The exact length of the curve for the function y = ln(1 - x²) is log(5/4) - 1/9
The general formula for the arc length of the curve y on the interval [a, b] is written as,
[tex]s=\int\limits^a_b {\sqrt{1+(\frac{dy}{dx})^2 } } \, dx[/tex]
Here we have given that the function is y = ln(1 - x²)
And the limit is 0 ≤ x ≤ 1/9
When we differentiate the function, then we get the value of y' as,
y' = 1/(1 - x²) × (-2x) = -2x/(1 - x²)
Now, we have to apply the values on the arc length formula, then we get,
[tex]s=\int\limits^{1/9}_0 {\sqrt{1+(\frac{-2x}{1-x^2} )^2 } } \, dx[/tex]
When we simplify this one then we get,
[tex]s=\int\limits^{1/9}_0 {\sqrt{\frac{1+x^4-2x^2+4x^2}{(1-x^2)^2} } } \, dx[/tex]
Now, we have to divide numerator by denominator and expressing using
the rule Dividend/Divisor = Quotient + (Remainder/Divisor)
Then we get the resulting equation as,
[tex]s=\int\limits^{1/9}_0 {-1 + \frac{2}{1-x^2} } \, dx[/tex]
When we apply the limit value, then we get
s = −1/9 + log∣10/8∣−log(1)
When we simplify this one then we get,
s = log(5/4) - 1/9
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What is the area of 4 in a circle?
On solving the provided question, we can say that, 16 square units make up the area of a circle with a radius of 4 units.
what is radius?The length of a circle or sphere, in more contemporary use, is the same as its radius in classical geometry, which is one of the line segments from its center to its circumference. The Latin word radius, which also refers to the spokes of a wagon wheel, gave rise to the term. Through the center of the circle, a straight line defines the diameter. Half of the diameter is the radius. End in the circle's center after beginning at one of its points.
what is area of circle?Pi times the radius squared equals the area of a circle (A = π r²). Learn how to apply this equation to determine a circle's area given its diameter.
16 square units make up the area of a circle with a radius of 4 units.
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Determine the largest integer value of x in the solution of the following inequality.
2x+6<-4
Answer: -6
Step-by-step explanation: To determine the largest integer value of x in the solution of the inequality 2x+6<-4, we first need to isolate x on one side of the inequality. We can do this by subtracting 6 from both sides of the inequality, which gives us 2x<-10. Next, we can divide both sides of the inequality by 2, which gives us x<-5. Since the inequality has a strict inequality symbol, we can conclude that the largest integer value of x that satisfies the inequality is -6.
The table represents a quadratic function. Write an equation of the function in
standard form.
The standard form of the equation of the line for the function is; y =6x + 18
What is the equation?We know that it is possible to obtain the equation of the line by obtaining the slope of the data points. The slope of the data points can be obtained by the use of the points that have been shown in the table.
Taking any two points on the table we have;
[tex]y_{1}[/tex] = 0
[tex]y_{2}[/tex] = -12
[tex]x_{1}[/tex] = -3
[tex]x_{2}[/tex] = -1
Using;
y - [tex]y_{1}[/tex] = [tex]y_{2}[/tex] - [tex]y_{1}[/tex] /[tex]x_{2}[/tex] - [tex]x_{1}[/tex] (x - [tex]x_{1}[/tex] )
We have;
y - 0 = (-12) - 0/(-1) - (-3) ( x - (-3))
y = 12/2 (x + 3)
y =6x + 18
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what is the slope between (-9,3) and (-1,1)
Answer:
m = -1/4
Step-by-step explanation:
The slope is rise/run or (y2 - y1) / (x2 - x1)
We see the y decrease by 2 and the x increase by 8, so the slope is
-2/8 = -1/4
Answer:
Slope = -1/4
Step-by-step explanation:
Now we have to,
→ find the needed slope.
Formula we use,
→ Slope(m) = (y2 - y1)/(x2 - x1)
Then the slope will be,
→ m = (y2 - y1)/(x2 - x1)
→ m = (1 - 3)/(-1 -(-9))
→ m = -2/(-1 + 9)
→ m = -2/8
→ [ m = -1/4 ]
Hence, the slope is -1/4.
