Answers
[tex]\frac{4}{\pi}\left[x*\sin^{-1}(x)+\sqrt{1-x^2}\right]-x+C\\\\[/tex]
====================================================
Proof:
Apply the derivative to choice A. The goal is to prove the derivative is equivalent to the given integrand.
[tex]y = \frac{4}{\pi}\left[x*\sin^{-1}(x)+\sqrt{1-x^2}\right]-x+C\\\\\frac{dy}{dx} = \frac{4}{\pi}\left[\sin^{-1}(x)+\frac{x}{\sqrt{1-x^2}}-\frac{x}{\sqrt{1-x^2}}\right]-1\\\\\frac{dy}{dx} = \frac{4}{\pi}\sin^{-1}(x)-1\\\\[/tex]
It's far from obvious, but we can apply a bit of algebra like so
[tex]\frac{dy}{dx} = \frac{4}{\pi}\sin^{-1}(x)-1\\\\\frac{dy}{dx} = \frac{4}{\pi}\sin^{-1}(x)-\frac{\pi}{\pi}\\\\\frac{dy}{dx} = \frac{4\sin^{-1}(x)-\pi}{\pi}\\\\[/tex]
Next, we divide every term by 2. This is so we can replace the pi terms with pi/2
[tex]\frac{dy}{dx} = \frac{4\sin^{-1}(x)-\pi}{\pi}\\\\\frac{dy}{dx} = \frac{2\sin^{-1}(x)-\frac{\pi}{2}}{\frac{\pi}{2}}\\\\[/tex]
We do this to take advantage of the trig identity [tex]\sin^{-1}(x)+\cos^{-1}(x) = \frac{\pi}{2}[/tex]
So we'll be replacing every instance of "pi/2" with the left hand side of that equation just mentioned.
Therefore,
[tex]\frac{dy}{dx} = \frac{2\sin^{-1}(x)-\frac{\pi}{2}}{\frac{\pi}{2}}\\\\\frac{dy}{dx} = \frac{2\sin^{-1}(x)-\left(\sin^{-1}(x)+\cos^{-1}(x)\right)}{\sin^{-1}(x)+\cos^{-1}(x)}\\\\\frac{dy}{dx} = \frac{2\sin^{-1}(x)-\sin^{-1}(x)-\cos^{-1}(x)}{\sin^{-1}(x)+\cos^{-1}(x)}\\\\\frac{dy}{dx} = \frac{\sin^{-1}(x)-\cos^{-1}(x)}{\sin^{-1}(x)+\cos^{-1}(x)}\\\\[/tex]
This shows that differentiating the expression in choice A leads to the given integrand.
If we reverse all of the steps mentioned, then we can show that:
[tex]\displaystyle\frac{dy}{dx} = \frac{\sin^{-1}(x)-\cos^{-1}(x)}{\sin^{-1}(x)+\cos^{-1}(x)}\\\\\\ \int\frac{dy}{dx}dx = \int\frac{\sin^{-1}(x)-\cos^{-1}(x)}{\sin^{-1}(x)+\cos^{-1}(x)}dx\\\\\\y = \frac{4}{\pi}\left[x*\sin^{-1}(x)+\sqrt{1-x^2}\right]-x+C\\\\[/tex]
since integrals and derivatives are tied together through inverse processes (one undoes the other more or less).
Related Questions
Is 9.5 an irrational number
Answers
Answer:
yes it is.....................
Step-by-step explanation:
9.5 = 19/2
So it is a rational number (and so is not irrational)
8a=4(a-9)
Show work I need help
Answers
Answer:
a = -9
Step-by-step explanation:
8a=4(a-9)
Divide each side by 4
8a/4=4(a-9)/4
2a = a-9
Subtract a from each side
2a-a = a-9-a
a = -9
Answer:
-9
Step-by-step explanation:
8a = 4(a-9)
Use the distributive property (Multiply 4 times a, and 4 times -9)
8a = 4a - 36
Bring the 4a to the other side
8a - 4a = -36
Add like terms
4a = -36
Divide both sides by 4 to get a by itself
a = -9
George plans to cover his circular pool for the upcoming winter season. The pool has a diameter of 20 feet and the cover extends 12 inches beyond the edge of the pool. A rope runs along the edge of the cover to secure it in place.
a. What is the area of the pool cover?
b. What is the length of the rope?
You must show all of your work to receive credit
Answers
Answer:
The cover has diameter of:
20 feet + 2*12 inches = 20 feet + 2 feet = 22 feeta.
Area of the pool cover:
A = πd²/4 = 3.14*22²/4 = 379.94 ft²b.
