Integrate the integral:
[tex]\int \frac{1}{\sqrt{x} \sqrt{1-x} }[/tex]
Answer:
[tex]\displaystyle \int {\frac{1}{\sqrt{x} \sqrt{1-x} } } \, dx = 2arcsin(\sqrt{x}) + C[/tex]
General Formulas and Concepts:
Calculus
U-SubstitutionIntegration Property: [tex]\int {cf(x)} \, dx = c\int {f(x)} \, dx[/tex]Arctrig Integration: [tex]\displaystyle \int\limits {\frac{1}{\sqrt{a^2-u^2} } } \, du = arcsin(\frac{u}{a} ) + C[/tex]Step-by-step explanation:
Step 1: Define
[tex]\displaystyle \int\limits {\frac{1}{\sqrt{x} \sqrt{1-x} } } \, dx[/tex]
Step 2: Identify
Set up variables for u-substitution and integral trig.
[tex]\displaystyleu = \sqrt{x}\\a = 1\\du = \frac{1}{2\sqrt{x}}dx[/tex]
Step 3: integrate
Rewrite Integral: [tex]\displaystyle 2\int {\frac{1}{2\sqrt{x} \sqrt{1-x} } } \, dx[/tex][Integral] U-Substitution: [tex]\displaystyle 2\int {\frac{du}{\sqrt{1^2-(\sqrt{x})^2 } }[/tex][Integral] U-Sub Arctrig: [tex]\displaystyle 2\int {\frac{du}{\sqrt{1^2-u^2 } }[/tex][Integral] Arctrig: [tex]\displaystyle 2arcsin(\frac{u}{1}) + C[/tex]Simplify: [tex]\displaystyle 2arcsin(u) + C[/tex]Back-substitute: [tex]\displaystyle 2arcsin(\sqrt{x} ) + C[/tex]We are given the expression:
[tex]\int\limits {\frac{1}{\sqrt[]{x} }*\frac{1}{\sqrt[]{ 1-x^{2}}} } \, dx[/tex]
U-substitution:
let u = [tex]x^{1/2}[/tex] [So, x = u²]
[tex]\frac{du}{dx} = \frac{1}{2\sqrt[]{x}}[/tex] [differentiating both sides wrt x]
dx = du*2√(x)
dx = 2u(du) [Since u = √x]
Finding the Integral:
Plugging these values in the given expression:
[tex]\int\limits {u^{-1}*(1-u^{2})^{-1/2} } \, 2\sqrt[]{x}*du[/tex]
[tex]\int\limits {\frac{1}{u}*\frac{1}{\sqrt[]{ 1-u^{2}}}*2u } \, du[/tex]
The 'u' in the numerator and denominator will cancel out
[tex]\int\limits {\frac{1}{\sqrt[]{ 1-u^{2}}}*2 } \, du[/tex]
Since 2 is a constant
[tex]2\int\limits {\frac{1}{\sqrt[]{ 1-u^{2}}} } \, du[/tex]
Using the property: [tex]\int\limits {\frac{1}{\sqrt[]{1-x^{2}} }} \, dx[/tex] = ArcSin(x) + C
2*ArcSin(u) + C
Since u = √x :
2*ArcSin(√x) + C
Find three solutions to the linear equation 4x+y=20
Answer:
[tex](0,20),(1,16),(2,12)[/tex]
Step-by-step explanation:
[tex]We\ are\ provided\ with\ the\ equation:\\4x+y=20\\In\ order,\ to\ find\ solutions\ to\ a\ linear\ equation\ in\ two\ variables,\ we\\ usually\ substitute\ a\ value\ to\ either\ the\ abscissa or\ the\ ordinate\ to\ get\\ the\ corresponding\ ordinate\ or\ the\ abscissa.\\Hence,\\Here,[/tex]
[tex]Let's\ plug\ in\ simpler\ value's\ of\ 0,1,2\ as\ the\ x-co-ordinate\ to\ obtain\ it's\\ y-coordinate.\\Hence,\\Coming\ back\ to\ our\ equation:4x+y=20\\Substituting\ x=0,\\4*(0)+y=20\\y=20\\Hence,\\x=0,y=20\ or\ (0,20)\ is\ a\ solution\ of\ the\ equation.[/tex]
[tex]Substituting\ x=1,\\4*(1)+y=20\\4+y=20\\y=20-4=16\\Hence,\\x=1,y=16\ or\ (1,16)\ is\ also\ a\ solution\ of\ the\ equation.[/tex]
[tex]Substituting\ x=2,\\4*(2)+y=20\\8+y=20\\y=20-8=12\\ Hence,\\x=2,y=12\ or\ (2,12)\ is\ a\ solution\ of\ the\ equation\ too.[/tex]
[tex]Hence,\ collecting\ all\ the\ solutions\ of\ the\ equations:\\(0,20),(1,16),(2,12)\ are\ all\ solutions\ of\ the\ given\ equation.\\[/tex]
Find the product. Your answer must be in simplest form.