HELP WHAT IS THIS !! i need help
Step-by-step explanation:
always remember Pythagoras for right-angled triangles :
c² = a² + b²
c is the Hypotenuse (the side opposite of the 90° angle), a and b are the legs.
this principle must be always fulfilled, otherwise it is not a right-angled triangle.
when your have a triangle problem (particularly for a right-angled triangle) with only side information, there is a high chance that you need to use Pythagoras.
in our case
(2×sqrt(3))² = x² + (sqrt(3))²
4×3 = x² + 3
12 = x² + 3
x² = 9
x = 3
that's all.
FYI : sqrt(x²) has actually 2 solutions : -x and +x, as both are squared equal to x².
but a negative number does not make any sense for general side lengths and similar things. so, the positive solution here is the only valid one.
When solving an equation, Anne's first step is shown below. Which property justifies Anne's first step?
\text{Original Equation:}
Original Equation:
3x-1 =
3x−1=
\,\, 3
3
\text{First Step:}
First Step:
3x =
3x=
\,\, 4
4
distributive property of multiplication over addition
addition property of equality
division property of equality
multiplication property of equality
The first step that justifies Anne's first step while solving the expression is the commutative law of addition.
The property that best justifies Anne’s first step is the addition property of equality. This allows you to add four on the left side of the equal sign to cancel it out. In order to be fulfill the property, what you do to one side you must do to the other so you add that same amount (4) to the right side of the equal sign.
3x-4 = 5
(3x-4) +4 = 5 + 4
3x = 9
Final Answer: Addition Property of Equality
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In the figure, Angle A =120° . Find the remaining angles.
The remaining angles ∠B ,∠C and ∠D is 90°,60°,90°.
Given : Angle A = 120°
To find: ∠B ,∠C , ∠D
Solution: In figure, an inscribed angle is the angle formed in the innards of a circle when two heartstrings cross on the circle. It can also be outlined as the angle subtended at a point on the circle by two presented junctures on the circle. Inversely, an incised angle is defined by two heartstrings of the circle sharing an endpoint .
∠A+∠C=180
∠C=180-120
∠C= 60;
In triangle ABC : ∠BAC + ∠ACB+∠ABC=180°
60° + 30° + ∠ABC = 180°
∠ABC = 180°-90°
∠ABC = 90° (so B is 90°)
Therefore, ∠B+∠D=180°
∠D=180°-90°
∠D=90°
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Where in an equation for photosynthesis does glucose belong?on the left, because it is a producton the left, because it is a reactanton the right, because it is a producton the right, because it is a reactant.
Answer:
carbon dioxide + water sunlight glucose + oxygen
Step-by-step explanation:
glucose on the right because it is a by product of photosynthesis.
How do you draw an angle ABC?
Draw a line segment, place the compass point on point A, and draw an arc that intersects the line segment. Next, place the compass point on point B, and draw another arc that intersects the first arc at a point on the line segment. Finally, place the compass on the point where the two arcs intersect without changing the width of the second arc, and draw another arc that intersects the line segment. Finally, connect the point where the second arc intersects the segment to point C.
What is an angle?When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together.
Why do we measure angles?Angle measures are helpful not just for academic purposes but also for understanding and using the objects around us. They may aid with spatial knowledge and the link between numbers and measurements.
Follow these steps to draw angle ABC:
The base of the angle should be represented by a section of a line.
With the compass's point on point A, draw an arc that crosses the line segment.
Draw a second arc that crosses the previous arc at a point on the line segment by setting the compass's point on point B.
Place the compass on the intersection of the two arcs and create another arc that intersects the line segment without adjusting the compass's width.
To finish the angle, join point C to the location where the second arc crosses the line segment.
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An Olympic-sized pool, which holds 660,000 gallons of water,
is only 63% full. The pool maintenance company adds more
water, filling the pool to 90% full. How many gallons of water
did they add?
P
7.AR 3.1
a
244 200
178 200
B) 594 000
415.800
134
Answer:
178,200
Step-by-step explanation:
You want to know the number of gallons added to a 660,000 gallon pool to raise it from 63% full to 90% full.
IncreaseThe increase from 63% to 90% is an increase of ...
0.90 -0.63 = 0.27
of the capacity of the pool. That fraction of the capacity is ...