The length of the rope:
C = πd = 3.14*22 = 69.08 ftAnswer:
346.19ft65.94ftStep-by-step explanation:
Add the length of the pool and the extent the pool cover [ 12in = 1ft ] has over the pool.
20 + 2 = 22ft
Part A:
The formula for the area of a circle is πr².
To find the radius just divide by two; 22 / 2 = 11ft
= π(11)²
= 121π
≈ 379.94ft
Part B:
We can use the circumference formula [ dπ ] to find how long the rope is.
= 22(3.14)
= 69.08ft
Best of Luck!
can someone solve this for me and explain it please
Answers
Answer:
Answer is Triangle P'R'Q' is larger, explain how you know is steps
Step-by-step explanation:
So a Dilation is the expansion or shrinkage of an object. Because this is being dilated by 1.5 it is growing by 1.5
So triangle PRQ is the smaller version of P'R'Q' because
Line PR = 3.1
Line RQ = 3.9
Line QP = 5
Multiplying these by 1.5 you get
Line P'R' = 4.65
Line R'Q'= 5.85
Line Q'P' = 7.5
Plz help me answer this question
Answers
Answer:
I think it's the top left one
Step-by-step explanation:
The length is 6, the width is 3, and the height is 4, which matches the expression.
Step-by-step explanation:
[tex](6 \times 3 + 3 \times 4 + 4 \times 6) \\ = (18 + 12 + 24) \\ = 54[/tex]
Sonia finished the 200-meter dash in 26.12 seconds. Gladys finished the 200-meter dash 1.08 seconds
faster than Sonia. How long did it take Gladys to run the 200-meter dash?
O 25.04 seconds
O 26.20 seconds
O 27.04 seconds
O 27.20 seconds
Answers
Answer:
25.04
Step-by-step explanation:
26.12-1.08
=25.04
Answer:
25.04
Step-by-step explanation:
For this problem we have to use subtraction
If Sonya finished the dash is 26.12 seconds and Gladys finished it 1.08 seconds faster, we have so subtract 26.12 by 1.08 to get her time
So we get 25.04
Hope this helps! :D
29 dekagrams equals 2900 what
Answers
Answer:
It equals 2900 decigrams
Step-by-step explanation:
29 dekagrams = 290 grams
290 grams = 2900 decigrams
Therefore, 29 dekagrams = 2900 decigrams
The equivalent weight in grams for a given weight in dekagrams is approximately 10 times the weight in dekagrams.
To find the equivalent weight in grams for a given weight in dekagrams, you can use the conversion factor that 1 dekagram (dag) is equal to 10 grams.
Given the information that 29 dekagrams equals 290 grams, you can set up a proportion:
[tex]\(\frac{29 \text{ dag}}{290 \text{ g}} = \frac{1 \text{ dag}}{x \text{ g}}\)[/tex]
Cross-multiplying:
[tex]\(29x = 290 \times 1\)[/tex]
Solving for x:
[tex]\(x = \frac{290}{29}\)\\\\\(x \approx 10\)[/tex]
Therefore, the equivalent weight in grams for a given weight in dekagrams is approximately 10 times the given weight in dekagrams.
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Complete Question:
If 29 dekagrams equals 290 grams, what is the equivalent weight in grams for a given weight in dekagrams?
I am the only toolkit function that has a start and end number for the range. I am also the only that is cyclic, meaning I repeat over and over.
Which toolkit function am I?
Answers
The Toolkit function that has a start and end number for the range and is also cyclic is ; The constant Function ( i.e. f(x) = a )
There are about (9) toolkit functions and some of these toolkit functions :
Constant function Cube root function Square root functionreciprocal squared functionreciprocal functioncubic and quadratic function Absolute value functionThe common characteristics between the various toolkit functions is that they all have undefined domains ( i.e. ( - ∞ , ∞ ) or ( -∞, 0 ), and undefined ranges as well. while the only Toolkit function with a defined range is the Constant function { a, a }
The range for a Constant function starts and ends with the value of the given constant. i.e. { a, a }. while other functions have undefined range values.
Hence we can conclude that the Toolkit function with a start and end number for the range is the Constant function.
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Answer:
The constant Function
5.
A bank statement shows transactions of -$10.40 and $8.50.
A. Do these transactions represent deposits or withdrawals?
Plz help
Answers
A negative value is when money is taken out ( withdrawal). A positive value is when money is added to the account(deposit)
-10.40 is a withdrawal
8.50 is a deposit
Answer:
Hint :- Withdrawal is denoted as the -ve sign and deposit are denoted by the +ve sign. This is because if we deposit money then the money increase and if we withdraw then the money decreases.
