The work required to stretch the spring is 91.6 Ibs-inch
What is work?
Work is defined as force applied across a distance. Work examples include pushing an object against gravity, driving a car up a hill, and lowering a captive helium balloon. Work is the mechanical expression of energy.
Δx : displacement from equilibrium position
f = k Δ x (force due to spring = -kΔx)
where, k is the spring constant
Given,
f = 20ibs
Δx = 24 -18 Inches = 6 inches
∴ k = 20/6 ibs/inch
Now, PE stored in spring = 1/2 k (Δx)²
Δx : displacement from equilibrium position
Work done = change in PE
= 1/2K (Δx₂)² -1/2k (Δx₁)²
given,
Δx₁ = 21-18 inches = 3 inches
Δx₂ = 26-18 inches = 8 inches
∴work done = 1/2 * 20/6 (8² - 3²)Ibs-inches
=10/6 *5*11
work done = 91.6 ibs-inch
The spring must be stretched with 91.6 Ibs-inch of force.
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change from rectangular to cylindrical coordinates. (let r ≥ 0 and 0 ≤ θ ≤ 2π.) A) (-1,1,1) B) (-7,7√3,7)
(A) cylindrical coordinate = (r, θ, z) = (√2, -π/4, 1)
(B) cylindrical coordinate = (r, θ, z) = (14, -π/3, 7)
In the given question, we have to change from rectangular to cylindrical coordinates. (let r ≥ 0 and 0 ≤ θ ≤ 2π.)
A) (-1,1,1)
Given rectangular coordinates(x, y, z) = (-1,1,1)
The cylindrical coordinates are (r, θ, z)
So we find the value of r and θ one by one.
r = √x^2+y^2
r = √(-1)^2+(1)^2
r = √1+1
r = √2
θ = [tex]\tan^{-1}[/tex](y/x)
θ = [tex]\tan^{-1}[/tex](1/-1)
θ = [tex]\tan^{-1}[/tex](-1)
θ = -π/4
So cylindrical coordinate = (r, θ, z) = (√2, -π/4, 1)
B) (-7,7√3,7)
Given rectangular coordinates(x, y, z) = (-1,1,1)
The cylindrical coordinates are (r, θ, z)
So we find the value of r and θ one by one.
r = √x^2+y^2
r = √(-7)^2+(7√3)^2
r = √49+147
r = √196
r = 14
θ = [tex]\tan^{-1}[/tex](y/x)
θ = [tex]\tan^{-1}[/tex](7√3/-7)
θ = [tex]\tan^{-1}[/tex](-√3)
θ = -π/3
So cylindrical coordinate = (r, θ, z) = (14, -π/3, 7)
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the volume of a rectangular box with a square base remains constant at 1,100 cm3 as the area of the base increases at a rate of 2 cm2/sec. find the rate at which the height of the box is decreasing when each side of the base is 12 cm long. (do not round your answer.)
If the area of the area of the base increases at rate of 2 cm²/sec then the rate at which the height of the box is decreasing is 0.11 cm/sec .
In the question ,
it is given that ,
the volume of the rectangular box having square base is 1100 cm³ ;
the rate of decrease of the area is (dA/dt) is = 2 cm²/sec ;
we know that ; Volume = Area × Height ;
the area of the square base of side 12 cm is = 12 × 12 = 144 ;
So , height = Volume/Area ;
= 1100/144 ;
Now , V = A × h ;
differentiating the above equation w.r.t. "t" ,
we get ;
dV/dt = A×(dh/dt) + h×(dA/dt)
0 = 144×(dh/dt) + (1100/144)×(2)
dh/dt = -2200/(144 × 144)
= -0.106095
≈ -0.11
Therefore , the rate of change of height is = 0.11 cm/sec .
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Math question 20 PTS
(h – k)(3) =
Answer:
3h - 3k
Step-by-step explanation:
I hope that this answer will help
You have to distribute
How do you integrate 1/ln(x)?
The integration of 1/ln(x) is not possible as We permit y = lnx, we then recognize that x = ey.
By differentiating each aspects of this equation with admire to y we get:dx/dy = ey, because the exponential characteristic differentiates to itself whilst differentiated with admire to its power.