0.27 × 660,000 gallons = 178,200 gallons
The maintenance company added 178,200 gallons.
The point (5,5) is on a line with slope 1/3. How much is is the bonus/penalty in this equation?
The equation is y = 1/3 x + 10/3. The y-intercept is 10/3.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given that the point (5,5) is on a line with slope 1/3. The y-intercept will be calculated as,
y = mx + c
5 = (5/3)) + c
c = ( 15 - 5 ) / 3
c = 10 / 3'
y = 1/3x + 10/3
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What is the asymptote calculator?
An asymptote calculator is a tool that can be used to find the asymptotes of a given function.
What is an asymptote calculator?Generally, An asymptote is a straight line that a curve approaches, but never touches, as it extends indefinitely in one direction or another. There are three types of asymptotes: horizontal, vertical, and oblique.
To use an asymptote calculator, you would typically enter the equation of the function for which you want to find the asymptotes. The calculator will then analyze the equation and determine the type and location of the asymptotes, if any. Some asymptote calculators may also provide a visual representation of the function and its asymptotes, using a graph.
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What is the area of a triangle with a base of 7 1/2 feet and a height of 8 feet
Answer:
[tex]30ft^{2}[/tex]
Step-by-step explanation:
How do you know if it's AAS or ASA?
The triangles are congruent if two sets of comparable angles and the side separating them are known to be congruent. Angle-side-angle is the name of this shortened phrase (ASA). Angle-angle-side (AAS), which takes use of the fact that two sets of angles and the excluded side are known to be congruent, is another shortcut.
ASA is another name for angle side angle. According to the criterion, any two angles and the side that is contained between them in one triangle are equivalent to the corresponding angles and the included side of the other triangle if the two triangles are congruent.
According to the Angle Angle Side (AAS) Postulate, two triangles are congruent if two consecutive angles and a non-included side of one triangle are congruent with the equivalent two consecutive angles and a non-included side of another triangle.
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Solve pls brainliest
y-8=6x+10
y=6x+10+8
y=6x + 18
this follow y = mx+x it means it's a linear
2y= 5x²+19
it doesn't follow y = mx+x so it's a Non Linear
34y = x
it doesn't follow y = mx+x so it's a Non Linear
4y = 2x + 9
this follow y = mx+x it means it's a linear
Which equation is the inverse of y 16x2 1?
This equation expresses x as a function of y, meaning y is the input and x is the output. This inverse equation can be used to solve for x when given a value of y
x = (y - 1) / 16
In order to find the inverse of a given equation, we need to switch the x and y values and solve for the new x. To do this, we start by subtracting 1 from both sides of the equation to isolate the y variable. Then, we divide both sides of the equation by 16 to find the inverse equation, x = (y - 1) / 16. This equation expresses x as a function of y, meaning y is the input and x is the output. This inverse equation can be used to solve for x when given a value of y
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How to get Universal Credit Loophole $1,500?
You can get Universal Credit Loophole for $1,500 through Advance Payment.
While you wait for the first distribution of Universal Credit, advance payments up to the full amount of the first anticipated payment are available if you need money to pay bills and other household needs. In your online account or by contacting your Job-Centre Plus job coach, you can submit an application for an advance payment.
You will require:
Describe why you require an advance.the identity of the person (you do this when you apply online or on the phone with a work coach)supply the advance's bank account information (talk to your work coach if you cannot open an account)The money must be repaid within a year by taking deductions from your Universal Credit installments.
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What is an example of f x G X?
The example of composition function f(g(x)) is given by f(x) = 2x + 1 and g(x) = 3x then f(g(x)) = 6x + 1.
As given in the question,
Composition function is written as :
(fog)(x) = f(g(x))
Here substitute the value x in the function f(x) as function g(x) :
Example of the composition function is:
f(x) = 2x + 1
g(x) = 3x
(fog)(x)
= f(g(x))
=f(3x)
= 2(3x) + 1
= 6x + 1
Therefore, the example of the composition function f(g(x)) is given by :
f(x) = 2x + 1 and g(x) = 3x then f(g(x)) = 6x + 1.
The above question is incomplete, the complete question is:
What is an example of the function f (g(x))?
