex]Step-by-step explanation:
Use the slope formula.
[tex]\Longrightarrow: \sf{\dfrac{y_2-y_1}{x_2-x_1} }[/tex]
Use the distance formula.
[tex]: \Longrightarrow \sf{\sqrt{\left(X_2-X_1\right)^2+\left(Y_2-Y_1\right)^2}}[/tex]
[tex]\sf{x_2=8}\\\\\\\sf{x_1=3}\\\\\\\sf{y_2=2}\\\\\\\sf{y_1=2}[/tex]
Rewrite the problem down.
[tex]\sf{\sqrt{\left(8-3\right)^2+\left(2-2\right)^2}}[/tex]
Solve.
Use the order of operations.
PEMDAS stands for:
ParenthesesExponentsMultiplyDivideAddSubtract⇒ (8-3)²+(2-2)²Solve parentheses, first.
⇒ (8-3)²
⇒ 8-3=5
⇒ 5²+(2-2)²
⇒ (2-2)=0
⇒ 0²
Rewrite the problem down.
⇒ 5²+0²
Do exponents next.
⇒ 5²=5*5=25
⇒ 0²=0*0=0
⇒ 25+0
Add.
⇒ 25+0=25
You can also divide the numbers from left to right.
→ 25/5=5
Therefore, the distance between (3, 2) and (8,2) is "5 units", which is our answer.I hope this helps. Let me know if you have any questions.
Cindy counted 8,723 blue beads, 4,632 red beads, 3,512 green beads, and 5,971 white beads.
Doris counted 6,802 blue beads, 3,162 red beads, 987 green beads, and 2,689 white beads.
How many did Cindy and Doris count in all.
Answer:
36,478 beads
Step-by-step explanation:
8723+4632+3512+5971=22,838
6,802+3,162+987+2,689=13,640
22,838+13,640= 36,478
So Cindy and Doris have 36,478 beads in total.
What is the missing vertex of a rectangle that has (0, 0), (0, 6), and (8, 0) as three of its vertices?
Answer:
(8,6)
Step-by-step explanation:
Refer to the graph below
Question in picture below.
The product of two positive integers is 20. Find the two numbers
Answer:
1 and 20 or 2 and 10 or 4 and 5
Step-by-step explanation:
the divisors of 20 are 1 , 2 , 4 , 5 , 10 , 20
Then
20 = 1 × 20
= 2 × 10
= 4 × 5
Joan believes the best way to play roulette is to place a bet on a 6 block of numbers as her probability of winning is 638. She decides to place a $20 bet with this probability. She will win $100 (and keep her bet!) if one her numbers come up but she will lose if any other number is shown, a probability of 3238. What is the expected value for Joan? Round to the nearest cent. Do not round until your final calculation.
Answer:
-1.05
Step-by-step explanation:
1. The width of a rectangular table is 7 - 2x feet and the length is 5x + 2 feet. Write a polynomial that represents the perimeter.
2. Base from problem number 10, what is the perimeter of the rectangular table if x is 3.
Answer:
perimeter is 36
Step-by-step explanation:
if x=3
then it turns into
Width 7-2(3)
length 5(3)+2
which equals
width 1
length 17
since it's a perimeter you add all four corners
which is 1+1+17+17=36
What is the discriminant of the polynomial below?
2x^2 + 3x - 7
A. -5
B. -47
C. 23
D. 65
Answer:
2x^2 + 3x - 7 (a= 2 , b= 3 , c= -7)
discriminant= b^2 - 4ac
= (3)^2 - 4(2)(-7)
= 9 + 56 = 65
The answer is D. 65
Hope this helps :)
Which expression is equivalent to 2(3 - x)?
pls help pls help pls help
Answer: 336ft²
Step-by-step explanation:
The polygon in the image provided is a trapezoid.
The formula for the area of a trapezoid is [tex]A=(\frac{a+b}{2} )(h)[/tex]
Where
A is the area
a is one of the bases (24 for this)
b is the other base (32 for this)
and h is the height (12 for this)
Sub the values into the formula and solve
[tex]A=(\frac{24+32}{2} )(12)\\A=(\frac{56}{2} )(12)\\A=(28)(12)\\A=336[/tex]
Answer:
336
Step-by-step explanation:
24 x 12 = 288. 12 x 8 = 96 divided by 2 is 48. 288 + 48 = 336
a bathing suit is on sale for 40% off including 7% sales tax the final price is $57.78 what was the original cost without tax or discount
Answer:
38.7126
step-by-step explanantion:
so it's technically 33 percent off because the taxes is 7 percent.
and 33 percent of 57.78 is 19.0674. so 57.78-19.0674 will equal 38.7126
The original cost of the bathing suit without tax or the discount is $38.72.
DiscountThe term "discount" refers to a pricing scheme in which a commodity's (goods or services) price is lower than its marked price. Simply said, a discount is a proportion of the advertised price.
How to find the original cost?The bathing suit is 40%off including 7% tax.This means that the discount of 40% includes the tax of 7%.Thus the discount without tax will be calculated by: 40%-7%=33%
Now we will calculate the discount without tax on the final cost of the bathing suit, i.e, 33% of the final cost.