In mathematics, the logarithmic quintessential characteristic or quintessential logarithm li(x) is a unique characteristic. It is applicable in issues of physics and has variety theoretic significance. In particular, in keeping with the high variety theorem, it's far a excellent approximation to the high-counting characteristic, that is described because the variety of high numbers much less than or same to a given value x.
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The sum of two numbers is 20. What is the least possible sum of their squares and what are the numbers?
The numbers are 10 and 10. And the sum of their squares will be 200.
What are the maxima and minima of a function?For the maximum value of the function if f''(x) < 0 and for the minimum value of the function if f''(x) > 0.
The maximum and minimum value of the function is at f'(x) = 0.
The sum of the two numbers is 20.
Let the first number be 'x'. Then the other number is (20 - x). Then the equation is given as,
y = x² + (20 - x)²
Differentiate the function, then we have
y' = 0
2x + 2(20 - x)(-1) = 0
x - 20 + x = 0
2x = 20
x = 10
Then the other number is given as,
⇒ 20 - 10
⇒ 10
The sum of their squares is given as,
⇒ 10² + 10²
⇒ 100 + 100
⇒ 200
The numbers are 10 and 10. And the sum of their squares will be 200.
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a popular magazine tests cars and trucks for mileage on the road and around the city. the magazine reports that 50% of the cars tested had mileages below 24.7 mpg on the road, and the other 50% of the cars tested had mileages above 24.7 mpg. which statistic does this 24.7 represent?
The decimal number 24.7 represents the average mileage of the vehicle.
What are statistics?Statistics is the study of collection, analysis, interpretation, and presentation of data or discipline to collect and summarise the data.
A famous magazine tests vehicles and trucks for mileage out and about and around the city. the magazine reports that half of the vehicles tried had mileages beneath 24.7 mpg out and about, and the other half of the vehicles tried had mileages above 24.7 mpg.
The decimal number 24.7 means the vehicle can cover 24.7 miles with each gallon of gas.
The decimal number 24.7 represents the average mileage of the vehicle.
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Which is the smallest positive integer that can be written as the product of two cubic integers?
Answer: 8
Step-by-step explanation:
=(1) ^3×(2) ^3
=1×1×1×2×2×2
=1×8
=8
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A figure has vertices (−13, 13),(26, 52), (39, 39). What would be the new coordinates of the vertices to the nearest tenth if the image were reduced by a scale factor of 0.77 with the origin as the center of dilation?
A. −16.9, 16.9), (33.8, 67.6), (50.7, 50.7)
B. (−10, 10), (20, 40), (30, 30)
C. (10, 10), (−20, 40), (−30, 30)
D. (16.9, 16.9), (33.8, 67.6), (50.7, 50.7)
The new coordinates after a reduced scale factor of 0.77 with the origin will be equal to (−10, 10), (20, 40), (30, 30). Hence, option B is correct.
What is a graph?In math, graph science is the theory of geometric structures called graphs that are used to represent pairwise different objects. Vertices—also known as nodes or points—that are joined by edges make form a network in this sense.
Undirected graphs, where edges connect two vertices equally, and focused therapy, where edges connect two vertices unevenly, are distinguished.
As per the data given in the question,
We will combine the x and y dimensions even by scale factors to shrink the picture by a multiplier of 0.77 with both the origins as that of the center of dilatation because the figure's vertices are (-13, 13), (26, 52), and (39, 39).
So, the first point is (-13, 13)
-13 × 0.77 = -10 and,
13 × 0.77 = 10
So, the new point is (-10, 10).
The second point is (26, 52).
26 × 0.77 = 20
52 × 0.77 = 40
So, the new point is (20, 40)
The third point is (39, 39)
39 × 0.77 = 30
39 × 0.77 = 30
So, the new point is (30, 30).
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On a tree farm, 3/4
of each acre is planted with blue spruce trees.
If there are 15 1/2 acres of trees on the farm, how many acres are
planted with blue spruce trees?