-10.40
See there is a negative sign. This means it is a withdrawal
8.50
See there is a positive sign. This means it is a deposit
I have two ice cream and I - 5 ice creams how many ice cream will be left
Answers
Answer:
2 1/5
Step-by-step explanation:
Give the geometric representation of 2x+ 1= x-4 as an equation in (a) one variable (b) two variables
please help
Answers
Answer:
Step-by-step explanation:
2x+1=x-4
2x-x= -4-1
1x=-5
x=-52. When a number n is subtracted from 18
and the difference is divided by n, the
result is 2. What is the value of n?
(A) 4
(B) 6
(C) 8
(D) 10
(E) 14
Answers
Answer:
e) 14
Step-by-step explanation:
(18-n)/2 = 2
18-n = 4
-n = -14
n = 14
The value of n when n is subtracted from 18 and the difference is divided by n, the result is 2 is 6.
What is Algebra?The representation of mathematical statements as solutions to problems is the focus of the branch of mathematics known as algebra. Mathematical operations like addition, subtraction, multiplication, and division are combined with variables like x, y, and z to produce a meaningful mathematical statement.
Given:
When a number n is subtracted from 18
=(18- n)
and, the difference is divided by n
=(18 - n)/n
so, result is 2
(18 - n)/n = 2
18 - n = 2n
3n = 18
n= 18/3
n= 6
Hence, the value of n is 6.
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9/x + 2 = 20
WAHT IN THE WORLD? HOWWWW?!
Answers
Answer:
1/2 =x
Step-by-step explanation:
9/x + 2 = 20
Subtract 2 from each side
9/x + 2-2 = 20-2
9/x =18
Multiply each side by x
9/x *x = 18*x
9 = 18x
Divide each side by 18
9/18 = 18x/18
1/2 =x
If I start at 6:05 and end at 3:30. How much time is that.
Isn’t is 2 hours and 25 minutes or 2 hours and 34 minutes?
Answers
Answer:
The answer is 9 hours and 25 minutes
Step-by-step explanation:
if it starts at 6:05 am and then ends at 3:30 pm then thats 9 hours in total and 25 minutes
hope that helps>3
Find the circumference of a circle if the area of the circle is 256 π in².
Answers
Answer:
32π in
= 100.48 in.
Step-by-step explanation:
From Area:
radius, r = √(A/π)
= √(256 π in²/π)
= 16 in
where π = 3.14
》 Circumference = 2π(r)
= 2π(16)
= 32π in.
= 100.48 in
Find the smallest number that must be added to 7653 to make it a perfect square? Explain.
Answers
9514 1404 393
Answer:
91
Step-by-step explanation:
√7653 is about 87.48
The next largest perfect square is 88^2 = 7744. The value that must be added to 7653 to get 7744 is ...
7744 -7653 = 91
Adding 91 to 7653 will make it a perfect square.
HELP!! Will mark as brainliest!!!
In school, pupils study one language.
They choose either French, Spanish or Italian.
3/20 of the pupils study Italian and 5/8 of the pupils study French
What fraction of the pupils study Spanish?
Answers
Answer:
19/40
Step-by-step explanation:
mark meeeeeee
Which choice is equivalent to the product below when x > 0?
Square root of 2/x time square root of x^2/8
Answers
Answer:
A.
[tex] \sqrt{x } \div 2[/tex]
is the answer
The choice which is equivalent to [tex]\sqrt{\frac{2}{x}}\cdot\sqrt{\frac{x^2}{8}}[/tex] is given by (A) [tex]\frac{\sqrt{x}}{2}[/tex].
What is expression?Expression is a mathematical term that involves variables, numbers and other mathematical quantities and operations or combinations of them.
The given expression is [tex]\sqrt{\frac{2}{x}}\cdot\sqrt{\frac{x^2}{8}}[/tex]
Calculating the expression we get,
[tex]\sqrt{\frac{2}{x}}\cdot\sqrt{\frac{x^2}{8}}=\sqrt{\frac{2}{x}\cdot\frac{x^2}{8}}=\sqrt{\frac{x}{4}}=\frac{\sqrt{x}}{2}[/tex]
So the expression equals to [tex]\frac{\sqrt{x}}{2}[/tex].
Hence the correct option is (A).
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HELP HELP HURRYYY the product of two numbers is rational. The first number is 3 sqrt2. What is the possible value of the other number?
Answers
The possible value of the other number will be 7√32. The correct option is D.
