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
Evaluate.
(4/9)^2 pleaseee
Answer:
simplified: (16/81)
rewritten: (2/3)^4
Step-by-step explanation:
hope this helps! if wrong you can delete it :)
Elena's distances and times for a training run are given by the equation , where represents distance in miles and represents time in minutes. Who ran faster during the training run?
Answer:
Elena's run for 1.17 miles in ten minutes
Step-by-step explanation:
From the question
y = 8.5 x ; where x is Distance in miles, and y is time in minutes
and y= 10 minutes
thus on substituting the respected values we get
10 = 8.5 x
⇒ x = [tex]\frac{10}{8.5}[/tex] = 1.17 miles
Therefore Elena's run for 1.17 miles in ten minutes
You want to buy some noodles. A 9 -ounce package costs $3.15. A 15-ounce package costs $5.55. A 24-ounce package costs $7.92. Which package is the best buy?
PLEASE ANSWER QUICKLY
Answer:
A 14-ounce package that costs $5.46
Step-by-step explanation:
hope it helps ;)
Which expression is equivalent to 2( 7c - 8 )?
Answer:
14c-16
Step-by-step explanation:
Answer:
14c - 16
Step-by-step explanation:
2( 7c - 8 ) All you do is distribute:
14c - 16
Ace
Help meeeee someone I will give u 5 point
Answer:
Length of the ladder = 9.5 feet
Step-by-step explanation:
Point A of ladder AC is at 9 ft from the ground and point C is 3 feet from the base of the wall,
AB = 9 feet
BC = 3 feet
By applying Pythagoras theorem in the right triangle,
AC² = AB² + BC²
AC² = 9² + 3²
AC² = 81 + 9
AC = √90
= 9.486 feet
≈ 9.5 feet
Therefore, length of the ladder is 9.5 feet.
Use the Zero Product Property to find the x-intercepts for y=3(x−5)(2x+3)
Answer: The X intercepts are 5 and -3/2
HELP PLEASE
Consider the line y = 6x-7. Find the equation of the line that is perpendicular to this line and passes through the point (8, 3). Find the equation of the line that is parallel to this line and passes through the point (8, 3).
Answer:
y = (-x + 8)/6
Step-by-step explanation:
y =6x-7
gradient of perpendicular to the line above is -1/6.
using the point (8,3)
y - y1 = m(x - x1)
y - 3 = -1/6(x - 8)
6y-18 = -1(x - 8)
y = (-x + 26)/6
Simplify the fraction.
Answer:
3b/4a²
Step-by-step explanation:
3a²*4b³/16(a²b)²
12a²b³/16a⁴b²
12b/16a²
3b/4a²
Question 6
What does the relationship between the slopes of corresponding line segments in the prelmage and in the image imply about the line segments?
In other words, what do you know about two or more line segments that have the same slope?
Therefore, when we draw the slope of line then the slope of corresponding line segment in the preimage and image apply about the line segments both are equal.
What is the slope of line?
The slope of a line is its vertical change divided by its horizontal change, also known as rise over run.
When the two or more line segments that have the same slope are parallel to each other.So, the lines graphed by a system of equation is also same slope which would be parallel to each other.
Hence, when we draw the slope of line then the slope of corresponding line segment in the preimage and image apply about the line segments both are equal.
To know more about the slope
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A robin perched in a tree 40 feet above sea level. Directly below the robin, a seagull is flying 13 feet above sea level. Directly below the birds is a clownfish, swimming 33 feet below sea level.
Answer:
See explanation
Step-by-step explanation:
The question is incomplete. However, I'll solve on a general terms.