Answer:
11[tex]\frac{5}{8}[/tex]
Step-by-step explanation:
15-1/2 = 31/2
(31/2)(3/4) = 93/8 = 11[tex]\frac{5}{8}[/tex]
how many ways are there to make an r-arrangement of pennies, nickels, dimes, and quarters with at least one penny and an odd number of quarters? (coins of the same denomination are identical
The exponential generating function is,
G(x) = (x¹/1! + x²/2! + ...)(x¹/1! + x³/3! + x⁵/5! +...)(x°/0! + x¹/1! + x²/2! + ...)²
where the first factor describes the pennies, the second describes the quarters, and the last describes nickles and dimes.
We want the coefficient of [tex]x^{r}[/tex]/r!.
Using exponential identities we get,
G(x) = ([tex]e^{x}[/tex] - 1)([tex]\frac{e^{x}-e^{-x} }{2}[/tex]) ([tex]e^{x}[/tex])² = [tex]\frac{1}{2}[/tex] ([tex]e^{4x} - e^{2x} - e^{3x} + e^{x}[/tex]),
and the coefficient is
[tex]\frac{1}{2} (4^{r} - 2^{r}- 3^{r} + 1 )[/tex]
The generating function is
G(x) = (x¹/1! + x²/2! + ...)⁴(x°/0! + x¹/1! + x²/2!+...)²² = ([tex]e^{x}-1[/tex])⁴[tex]e^{22x}[/tex],
and we again want the coefficient of [tex]x^{10}[/tex]/10!.
Multiplying we get,
G(x) = ([tex]e^{4x}-4e^{3x}+2e^{2x}+1[/tex])[tex]e^{22x}[/tex] = [tex]e^{26x}-4e^{25x}+2e^{24x}+e^{22x}[/tex]
so the coefficient of [tex]x^{10}[/tex]/10! is
26¹⁰ - 4 × (25)¹⁰ + 2 × (24)¹⁰ + 22¹⁰
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what is the instantaneous rate of change at x=2 of the function f given by
Answer:
its 3
Step-by-step explanation:
the rate is 3
Rewrite <8,-5> In coordinate notation
The vector <8,-5> when expressed in coordinate notation is (8, -5)
How to express the vector in coordinate notation?From the question, we have the following parameters that can be used in our computation:
Notation = <8, -5>
The above expression is in vector notation
To express the vector notation in a coordinate notation, we simply express the <> as ()
So, we have the following representation
(8, -5)
Hence, the coordinate notation is (8, -5)
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2x-1(4x+3)=-7x+2 help me find x please
Answer:
X=1
Step-by-step explanation:
For step one you have to Distribute
2x-1(4x+3)=-7x+2 --> 2x-4x-3=-7x+2
For step two you have to Combine Like Terms
2x-4x-3=-7x+2 --> -2x-3=-7x+2
For step three you have to Add Three To Both Sides
-2x-3=-7x+2 --> -2x=-7x+5
For step four you have to Add 7x To Both Sides
-2x=-7x+5 --> 5x=5
For step 5 you have to Divide Both Sides By The Same Factor (5)
5x=5 --> x=1
Hope This Helps!
An elevator can carry 25 adults or 30 children at one time. During the course of a day, the elevator carries a full passenger load 36 times. If all the passengers were children, how many more people would the elevator carry than if all the passengers were adults?
180 people would the elevator carry than if all the passengers were adults.
What is the meaning of times?
The mathematical symbol is used to represent the multiplication operation and the consequent product. It is often referred to as the times sign or the dimension sign.
Given an elevator can carry 25 adults or 30 children at one time.
One day the elevator carries a full passenger load 36 times.
If the elevator carries all adults, then it carries (25 × 36) = 900 adults.
If the elevator carries all children, then it carries (30 × 36) = 1080 adults.
If all the passengers were children, then the elevator carry more than (1080 - 900) = 180 people if all the passengers were adults.
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write a system of linear equations in which (2, -1) is a solution of equation 1 but not a solution of equation 2, and (5, 5) is a solution of the system.
The system of linear equation of the line are y=2x-5 when (2,-1) is a solution of the first equation but not for the second equation.
Given that,
We have to find the system of linear equation in which (2,-1) is a solution of the first equation but not for the second equation and (5,5) is a solution for system of equation.
