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
Find the value of
5³
(3/2)³
(-1/2)³
Answers
[tex]\huge\boxed{\underline{\bf \: Answer}}[/tex]
(1) Value of 5³
[tex] \sf{5}^{3} \\ = \sf5 \times 5 \times 5 \\ = \boxed{\bf 125}[/tex]
(2) Value of (3/2)³
[tex] \sf( { \frac{3}{2} })^{3} \\ \sf = \frac{ {3}^{3} }{ {2}^{3} } \\ \sf= \frac{3 \times 3 \times 3}{2 \times 2 \times 2} \\ = \boxed{ \bf \frac{27}{8} }[/tex]
=> The answer in decimal format is [tex]\boxed{\underline{\bf \: 3.375}}[/tex]
(3) Value of (-1/2)³
[tex] \sf( \frac{ - 1}{2} ) ^{3} \\ = \sf \frac{ { - 1}^{3} }{ {2}^{3} } \\ \sf = \frac{ - 1 \times - 1 \times - 1}{2 \times 2 \times 2} \\ = \boxed{ \bf \frac{ - 1}{8} }[/tex]
=> The answer in decimal format is [tex]\boxed{\underline{\bf \: -0.125}}[/tex]
_______
Hope it helps.
RainbowSalt2222
What are the domain and range of the function f(x) = 3/4 x+5?
Answers
Answer:
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined. The range is the set of all valid y values
What is 40 kilometers per hour in meters per hour?
Answers
Answer:
D. 40,000
BRAINLIEST, PLEASE!
Step-by-step explanation:
There are 1000m in 1km.
40 x 1000 = 40,000
The smallest number when subtracted from the difference of the square of 29 and 22 gives a perfect square is
Answers
Answer:
Your answer is 33.
step- by step :
29×29-22×22=841-484
= 357
Closest square of 18 which is 324.
So, 357-324= 33. ans.
if i have one quarter,7 dimes, and four nickes how much money do i have.
Answers
answer quick pls!!
Find the ordered-pair solution of y = 4x + 1 that corresponds to x = -1
Answers
Answer:
(- 1, - 3 )
Step-by-step explanation:
Substitute x = - 1 into the equation and evaluate for y
y = 4(- 1) + 1 = - 4 + 1 = - 3
solution is (- 1, - 3 )
HELPPGPGPPHPHGPPFPSLLSLSL
Answers
If she would have bought them for the grocery store it would have been 14 dollars
So in conclusion she saved 1 dollar
Option 3
a times b whole cube
Answers
Answer:
i don't know what's the question
Step-by-step explanation:
like I don't know
Write an equation for the situation then solve for x.
Julio rented a bike from Krystal's Bikes. It
cost $13 plus $2 per hour. If Julio paid $17,
then he rented the bike for how many hours?
Answers
The first thing we need to determine is: what exactly are we trying to find? Well, in this case, that would be the amount of hours Julio rented a bike for. We can set that number as a variable: x
We know that the rental total was 17 dollars. Therefore, we will set our equation equal to 17: (equation)=17
Next, we know that the rental costed 13 dollars upfront plus 2 dollars for every hour he rented it for. We can substitute “x” in for the amount of hours he rented it for, since that is what we are trying to find. We will multiply that by 2, since he has to pay 2 dollars for ever “x” hour he rents the bike. Add 13 dollars to that, since he has to pay that upfront: 2x+13=17
Now, let’s solve for x! Start by subtracting 13 from each to get the “2x” by itself:
2x=4
Now divide each side by 2 to get the value of x
X=2
Therefore, Julio rented the bike for 2 hours!
I hope this helped! Comment if you have any questions!
The number of hours should be 2.
Given that,
There is the cost of $13 plus there is $2 per hour.And, the amount paid is $17.Here we assume the number of hours be x.Based on the above information, the equation is as follows:
2x + 13 = 17
2x = 17 - 13
2x = 4
x = 2
Therefore we can conclude that the number of hours should be 2.
Learn more: brainly.com/question/3530056
Anna finishes 5 homework problems in 15 minutes. Kailey finishes 10
homework problems in hour. Are they working at the same rate?
Answers
Answer:
no, they are not working at the same rate.
Step-by-step explanation:
Annah takes only 3 minutes to complete 1 homework while Kailey takes 6 minutes to complete 1 homework
Answer:
no no they are not
Step-by-step explanation:
cause if you do 5 times 5 timess 5 times 5 times 5 it it 75 but 10 homework an hour is not equal to it
Is the inequality sometimes, always, or never true?
Answers
Answer:
never true.