7/8 of 56
Answer:
You probably know that the number above the fraction line is called the numerator and the number below it is called the denominator. To work out the fraction of any number, we first need to convert that whole number into a fraction as well.
Here's a little tip for you. Any number can be converted to fraction if you use 1 as the denominator:
56
1
So now that we've converted 56 into a fraction, to work out the answer, we put the fraction 7/8 side by side with our new fraction, 56/1 so that we can multiply those two fractions.
That's right, all you need to do is convert the whole number to a fraction and then multiply the numerators and denominators. Let's take a look:
7 x 56
8 x 1
=
392
8
In this case, our new fraction can actually be simplified down further. To do that, we need to find the greatest common factor of both numbers.
You can use our handy GCF calculator to work this out yourself if you want to. We already did that, and the GCF of 392 and 8 is 8.
We can now divide both the new numerator and the denominator by 8 to simplify this fraction down to its lowest terms.
392/8 = 49
8/8 = 1
When we put that together, we can see that our complete answer is:
49
1
The complete and simplified answer to the question what is 7/8 of 56 is:
49
Hopefully this tutorial has helped you to understand how to find the fraction of any whole number. You can now go give it a go with more numbers to practice your newfound fraction skills.
Step-by-step explanation:
Answer:
forty nine
Step-by-step explanation:
convert 56 into a fraction (56/1) then multiply 7/8 × 56/1. it equals out to 392/8. then find the GCF of 392 and 8, which is 8. now divide boht the new numerator and denominator by 9 to simplify it to lowest terms. 49 is the answer
A bottle contains 15 marbles: 9 are white and 6 are green. What is the
probability of picking a white?
Answer: 3/5
Step-by-step explanation:
Fist find out how many whites are there and divide it by the total to find the probability.
9/15 simplify it to 3/5
HELP PLEASE I WILL MARK BRAINLIEST
Answer:
M<1 = 131
M<2 = 49
Step-by-step explanation:
1. Alternate interior angles theorem
2. 180-131 = 49
PLZ HELP Will give you brainly if it works
Answer:
The prime number is only 11
11 is the only one i seee
1.) Multiply 2ab(−a+2b+3).(1 point)
8a2b2
−2a +2ab+3b
8ab
−2a2b+4ab2+6ab
2.) Simplify the polynomial using multiplication.
xy(3x2+2x−3y)
(1 point)
3x3y+2x2y−3xy2
3x3+2xy−3y
2x3y2
3x3+2x2−3y2
The area of a rectangle is given by the expression (x+3)(4x−2). Which of the following is an equivalent expression for the area?(1 point)
13x−2
4x2+14x+6
4x2+10x−6
14x−6
Multiply (x+2)(x2−3x +4)(1 point)
x3+5x2+10x+8
x3−x2−2x+8
x2−2x+6
2x2−6x+8
Simplify the polynomial using multiplication.
−5b(2a−3a2)
(1 point)
−10ba+15ba2
10ba−15ba2
−10a+3ba2
−5b+2a−3a2
Answer:
(x+3)(4x−2) = 4x2+10x−6
(x+2)(x2−3x +4) = x3−x2−2x+8
Step-by-step explanation:
Explain how to solve 5d = 35
Answer:
D=7
Step-by-step explanation:
SO isolate the variable y dividing 5 on both sides
d=7
Answer: d = 7
Step-by-step explanation:
5d = 35
You have to divide both sides by 5 since we need to isolate the variable 'd' to figure out what d is.
5d ÷ 5 = d
35 ÷ 5 = 7
So d = 7
Javon has 1/2 a cup of flour, Sam has 1 1/6 cups of flour, and Antoine has 1 3/4 cups of flour. How many cups of flour do they have all together A. 41/12 B. 17/12 C 2.17 D 2.1712
Can someone help me find X for number 4
3/ If f(x) = 2x -5 Find f(x-1)=
Explanation: Here we have function f(x) = 2x - 5
and we're asked to find f(x - 1).
Don't be thrown off if you're asked to plus a variable into a function.
If f(x) = 2x - 5, then f(x - 1) = 2(x - 1) - 5.
Remember to use parenthses when substituting into a function.
So simplifying on the right side, we would distribute the 2
through the parenthses and we have 2x -2 - 5.
Now combining like terms, we have 2x - 7
2(x + 5) = -10x + 34
Answer: X = 2
Step-by-step explanation: calculator
A restaurant borrowed
$15,000 to remodel.
The loan is for 7 years and
the yearly interest rate is
4.25%. How much interest
will the restaurant pay?
Answer:
$4462.50
Step-by-step explanation:
simple interest =principal × rate × time\100
This is an absolute value problem with LETTERS?! Absolute madness (no pun intended)
Answer:
a
Step-by-step explanation:
sjejeneissbebdejjesj
help me plz
Follow right steps
Here is the answer:
75 - 40 = t
Brainliest pls
Answer:
75=T+40
35
Step-by-step explanation:
75=T+40 subtract 40 from both sides and we get 35
which statement is not true of the given diagram?
10.You can buy 5 stickers for $3. How many stickers could you buy for $12 if the price remains proportional?