We know that,
To find the system of equation we have a formula that is
y=mx-mx₁+y₂
Here m is slope
m=-1-5/2-5
m=-6/-3
m=2
The equation is
y=2x-2(5)+5
y=2x-10+5
y=2x-5
Therefore, The system of linear equation of the line are y=2x-5 when (2,-1) is a solution of the first equation but not for the second equation.
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Question 9 An S corporation is generally set up to: implement an expansion strategy attract capital reduce tax burdens easy entry into an industry take advantage of limited liability
Generally speaking, a S corporation is put up to reduce the tax obligations. It is Option (3).
A business form known as a S corporation is one that is allowed by the tax code to distribute its taxable income, credits, deductions, and losses to its shareholders directly. This provides it certain advantages over the more popular C corp. The S corp, an alternative to the limited liability company, is only available to small firms with 100 or fewer stockholders (LLC). S corporations and LLCs are both referred to as "pass-through entities" since they don't pay corporate taxes, instead, they pay their owners, who are then in charge of paying the necessary taxes.
One sort of legal corporate structure that is popular among small businesses is the S corporation, commonly referred to as a S corp or S corp or S subchapter. Another is a limited liability company (LLC). A corporation with 100 shareholders or fewer can profit from incorporation while still being taxed as a partnership thanks to the requirements of a S corp. S corporations and LLCs are both pass-through companies, which means they don't pay corporate taxes and provide their owners and principals with limited liability protection. LLCs, however, offer more flexibility.
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Correct Question:
An S corporation is generally set up to:
1. implement an expansion strategy
2. attract capital
3. reduce tax burdens
4. easy entry into an industry
5. take advantage of limited liability
an equation is written to represent the relationship between the temperature in alaska during a snow storm, y, as it relates to the time in hours, x, since the storm started. if the storm lasted five hours and the temperature saw a drop from 0o to - 20o, which quadrant(s) of a coordinate grid should be used to display this data?
The first and fourth quadrant of a coordinate grid should be used to display the given data .
In the question ,
it is given that ,
from the time the storm has started the temperature change is from 0° to - 20° .
we know that time cannot be in negative , and temperature can be both negative and positive .So only quadrant 1 and 4 can be used for representation .
Y = temperature
X = time
Quadrant 1 = (+x , +y) this can be used because x can only be positive and y is also positive.
Quadrant II = (-x , +y) this cannot be used because x cannot be negative
Quadrant III = (-x , -y) this cannot be used because x cannot be negative
Quadrant IV = (+x , -y) this can be used because x can only be positive and y can be negative.
Therefore , only 1 and 4 quadrants can be used .
The given question is incomplete , the complete question is
An equation is written to represent the relationship between the temperature in Alaska during a snow storm, y, as it relates to the time in hours, x, since the storm started. if the storm lasted five hours and the temperature saw a drop from 0° to - 20°, which quadrant(s) of a coordinate grid should be used to display this data ?
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dollar general sends out a $5 off coupon to its email subscribers. what percentage of customers between 20 and 30 years of age who lived within 5 miles of the store used the coupon?
The classification model is used to define the percentage of customers between 20 and 30 years of age who lived within 5 miles of the store used the coupon.
Percentage:
In math, number or ratio that can be expressed as a fraction of 100 refers the percentage.
Given,
Here we have a dollar general sends out a $5 off coupon to its email subscribers.
And we need to find the percentage of customers between 20 and 30 years of age who lived within 5 miles of the store used the coupon.
Then the model used to define the this type of situation is refers as the classification model, because in this model, we have classify the given group of people based on the constraint.
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The inequality x < 9 or x ≥ 14 can be used to represent the hourly wage, x, of each employee at a store. Which are possible values for x? Select two options.
$8
$9
$11
$13
$14
The stated inequality, x < 9 or x >=14, indicates that the two potential values for x are $8 and $14.
what is inequality in equation ?The two expressions that make up an equation or an inequality are connected in a mathematical statement. The equal sign (=) in an equation denotes the equality of the two expressions. The symbols >,,, or are used to denote an inequality, when the two expressions aren't always equal.
x < 9 or x ≥ 14
This indicates that x must be more than 9 but not equal to 14.
In the choices
All values below nine are
$8
There are no values larger than or equal to 14.