Since the robin, seagull and fish are on directly below one another; a possible question could be to calculate the distance between the robin and the clownfish
The given parameters are:
[tex]Robin = +40ft[/tex]
[tex]Seagull= +13ft[/tex]
[tex]Clownfish= -33ft[/tex]
+ represents above sea level while i represents below
The distance is then calculated as:
[tex]Distance = Robin - Clownfish[/tex]
[tex]Distance = +40ft - (-33ft)[/tex]
[tex]Distance = +40ft +33ft[/tex]
[tex]Distance = 73\ ft[/tex]
question 1 and 2 please :) (exact form)
Answer:
1. x = 6 cm
2. The coordinates of the x-intercept are (-15.798879, 0) and (8.177004, 0)
b) The maximum value of is y is approximately 459.874
The value of 'x' for which the maximum occurs is x is -3.8109375
c) 'k' is approximately -15.63748 or 'k' is approximately 8.0156
Step-by-step explanation:
1. The area of rectangle ABCD - Area of triangle ABP = 114 cm²
Therefore, we have;
The area of rectangle ABCD = (2·x - 3)·(3·x + 1)
∴ The area of rectangle ABCD = 6·x² + 2·x - 9·x - 3 = 6·x² - 7·x - 3
The area of triangle ABP = 1/2 × (3·x + 1)·x = 3·x²/2 + x/2
The area of rectangle ABCD - Area of triangle ABP = 6·x² - 7·x - 3 - 3·x²/2 - x/2
6·x² - 7·x - 3 - 3·x²/2 + x/2 = 9·x²/2 - 13·x/2 - 3 = 114
9·x²/2 - 15·x/2 - 3 = 114
9·x² - 15·x - 6 - 228 = 0
9·x² - 15·x - 234 = 0
x = (15 ± √((-15)² - 4 × 9 × (-234)))/(2 × 9) = (15 ± 93)/18
∴ x = 6 or x = -13/3
Given that x is a natural number, we have that x = 6 cm
2. The given equation is 'y = -3.2·x² - 24.39·x + 413.4'
Therefore, we have;
The x-intercept are the values of 'x', where the value of 'y' is 0
Therefore, we have, at the x-intercept;
y = 0 = -3.2·x² - 24.39·x + 413.4
By the quadratic formula, we have;
x = (24.39 ± (√((-24.39)² - 4×(-3.2)×413.4)))/(2 × (-3.2))
x ≈ -15.798879 or x ≈ 8.177004
The coordinates of the x-intercept are;
(-15.798879, 0) and (8.177004, 0)
b) The maximum is given at dy/dx = 0
Therefore, at the maximum point, we have;
dy/dx = d(-3.2·x² - 24.39·x + 413.4)/dx = -6.4·x - 24.39 = 0
dy/dx = -6.4·x - 24.39 = 0
∴ x = 24.39/(-6.4) = -3.8109375
x = -3.8109375 at the maximum point
At the maximum point, we have;
y = -3.2·x² - 24.39·x + 413.4 = -3.2·(-3.8109375)² - 24.39·(-3.8109375) + 413.4 ≈ 459.874
y ≈ 459.874
Therefore, the maximum value of 'y' is given as follows
[tex]y_{max}[/tex] ≈ 459.874
The value of 'x' for which the maximum occurs is x = -3.8109375
c) The coordinate of the point is (12.3, k), therefore, we have;
y = -3.2·x² - 24.39·x + 413.4
When y = 12.3, therefore, -3.2·x² - 24.39·x + 413.4 = 12.3
-3.2·x² - 24.39·x + 413.4 = 12.3
-3.2·x² - 24.39·x + 413.4 - 12.3 = -3.2·x² - 24.39·x + 401.1 = 0
By the quadratic formula, we have;
x = (24.39 ± √((-24.39)² - 4×(-3.2)×401.1))/(2 × (-3.2))
x ≈ -15.63748 or x ≈ 8.015600
Therefore, k ≈ -15.63748 or k ≈ 8.015600
The diagram below shows an angle, 0, graphed in the xy -coordinate plane. Segment RT is the initial side of the angle, and segment RM is the terminal side. Segments RT
and RM are radii of the unit circle centered at the origin R (0,0).
The x-coordinate of point M is -1/2. What is the measure of 0 to the nearest thousandth of a radian.
Answer:
Step-by-step explanation:
for this problem u need the unit circle.