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help me please asaaaaaapppp
The continuity of the piece-wise functions is defined as follows:
1. Not continuous.
2. Not continuous.
3. Not continuous.
How to define the continuity of the functions?A piece-wise function is a function that has multiple definitions, depending on the input.
Then the function is classified as continuous if the lateral limits at the points that the function change the definition are equal, and also equal to the numeric values of the function.
None of the functions in this problem are continuous, as:
For function 1, lim x -> 0^- = 0, lim x -> 0^+ = 2, hence different lateral limits. At x = 3, the lateral limits are also different.For function 2, lim x -> -6^- = 0, lim x -> -6^+ = 4. At x = 2, the lateral limits are also different.For function 3,lim x -> 0^- = 3, lim x -> 0^+ = -3.More can be learned about the continuity of a function at https://brainly.com/question/24637240
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What is edge computing and how does it work Mcq?
What are the solutions of x2 3x 4 0?
The solution of [tex]x^{2} - 3x-4=0[/tex] is x=(4,−1).
What is fraction ?
A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator. In Maths, there are three major types of fractions. They are proper fractions, improper fractions and mixed fractions.
Have given ,
[tex]x^{2} - 3x-4=0\\x^{2} -4x +x-4=0\\x(x-4)+1(x-4)=0\\(x-4)(x+1) = 0\\[/tex]
x - 4 = 0
x = 4
and x + 1 = 0
x = -1
The solution of [tex]x^{2} - 3x-4=0[/tex] is x = (4,−1).
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у +4=3x
2y-6x=-8
Help
Answer:
x=0, y=-4
Step-by-step explanation:
y=3x-4
2(3x-4)-6x=-8
6x-8-6x=-8
urgent..................
Answer:
√6
Step-by-step explanation:
the altitude is √a*b
and and b being the base so find their distance then multipky them under the root
subtracdt the x values to find the distance
4-1=3
6-4=2
the root of 2*3 is the root of 6
done
Answer:
x = 4
Step-by-step explanation:
You want the equation of AD perpendicular to BC, where the point coordinates are A(4, 6), B(1, 2), C(6, 2).
Horizontal lineWe notice the y-coordinates of point B and C are the same, indicating the line is horizontal. Its equation is y = 2.
Perpendicular lineThe line perpendicular to the horizontal line y = 2 will be a vertical line. Its equation will be of the form ...
x = c
where c is some constant.
We want this line to go through the point (4, 6), which has an x-coordinate of 4. That means the constant in the equation must be 4:
x = 4 . . . . . . equation of AD
if the percentage increase is 79%, what is the growth factor?
PLS HELP TYSMMM
With an increase of 79% the growth factor is 1.79.
What is growth factor?The rate at which a quantity multiplies itself over time is known as its growth factor.
A quantity's growth rate is the factor by which it grows (or shrinks) over time.
An increase of 79% is the same result as multiplying with 1.79.
We call 1.79 a growth factor.
In other words:
With an increase of 79%,
you will get 100+ 79 = 179%.
The growth factor that corresponds with 179% = 179 : 100 = 1.79.
Written as a formula, it looks like this:
With an increase of p % the growth factor is
g = (100 + p) / 100
Simplifying,
g = 1 + p /100
g = 1 + 79/100
g = 1 + 0.79
g = 1.79.
Therefore, the growth factor is 1.79.
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The Cruisers scored a total of 105 points in a basketball game against the Strikers. The Cruisers had a total of 43 baskets, some of which were two-point shots and some of which were three-point shots. How many two-point and three-point shots did the Cruisers score?
The number of two-points and three points shot the cruisers scored are 24 and 19 respectively.
How to find the number of two and three points made?The Cruisers scored a total of 105 points in a basketball game against the Strikers. The Cruisers had a total of 43 baskets, some of which were two-point shots and some of which were three-point shots.