$14
The stated inequality, x < 9 or x >=14, indicates that the two potential values for x are $8 and $14.
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The volume of a cone with height 29 cm is 1758 CM3, find the radius of the conw
Answer:13.77 cm.
Step-by-step explanation:
r = sqrt((3V)/(pih))
= sqrt((31758)/(pi29))
= sqrt((5274)/(pi*29))
= sqrt(182.16)/(pi/29)
= 13.77 cm
3.8x10^-2 as an ordinary number
Answer:0.038
Step-by-step explanation:
The ordinary number equivalent of 3.8x10⁻² is expressed as 0.038.
To express the number 3.8x10⁻² as an ordinary number, we need to understand scientific notation. In scientific notation, numbers are written in the form of a coefficient (a decimal number greater than or equal to 1 but less than 10) multiplied by 10 raised to a certain power (positive or negative). This notation is commonly used to represent very large or very small numbers in a concise and standardized way.
Let's break down 3.8x10⁻² step by step:
The coefficient: 3.8
The coefficient is the decimal part of the number, which should be greater than or equal to 1 but less than 10. In this case, the coefficient is 3.8.
The exponent: -2
The exponent indicates the power of 10 to which the coefficient is raised. If the exponent is negative, it means the number is less than 1. In this case, the exponent is -2, which means we are dividing the coefficient by 100 (10 raised to the power of -2 is 1/100).
Now, to express 3.8x10⁻² as an ordinary number, we simply perform the calculation:
3.8 × 10⁻² = 3.8 ÷ 100 = 0.038
So, the ordinary number equivalent of 3.8x10⁻² is 0.038.
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x^2-4x 15=0 complete tthe sqaure
The solution of the equation after completing the square of the equation is found as; x = ±√19 + 2.
Explain the term completing square?When a square is complete, a quadratic is written in the shape of a squared bracket, and if necessary, a constant is added.The given steps are-
On both sides of this argument, add 15.x² - 4x = 15.
Find a number that is comparable to the square of half of b in order to construct a trinomial square just on left side of the equation.(b/2)² = (-2)²
To either side of the equation, add the term.x² - 4x + (-2)² = 15 +(-2)²
Simplify;x² - 4x + 4 = 19
The exact trinomial square be factored into; (x - 2)²There are various ways to display the outcome.
(x - 2)² = 19
Taking square root each side;x = ±√19 + 2
Thus, the solution of the equation after completing the square of the equation is found as; x = ±√19 + 2.
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How do you write 38000 in scientific notation?
Answer 3.8 x 104
Step-by-step explanation:
Which of the following is an example of the Closure Property of multiplication for the set of whole numbers?
A. 74 + 59 = 59 + 74
B. 65 × 3 = 3 × 65
C. 6× 4 = 24
D (2 + 4) + 5 = 2 + (4 + 5)
Answer:
Step-by-step explanation:
The correct option is A 6
×
4 = 24
Closure property of multiplication for whole numbers states that product of two whole numbers a and b is always a whole number c.
Only options B and C have a multiplication sign. Of them, option B is of the form a
×
b = b
×
a
So 6
×
4 = 24 is an example for closure property of multiplication.
with one method of a procedure called acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is accepted if every item in the sample is okay. the abc electronics company has just manufactured 1200 write-rewrite cds, and 150 are defective. if 3 of these cds are randomly selected for testing, what is the probability that the entire batch will be accepted?
The probability that the entire batch will be accepted.
What is Acceptance Sampling?
Acceptance sampling is a statistical measure used in quality control. It allows a company to determine the quality of a batch of products by selecting a specified number for testing.
abc Electronics Company manufactured 1200 write-rewrite cds, and 150 are defective. Since 150 are defective, the number of write-rewrite cds that would be accepted is (1200 - 150 = 1050).
Since the items at selected without replacement, the number of write-rewrite cds will continue to decrease anytime a write-rewrite cds is taken out. For example if they are 1050 accepted write-rewrite cds if one is taken out they would then be 1049 accepted write-rewrite cds, and if another one is taken out they would be 1049 accepted write-rewrite cds and so on.