20
12
10
15
Solve for x; round to the nearest tenth of meter (please help will definitely give Brainliest❤️❤️)
Answer:
the first answer
Step-by-step explanation:
In SOHCAHTOA, we are using soh
sin(23)=2500/x
The abbreviation for interquartile range is IQR.
A
False
B
True
Answer:
B, True
Step-by-step explanation:
Answer:
B)True
Step-by-step explanation:
IQR= Interquartile Range
ABCD is a parallelogram, find the value of y
Answer:
33
Step-by-step explanation:
angles A and B should add up to 180, so A must be 40, and because it is a parallelogram the anlge across from it should also equal 40. 33+7=40.
If z = 1 - square root 3i, what is z^3
Answers
-8
8
-8i
8i
Answer:
[tex]z = 1 - \sqrt{3} i \\ {z}^{3} = (1 - \sqrt{3} i) ^{3} \\ =(1 - \sqrt{3} i)(1 - \sqrt{3} i)(1 - \sqrt{3} i) \\ open \: brackets \\ = (1 - 2 \sqrt{3} i + ( { \sqrt{3} i})^{2} )(1 - \sqrt{3} i) \\ but \: {( \sqrt{3}i) }^{2} = - 3 \: since \: {i}^{2} \: is \: - 1 \: in \: complex \: numbers \\ = (1 - 2 \sqrt{3} i - 3)(1 - \sqrt{3} i) \\ = ( - 2 - 2 \sqrt{3} i)(1 - \sqrt{3} i) \\ = ( - 2 + 2 \sqrt{3} i - 2 \sqrt{3} i + 2( { \sqrt{3} i)}^{2} ) \\ = - 2 - 6 \\ = - 8[/tex]
Answer:
A
Step-by-step explanation:
Edge 2023
Look/read the picture please!
Factor using the GCF method
8r3 + 16r2
Answer:
8r^2(r + 2)
Step-by-step explanation:
Factor 8r^3 + 16r^2
= 8r^2(r + 2)
Answer:
56 r
Step-by-step explanation:
8r x 3 + 16 r x 2
24 r + 32 r
56 r
What is the opposite of -|-32|
K/-3 + 3 =-2
Find the estimate of k
Answer:
K= 15
Step-by-step explanation:
K/-3 +3 = -2
Simplify by subtracting 3 on each side:
K/-3 = -2-3
K/-3 = -5
Simplify further by multiplying each side by -3:
K= -5*-3
K = 15
can I get some B plz
Answer:
What do you mean?
Step-by-step explanation:
Write a linear function f with the given values. f(6)=-2, f(0)=-5
Answer:
y = 0.5m - 5
Step-by-step explanation:
the equation of a line can be written as
y = mx + b, with x being the input and y the output
let's plug in our two values.
-2 = m(6) + b
-2 = 6m + b
-5 = 0m + b
-2 = 6m+b
-5 = b
plug -5=b into the first equation
-2 = 6m - 5
add 5 to both sides
3 = 6m
divide both sides by 6
0.5 = m
our function is now
y = 0.5m - 5
A circle of radius 90 inches has a central angle that intercepts an arc of length 120 inches. Explain whether the measure of the central angle is 34 radians
A. The measure is not 34 radians. The measure is 32 radians because the angle measure in radians is the diameter divided by the arc length.
B. The measure is not 34 radians. The measure is 43 radians because the angle measure in radians is the arc length divided by the radius.
C. The measure of the angle is 34 radians because the angle measure in radians is the radius divided by the arc length.
D. The measure is not 34 radians. The measure is 23 radians because the angle measure in radians is the arc length divided by the diameter.
Answer:
D
Step-by-step explanation:
I really don't know not smart
Airline fares for a flight from Dallas to Austin are $30 for first class and $25 for tourist class. If a flight had 52 passengers who paid $1360, how many first class and tourist class passengers were there?
There were 40 tourist class passengers and 12 first class passengers.
Explanation:
Let the number of passengers who booked for tourist class be
=
x
Then, number of passengers who booked for first class
=
52
−
x
According to question,
Total money paid = $25(tourist class)+$30(first class)
$
1360
=
$
25
(
x
)
+
$
30
(
52
−
x
)
1360
=
25
x
+
1560
−
30
x
1360
−
1560
=
25
x
−
30
x
−
200
=
−
5
x
x
=
−
200
−
5
x
=
40
So, there were 40 tourist class passengers.
Now first class passengers
=
52
−
x
=
52
−
40
=
12
∴
There were 40 tourist class passengers and 12 first class passengers.
As a check
Total money paid = $25(tourist class)+$30(first class)
R
H
S
=
$
25
(
40
)
+
$
30
(
12
)
$
1000
+
$
360
=
$
1360
L
H
S
=
$
1360
Hence verified.
1) Sarah bought 12 meters of fabric to make a patchwork quilt. If the fabric was on sale for $6.29 per meter, how much did Sarah spend? HELP PLS
Answer:
She spent $75.48
Step-by-step explanation:
multiply the price per meter by the amount of meters she purchased.