In the unit circle there is a point with -1/2 as the x value that is at 240 degrees.
then you convert 240 degrees to radians --> 240 X pi/180 = 4.189
the unit circle is below, you needa remember for the test
Good luck on your EOC, i'm doing it too
The two scalene triangles seen below are similar figures. What is the scale factor from the small scalene triangle on the left to
the large scalene triangle on the right? The scalene triangles are not drawn to scale.
Step-by-step explanation:
Scale factor
= Side length of big triangle / Side length of small triangle
= 12/5 = 24/10 = 33.6/14 = 2.4.
Answer: 2.4
Step-by-step explanation:
10 × 2.4 = 24
5 × 2.4 = 12
14 × 2.4 = 33.6
What is the quotient of 25.95 divided by 50.25? *
Answer:
Quotient: 2
Remainder: 0
50 = 25 × 2 + 0
Step-by-step explanation:
Answer:0.516
Step-by-step explanation:You need to divide 29.25 by 50.25.
Simplify the expression.
3.7 - 4.7n - 3n + 8
Please help me I don’t know this
Answer:
Quotient: 56 Remainder: 3
What operations would you perform, and in what order would you perform them to solve
1 ÷ 5n = 20?
Answer:
cross multiplication
Step-by-step explanation:
1 5n
_ _
_
What is the value of the expression below when
x = 3?
7x -4
Answer:
17
Step-by-step explanation:
7(3) - 4
21 - 4
17
Answer:
i dont know
Step-by-step explanation:
i dont know
Madelyn is in a hot air balloon that has just taken off and is floating above its launching point. Eddie is standing on the ground, 6 meters away from the launching point. If Madelyn and Eddie are 9 meters apart, how high up is Madelyn? If necessary, round to the nearest tenth.
Ill be marking brainliest
Answer:
8.9 meters
Step-by-step explanation:
this seems like a problem where you can use the pythagorean theorem:
you know one of the two legs (6m) and the hypotenuse (9m), you must find the other leg
a^2 + 6^2 = 9^2
a^2 + 36 = 81
a^2 = 45
a = [tex]\sqrt{45}[/tex] or [tex]\sqrt{9}[/tex] · [tex]\sqrt{5}[/tex] which simplifies to be 3[tex]\sqrt{5}[/tex] or approx. 8.9 meters
A quadrilateral has
no pairs of parallel
sides. What two
Shapes could it be?
(Not trapezium/trapezoid
kite, rhombus)
Answer:
parallelism
Step-by-step explanation:
I'm just looking also the answer!
Solve the system of equations - 9x - 2y = -3 and -20 – 3y = 7 by combining the equations.
EASY POINTS!?!?!?!?!?!
Write an equation with a variable for the situation below: Mike's high school played 17 hockey games this year. The team won most of their games. They were defeated during 4 games. How many games did they win?
find the measure of the indicated angle ? no l
The interior angle of any triangle sum to 180° in measure, so that angle ACB has measure
m∠ACB = 180° - 67° - 35° = 78°
Angles ACB and BCD are supplementary because they occur on the same ray AD, which means they also sum to 180° in measure. Then angle BCD has measure
m∠BCD = 180° - 78° = 102°
Answer:
102 degrees
Step-by-step explanation:
for this problem, add the angles given to 180 degrees to find the remaining angle ACB in the triangle. Once you have that angle, you can subtract it from 180 degrees to find BCD, because side ACD is straight. By adding Angle CAB (67 degrees) and Angle ABC (35 degrees), you end up with the missing 98 degrees to reach 180 degrees. thus, when subtracting to find BCD on the straight of ACD, a value of 102 degrees remains for Angle BCD
A baker buys a 5 lb bag of sugar. She uses 1 2/3 lb to make some muffins and 2 3/4 lb to make a cake. How much sugar does she have left?
do step by step
Answer:
7/12 lb of sugar.