What is a rational number?A rational number is one that can be stated mathematically as the ratio or fraction p/q of two numbers, where p and q are the numerator and denominator, respectively. For instance, every integer and 3/7 are rational numbers.
It is given that the first number is 3√2 the value of the second number will be:-
Rational number = 3√2 x 7√32
Rational number = 21√64
Rational number = 21√( 8 x 8 )
Rational number = 21 x 8
Rational number = 168
Therefore, the possible value of the other number will be 7√32. The correct option is D.
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Vertical Stretch of 7, up 8, reflect over the x axis???
Answers
Answer:
f(x) = -(7x) + 8
Step-by-step explanation:
The negative on the outside reflects over the x-axis.
The 7 on the inside stretches the function vertically.
The +8 on the outside moves the function up 8.
Which of the following is true ?
Select one:
O a. 70<7-3
O b. 4-5<4-3
O c. 5-2 <5-3
O d. 25223
Answers
Answer:
b. 4 - 5 < 4 - 3
Step-by-step explanation:
a. 70 < 7 - 3
70 < 4
false, 70 is not greater than 4
b. 4 - 5 < 4 - 3
- 1 < 1
true, 1 is greater than -1
c. 5 - 2 < 5 -3
3 < 2
false, 2 is not greater than 3
d. 25223
?
hope this helps! if you have any questions, let me know!
can someone help me with this question?
Answers
Answer:
128 grains.
I think so..
Step-by-step explanation:
SEE the image for solution.
HOPE it helps
Have a great day
Answer:
Step-by-step explanation:
[tex]u_1=1=2^0\\u_2=2=2^1\\u_3=4=2^2\\u_4=8=2^3\\\\...\\u_{64}=2^{63}\\\\we\ must\ calculate\\\\u_1+u_2+u_3+u_4+...+u_{64}\\\\=1+2^1+2^2+2^3+2^4+....+2^{63}\\\\=\dfrac{2^{64}-1}{2-1} \\\\=2^{64}-1\\\\=18446744073709551615\\\\=1.8446744073709551615*10^{19}[/tex]
Uma indústria produz mensalmente x lotes de um produto. O valor mensal resultante da venda deste produto é V(x) = 3x² + 400x e o custo mensal da produção é dado por C(x) = 5x² − 100x − 540. Sabendo que o lucro é obtido pela diferença entre o valor resultante das vendas e o custo da produção, calcule:
A) O número de lotes de produtos para maximizar o lucro?
B) Qual o lucro Mensal a indústria pode alcançar?
Answers
Answer:
The answer would be A
Step-by-step explanation:
Last question pls help then i will give away al points pls help.
Answers
Answer: i give up typing essays ill just give it to you straight azure clicks per second is 8.5 or 17/2
bronze click per second is 9.5 38/4
crimsons time is 2.28 i guessed the closest and used a calulator good thing i learned this recently
clicks for desert is 34.9 or 35 not too clear but 34.9 is closer but you can choose i got this from guesing the division and i got 35/4.2 and 34.9/4.2
emeralds time is 0.40 3/.40 or 3/0.40
clicks for the last one or fuscia is 6 6/0.70 is well 8 gawd dammit you made me rite anotha essay
I need help from big brain
Answers
Answer:
[tex]\frac{8}{3}[/tex] ÷ [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
If you are asking how many times does 8/3 goes into 2/3 then this means 8/3 is the dividend. The dividend is the number that is being divided by another number. This means the answer would be 8/3 divided by 2/3. I hope this makes sense.
I hope this helps :). If you have any questions let me know. Have a good day.
help me find the area pls
Answers
Area = 30
Step-by-step explanation:
a^2 + b^2 = c^2
12^2 + b^2 = 13^2
144 + b^2 = 169
b^2 = 169 - 144
b^2 = 25
b = 5
Area = 1/2 bh
Area = 1/2 (12)(5)
Area = 1/2 (60)
Area = 30
I need help with my homework pls somone help….
Answers
Answer:
x > 9
Step-by-step explanation:
since the dot is open there won't be a line under
I'm sorry to bother. I really can't understand this and my teacher isn't offering help after school today. Could someone help? I've already done 5-8
Answers
Answer:
Step-by-step explanation:
is this involved with the pythagorean angles?\
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
4x + 2y = -18
Answer:
Submit Answer
attestato
PLSSS HELP ASAP
Answers
c) Convert 120 into quinary equivalent.
Answers
Assuming 120 is a base 10 numeral, then
120 = 100 + 20 = 4×5² + 4×5¹
so you have
120₁₀ = 440₅