[tex]\frac{33}{100} \times 57.78=19.06[/tex]
So, we get a discount of $19.06 on the final cost.Then the original cost of the bathing suit without the tax or the discount will be the final cost less than the discount: $57.78-$19.06=$38.72
So, the original cost of the bathing suit without tax or the discount is $38.72.
Learn more about discount here- brainly.com/question/843074
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At the school carnival, the student council sold
temporary tattoos of the school mascot. They
purchased a batch of the tattoos for $10, and sold
each one for $4.
Define a unit for the amount of money made.
1. How much money did the student council make
by selling five tattoos?
Answer:
$10
Step-by-step explanation:
4 x 5 = 20
But then we need to subtract the $10 the tattoos cost.
So the amount of money they made was $10.
Hope this helps!
Answer:
$20
Step-by-step explanation:
$4 × 5 = $20
basically just multiply 4 by 5
find the area of each plane figure 10.5 km 3.7 km
Answer:
28.4
Step-by-step explanation:
10.5x2= 21
3.7x2= 7.4
21+7.4 = 28.4
Pls answerrrrrrrrrrrrrrrrrrrrrrrrrrr
Answer:
The answer should be 2
Step-by-step explanation:
P
r
=
n
!
(
n
−
r
)
!Subtract
1
from
2
.Simplify
2
!
(
1
)
!
.
factor 1-2sin^2(x)+sin^4(x)
Answer:
[tex]\left(1 - \sin^{2}(x)\right)^{2}[/tex].
Step-by-step explanation:
Notice that "[tex]1[/tex]" is equal to "[tex]1^{2}[/tex]" whereas [tex]\sin^{4}(x) = {\left(\sin^{2}(x)\right)}^{2}[/tex]. Therefore:
[tex]\begin{aligned} & 1 - 2\, \sin^{2}(x) + \sin^{4}(x) \\ =\; & 1^{2} - 2\, \sin^{2}(x) + {\left(\sin^{2}(x)\right)}^{2}\end{aligned}[/tex].
Make use of the identity [tex](a - b)^{2} = a^{2} - 2\, a\, b + b^{2}[/tex]. In this case, set [tex]a = 1[/tex] whereas [tex]b = \sin^{2}(x)[/tex]. Therefore:
[tex]\begin{aligned} & 1^{2} - 2\, \sin^{2}(x) + {\left(\sin^{2}(x)\right)}^{2} \\ =\; & a^{2} - 2\, a\, b + b^{2} \\ =\; & (a - b)^{2} \\ =\; & {\left(1 - \sin^{2}(x)\right)}^{2}\end{aligned}[/tex].
Fill in each blank of the table shown by converting
given form of a number into the missing form of the
number.PICTURE BELOW
IM SO CONFUSED PLEASE HELP THANK YOU
Answer:
A. 0.11111
B. 17/100
C.0.232323
D. 6/9 or 2/3
E. 1.8888889
F. 4/11
G. 1.45454545
H. 3/100
Step-by-step explanation:
Convert them to fractions and decimals
A store having a sale on chocolate chips
and walnuts. For 6 pounds of chocolate chips and 5 pounds of walnuts, the total cost Is $35. For 2 pounds of
chocolate chips and 3 pounds of walnuts, the total cost Is $15. Find the cost for each pound of chocolate chips and each pound of walnuts.
Cost for each pound ( chocolate chips: $
X
0
Cost for each pound of walnuts: $[
Answer:
chocolate chips: $3.75
walnuts: $2.5
Step-by-step explanation:
lets say chocolate chips cost x dollars and walnuts cost y dollars. we then have
6x + 5y = 35
2x + 3y = 15
multiply the second equation by 3 to get 6x + 9y = 45
subtract the 1st equation from the new equation to get 4y = 10, so y=$2.50
plug this value into the 2nd equation to get x=$3.75
Evaluate the sum of the finite geometric series -5- 10 - 20 - 40 - . . . - 2560
Answer:
-5015
Step-by-step explanation:
Sum of a Geometric Series (finite)
Sₙ = a(rⁿ - 1) / (r - 1)Step 1 : Finding n
aₙ = -2560r = -10/-5 = 2a = -5aₙ = arⁿ⁻¹ -2560 = -5(2)ⁿ⁻¹512 = (2)ⁿ⁻¹2⁸ = (2)ⁿ⁻¹8 = n - 1n = 9Step 2 : Substitute the values in the Sₙ formula
S₉ = -5(2⁹ - 1) / 2 - 1S₉ = -5 x 1023S₉ = -5015How many solutions does this
system have?
=
-x + 3y = 3
2x – 6у = 30
mrs. matthews gave a test to her 120 science students. if she gives 5 bonus points to each test grades , how will this affect the mean , median , and mode scores?
Maya is building a model of her city's downtown area. She is constructing part of an office building, as shown below. Each cube has an edge length of 1/6 foot.
The height of the model building is foot?
A.3/4
B.1/2
C.1/6
D.3/18
E.1/4
Answer: the answer is 1 over 2 which is e
Step-by-step explanation: 4 and 2 and 3 equal 9 so 1 over 6 times 9 cubes equal 1.5 which is 1 over 2