Step-by-step explanation:
first we add 1 2/3 and 2 3/4, which will give you 4 5/12 then subtract 5 lb by 4 5/12 and your answer will be 7/12
The number of grams of zero-calorie sodium in a restaurant meal is compared to the total number of calories in the meal. The correlation coefficient relating the two variables is 0.74.
Which best describes the strength of the correlation, and what is true about the causation between sodium and the number of calories in this meal?
It is a weak positive correlation, and it is not likely causal.
It is a weak positive correlation, and it is likely causal.
It is a strong positive correlation,and it is not likely causal.
It is a strong positive correlation, and it is likely causal.
Answer: It is a strong positive correlation,and it is not likely causal.
Step-by-step explanation: Correlation Coefficient value is used to determine the strength of linear relationship between two variables. The value ranges from - 1 to +1.with negative values depicting a negative relationship and positive values showing positive relationship. Value of 0 implies that, no relationship exists. The closer the correlation Coefficient value is to +1 or - 1, the greater the strength of the relationship between them. Also correlation does not mean causation. Hence, a correlation coefficient of 0.74 depicts a strong positive relationship. However it doesn't imply causation.
The given correlation is strong positive correlation,and it is not likely causal.
We have given that,
The correlation coefficient relating the two variables is 0.74.
What is the correlation coefficient?Correlation coefficient value is used to determine the strength of linear relationship between two variables. The value ranges from - 1 to +1.
The correlation coefficient value is used to determine the strength of linear relationship between two variables. The value ranges from - 1 to +1.
with negative values depicting a negative relationship and positive values showing positive relationship.
The value of 0 implies that, no relationship exists.
The closer the correlation coefficient value is to +1 or - 1, the greater the strength of the relationship between them.
Also correlation does not mean causation.
Hence, a correlation coefficient of 0.74 depicts a strong positive relationship.
However it doesn't imply causation.
We have the given correlation coefficient relating the two variables is 0.74 and it is near +1
Therefore,the given correlation is strong positive correlation,and it is not likely causal.
To learn more about the correlation coefficient visit:
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Write an equation that models the bee population (b), (w) weeks after it is first measured. You'll use the variable b for the bee population and the variable w for the weeks after it is first measured.
The required equation that models the bee population (b) is y = 2000x + 500
Equation of a line
The equation of a line in slope-intercept form is expressed as y = mx + b
where;
m is the slope of the line graphb is the y-interceptUsing the coordinate points on the graph (2, 2000) and (3, 4000)
Get the slope of the line
[tex]m=\frac{4000-2000}{3-2}\\m=\frac{2000}{1}\\m=2000[/tex]
Since one of the coordinate points lies on the y-axis at (0, 500), hence the y-intercept is 500.
The required equation that models the bee population (b) is y = 2000x + 500
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Help ....................
Answer:
(helps)
Step-by-step explanation:
What is 9 5/32 as a decimal
Answer:
The correct answer is 9.15625
✧brainliest appreciated✧
Answer:
9.15625
Step-by-step explanation:
step 1- Convert the proper fraction to decimal: Divide the numerator by the denominator: 5 ÷ 32 = 0.15625
step 2- Add this decimal number to the whole number of the mixed fraction: 9+ 0.15625 = 9.15625
Therefore, the mixed number 9 5/32 converted to decimal number is: 9.15625
(can i get brainliest)
Help, Please and thank you!
Answer:
Last one
Step-by-step explanation:
The slope intercept form is: y=mx +b
m=the slope and b is the y intercept
so it would be the last one
Jawad has seven rocks.
The total weight of all seven rocks is 5 kilograms.
6 of the rocks each have a weight of 720 grams.
Work out the weight, in grams, of the other rock.
I performed a transcriptome analysis (Clariom D Array, Affymetrix) of two groups of subjects (human tissue) by using Transcriptome Analysis Console (TAC; Affymetrix) and Partek software and same cutoff (n=20; FC greater than 1.5 and P value less than 0.05). However, the overlap between differential expressed genes between both software was quite low.
someone has some comment about why this may be happening?