Therefore, the number of two-points and three-points the cruiser scored is as follows:
let
x = number of two-points
y = number of three-points
Hence, using equation
x + y = 43
2x + 3y = 105
Multiply equation(i) by 2
2x + 2y = 86
2x + 3y = 105
subtract equation(i) from equation(ii)
y = 19
Let's find x as follows:
x = 43 - 19
x = 24
Therefore,
number of two points = 24
number of three points = 19
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Help me with this geometry pls
Answer:
Cos A = adjacent/hypotenuse
Cos A = 15/17
Cos A = 2.143
tan A = opposite/adjacent
tan A = 8/15
tan A = 0.533
sin A = opposite/hypotenuse
sin A = 8/17
sin A = 0.471
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Is 31 is a prime number or not?
There are only two factors of the number 31 which are 1 and 31. Then the integer number 31 will be a prime number.
What is a prime number?A prime number is a positive integer having exactly two factors which are 1 and the number itself. Any number that does not follow this is termed a composite number.
The prime numbers from 1 to 100 are given below.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
The factor of the 31 will be given as,
31 = 1 x 31
There are only two factors of the number 31 which are 1 and 31.
Thus, the integer number 31 will be a prime number.
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Which of the relations given by the following sets of ordered pairs is not a function?
{(−4,−2),(−1,−1),(3,2),(3,5),(7,10)}{(−4,−2),(−1,−1),(3,2),(3,5),(7,10)} ordered pairs is not a function. A mapping between two sets, which is a relation and can potentially be a function, can be represented by a set of ordered pairs.
Which relation is not a function?A relationship is not a function if each input does not have a distinct output. For a relation to be a function, each input must have a distinct output, and the order of the set's items must be paired in a unique way or the elements of sets must be mapped in a unique way.A function is a special type of relation in which each element in the domain is paired with exactly one element in the range. For example, the relation {(1, 2), (3, 4), (5, 6)} is a function because each element in the domain (i.e., {1, 3, 5}) is paired with exactly one element in the range (i.e., {2, 4, 6}). On the other hand, the relation {(1, 2), (3, 4), (1, 6)} is not a function because the element 1 is paired with two elements in the range (2 and 6).All the set ot values agrees with this definition except the B, because the third and fourth pair have the same first value (3)Complete question :
Which of the relations given by the following sets of ordered pairs is not a function?
a. {(5,2),(4,2),(3,2),(2,2),(1,2)}{(5,2),(4,2),(3,2),(2,2),(1,2)}
b. {(−4,−2),(−1,−1),(3,2),(3,5),(7,10)}{(−4,−2),(−1,−1),(3,2),(3,5),(7,10)}
c. {(−8,−3),(−6,−5),(−4,−2),(−2,−7),(−1,−4)}{(−8,−3),(−6,−5),(−4,−2),(−2,−7),(−1,−4)}
d. {(−6,4),(−3,−1),(0,5),(1,−1),(2,3)}
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For what value of k are the roots of the quadratic equation 3x 2 2kx 27 0?
The values of k are 9, – 9 for which roots of the quadratic equation are real and equal.
What is a quadratic equation?An equation containing one term in which the unknown is squared and no term in which it is raised to a power higher than 2.
Given: 3x² + 2kx + 27 = 0
Comparing with standard quadratic equation ax² + bx + c = 0
a = 3 b = 2k c = 27
Given that the roots of the equation are real and equal
Thus, D = 0
Discriminant D = b² – 4ac = 0
(2k)² – 4.3.27 = 0
4k² – 324 = 0
4k² = 324
k² = 81 taking square root on both sides
k = 9 or k = – 9
Hence, The values of k are 9, – 9 for which roots of the quadratic equation are real and equal.
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T/F if an > 0 and lim n→[infinity] an + 1 an < 1, then lim n→[infinity] an = 0.
The expression aₙ > 0 and lim n → [∞] aₙ + 1 is true.
The term expression in math is defined as a sentence with a minimum of two numbers or variables and at least one math operation.
Here we have given that if an > 0 and lim n→[infinity] an + 1 an < 1, then lim n→[infinity] an = 0.
And we need to check whether the given statement is true or not.
While we looking into the given question, we have identified the following expression,
=> lim n → [∞] aₙ + 1
Here we have also know that the value of aₙ > 0.
When we equate the given expression with zero, we have get the following expression,
=> lim n → [∞] aₙ + 1 = 0
=> lim n → [∞] aₙ = -1
Here we have given the condition that, aₙ >0, so
=> lim n → [∞] aₙ = 0
Therefore, the expression is zero.
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