Step-by-step explanation:
Answer: Never true
Work Shown:
-2(2x+9) > -4x+9
-4x-18 > -4x+9 ... distribute
-18 > 9 .... add 4x to both sides; they cancel
The last inequality is false regardless of which x value you pick. Since the last inequality is always false, that means the first inequality is always false.
what is ????????????????? 21x+28<10-3x
Answers
Answer:
x < -3/4
Step-by-step explanation:
21x + 3x < 10 - 28
24x < -18
x < -18/24
x < -3/4
Write 6.21 as a mixed number in simplest form.
Answers
Answer:
6.211=( 6.21×100) (1×100) =621100
Hope that helped you
Explanation:
6.21 = 621/100 = 6 21/100
f(x)= -2x^2 - 5 and f(2)= -13
can someone solve this in steps please?
Answers
This is one way you could write out the steps
f(x) = -2x^2 - 5
f(2) = -2(2)^2 - 5
f(2) = -2(4) - 5
f(2) = -8 - 5
f(2) = -13
Answer:
Step-by-step explanation:
First you have to get the meaning clear.
f(2) means that wherever you see an x on the right side of the equation, you put a 2.
f(2) means -2*(-2)^2 - 5
(-2)^2 = -2 * -2 = 4
f(2) = -2 * 4 - 5
f(2) = - 8 - 5
f(2) = -13
Jack walks onto an elevator at floor level 2. The elevator goes up 3 floors, down 8 floors, and back up 11 floors. What floor is Jack on now?
Answers
Answer the following questions.
1. Trish can complete 10 problems in 60 minutes. At this rate, could she complete 25 problems in 130 minutes? Write your answer as YES or
NO.
Answers
If f(x) = + 8, what is f(x) when x = 10?
O4
O 9
O 13
O 36
Answers
Answer:
4 step by step explanation
The at {x} = 10, the value of the function remains +8.
What is function?A function is a relation between a dependent and independent variable. We can write the examples of functions as -
y = f(x) = ax + b
y = f(x, y, z) = ax + by + cz
Given is that the function f(x) is defined as -
f(x) = + 8
The given function is a constant function. This means that the value of the function remains the same irrespective of the value of {x} or the value in the function domain. So, at {x} = 10, the value of the function remains +8 only. This is true for all the values of {x}.
Therefore, the at {x} = 10, the value of the function remains +8.
To solve more questions on functions, visit the link below-
https://brainly.com/question/30194223
#SPJ7
WILL.MARK BRAINLEST. ( The length of a rectangular garden is 5m longer than its breadth .If its perimeter is 150 m,find the area of the garden ) step by step
Answers
Answer:
1400m^2
Step-by-step explanation:
Solution,
Let the breadth of the rectangle be x m, then the length of the rectangle will be x+5 m,
Now,
Perimeter of the rectangle=2(l+b)
150=2(x+5+x)
150=2(2x+5)
150=4x+10
150-10=4x
140=4x
140/4=x
35=x
So, the breadth of the rectangle=35 m
and length=(35+5)m=40m
Again,
Area of the rectangle=l×b
=40m×35m
=1400 m^2
I hope it helped U
stay safe stay happy
Answer: Area= 1400[tex]meter^{2}[/tex]
Step-by-step explanation:
ok so we can assume the
breadth=X
so, length = X+5 (because the length is 5 meters more than the breadth)
perimeter= 150 meters
the formula of the perimeter of a rectangle = 2 x ( Length + Breadth)
so now if we put the values,
2 * ( X+5 +X) = 150 ( because 150 is the perimeter)
2 * (2X + 5) = 150 (the value became 2x because when we add two variables with the same value it will be written as 2(any variable)).
now we multiply 2 with both sides
so ( 2 * 2X) + (2 * 5)
hence, 4X + 10 = 150
now we will solve the equation,
4X= 150 -10 (because we did transposal the signs will change from "+" to "-")
4x= 140
again with the transposal (when we write a number with a variable it shows that it means the number multiplied by the variable in this case it is 4 multiplied by X ) so when we transpose we will have to divide because multiplication turns into division while transposing
so now,
X= 140÷4
which is equal to 35
so finally X = 35
so as we have written in the beginning breadth= X
and LENGTH= X+5
so now we have found X
BREADTH= 35
LENGTH= 40 (because 35+5 is 40)
now we have to find area the formula for finding the area is LENGTH×BREADTH
so, 40 × 35 = 1400
now we put the unit which is square meters also known as [tex]m^{2}[/tex]
so there is your final answer 1400[tex]m^{2}[/tex]
3x
Are 10 - 20 and 5(2 - 20) equivalent expressions? Explain.
Answers
Answer:
No.
Step-by-step explanation:
Take the second expression: 5(2 - 20)
To solve, you must distribute the 5 to all terms within the parenthesis:
5(2 - 20) = (5 * 2) - (5 * 20) = 10 - 100 = -90
On the other hand:
10 - 20 = -10
∴ the two expressions are not equivalent.
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\text{\bold{No, they are not equivalent because...}}\\\\\\\large\textsf{5(2 - 20)}\\\large\textsf{= 5(2) + 5(-20)}\\\large\textsf{= 10 - 90}\\\boxed{\large\textsf{= \bf -90}}\\\\\large\textsf{10 - 20}\\\large\textsf{\boxed{\large\textsf{= \bf -10}}}\\\\\\\large\boxed{\star}\large\textsf{-10}\neq\large\textsf{-90}\large\boxed{\star}[/tex]
[tex]\huge\boxed{\mathsf{Answer: \bold{NO,}\ because \ \bf -10 \ does \ NOT}}\\\huge\boxed{\mathsf{\bf equal \ to -90}}\huge\checkmark[/tex]
[tex]\bullet\ \frak{Random\ fact: negatives \ are \ on\ the\bf \ LEFT\ side\ of\ the \ number\ line\ \& \ positives}\\\frak{are\ on\ the\bf \ RIGHT\ side\ of\ the\ number\ line}[/tex]
[tex]\large\text{Good luck on your assignment \& enjoy your day!}\\\\\\\huge\boxed{\frak{Amphitrite1040}}[/tex]
Estimate the shaded areas of the following shapes.???
Answers
Answer:
436cm^2
Step-by-step explanation:
you're gonna have to round up to the nearest whole number.for no.2 split the shape so that it'll give u two rectangles.for no.3 find the area of the small rectangle and minus from the area of the big rectangle
Big rectangle =30*16=480
small rectangle =4*11=44
480-44=436
Express
as a trinomial.
(2x – 6)(x – 4)
Answers
Answer:
[tex]2x^2 - 14x + 24[/tex]
Step-by-step explanation:
Answer:
[tex](2x - 6)(x - 4) \\ 2 {x}^{2} - 8x - 6x + 24 \\ 2 {x}^{2} - 14x + 24 \\ thank \: you[/tex]
What is the area?
Write your answer as a fraction or as a whole or mixed number.
Answers
Answer:
1 2/3 cm^2.
Step-by-step explanation:
Area = 1 2/3 * 1
= 1 2/3
Is 17/2 rational or irrational?
Answers
Answer:
it's a Rational number
Step-by-step explanation:
because it repeats and stops
Hi, I'm happy to help!
A number is rational if it repeats itself, or stops. This number, both in fraction and decimal form (8.5), stops. This means that the number is rational.
I hope this was helpful, keep learning! :D
if jack is sitting on the chair no 14 from the left Find his place from the right if the chairs are numbered from 1 to 40 ?
Answers
Answer:
26
Step-by-step explanation:
if his chair is 14 away from the left he would be 26 away from the right
Which definition best describes vertical angles?
Answers
Vertical angles are a pair of opposite angles formed by intersecting lines
What is the solution of
2x = 3 + 4 = 7?
Answers
Answer:
x = 6
Step-by-step explanation:
Given
[tex]\sqrt{2x-3}[/tex] + 4 = 7 ( subtract 4 from both sides )
[tex]\sqrt{2x-3}[/tex] = 3 ( square both sides )
2x - 3 = 3² = 9 ( add 3 to both sides )
2x = 12 ( divide both sides by 2 )
x = 6
x+4+3(x)=x-8
Answer this for me
Answers
Step-by-step explanation:
3x= (-8) -4
x=(-12)/3
x= -4
Hello!!! I can help
Answer:
= − 4
Step-by-step explanation:
Write the descending chromatic scale beginning on C
Answers
Answer:
c(half note), b(flat, quarter note), a(quarter note), g(quarter note), f(quarter note), e(flat, quarter note), d(quarter note), c(half note)
Step-by-step explanation:
i cant draw it on the sheet music itself but I hope that helps
How many gallons, quarts, and pints are in 72 cups (not all together)
Answers
Answer:
72 cups=4.5 gallons
72 cups=18 quarts
72 cups=36 pints
Step-by-step explanation:
To find out how many pints are in 72 cups you have to divide the volume value by 2. To find out how many quarts are in 72 cups you have to divide the volume value by 4. To find out how many gallons are in 72 cups you have to divide the volume value by 16.
Hope this helped for you!
the expression x - 0.10 X gives the cost of an item that is discounted 10% write this expression in the other way
Answers
Answer:
Step-by-step explanation:
Take out a common factor (x)
x ( 1 - 0.10 )
Now do the subtraction
0.90x