If 3 of these cds are randomly selected for testing without replacement,
The probability that the entire batch will be accepted
= (1050/1200) × (1049/1200) × (1048/1200) × (1047/1200)
= 0.8750 × 0.8742 × 0.8733 × 0.8725
=0.5828
The probability that the entire batch will be accepted is 0.5828 .
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Three ballet dancers are positioned on stage. Oliver Is 6.3 feet straight behind Dana and 6.3
feet directly left of Ashley. When the music begins, Oliver twirls to Ashley's position, then
leaps to Dana's position, and finally walks back to his original position. How far did Oliver
travel? If necessary, round to the nearest tenth.
Oliver travelled the distance of 21.5 ft
What is perimeter?
The complete length of a shape's edge serves as its perimeter in geometric terms. Adding the lengths of all the sides and edges that surround a form yields its perimeter. It is calculated using linear length units such centimeters, meters, inches, and feet.
As shown in the figure, we need to find the perimeter of the triangle ABC.
Perimeter = g + h +f ............(1)
g=f = 6.3 ft
Finding h using pythogoras theorem formula:
h² = g² + f²
= 6.3² + 6.3²
= 79.38
h =√79.38 = 8.909 ≈ 8.9 ft
So, (1) => Perimeter = 6.3 + 6.3 + 8.9 = 21.5 ft
Thus, Oliver travelled the distance of 21.5 ft
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Figure shows rectangles have been drawn to approximate integrate g(x) dx. Between the limits 0 to 6.(a) Do the rectangles represent a left or a right sum? 09 Do the rectangles lead to an upper or a lower estimate? (c) What is the value of n? (d) What is the value of delta x? (e) If g(x) = x^2 , approximate the integral g(x)dx. Between the limits 0 to 6
(a) The rectangles represent a left sum, as the rectangles are drawn starting from the left endpoints of the intervals.
(b) The rectangles lead to a lower estimate of the integral, as the rectangles are drawn underneath the curve of the function.
(c) The value of n is 5, as there are 5 rectangles drawn.
(d) The value of Δx is 1, as the interval between the limits 0 to 6 is divided into 5 equal parts.
(e) The approximate value of the integral g(x)dx between the limits 0 to 6 is 22.5.
left-end points:
[tex]g(0)[/tex]Δ[tex]x[/tex] [tex]+ g(2)[/tex]Δ[tex]x + g(4)[/tex]Δ[tex]x[/tex]
Right-end points:
[tex]g(2)[/tex]Δ[tex]x + g(4)[/tex]Δ[tex]x + g(6)[/tex]Δ[tex]x[/tex]
[tex](g(2)+g(4)+g(6))^{2}[/tex]
Δ[tex]x=\frac{b-a}{n}[/tex]
[tex]2=\frac{6-0}{n} \\\\2=\frac{6}{n}\\\\n=\frac{6}{2}=3 \\\\n=3[/tex]
Δ[tex]x=2-0=2[/tex] (each sub-interval length)
[tex]g(x)=x^{2} \\\\\int\limits^6_0{g(x)} \, dx = \int\limits^6_0 {x^{2} } \, dx[/tex]
[tex]=[\frac{x^3}{3} ]^6_0\\\\=\frac{6^3}{3} -0\\\\=72[/tex]
The integral can be evaluated using the Fundamental Theorem of Calculus, which states that the integral of a function [tex]f(x)[/tex] with respect to [tex]x[/tex]from [tex]a[/tex] to [tex]b[/tex] is equal to the difference between the values of the antiderivative of [tex]f(x)[/tex] evaluated at [tex]b[/tex] and at [tex]a[/tex].
Therefore, the integral of [tex]f(x)[/tex] from [tex]a[/tex] to [tex]b[/tex] is given by:
[tex]\int\limits f{(x)} \, dx =f(b)-f(a)[/tex]
where[tex]F(x)[/tex] is the antiderivative of [tex]f(x)[/tex].
In this case, the antiderivative of f(x) is given by [tex]F(x) = \frac{x2}2 + c[/tex], where [tex]c[/tex] is the constant of integration. Therefore, the integral of f(x) from [tex]a[/tex] to [tex]b[/tex] is given by:
[tex]\int\limits f(x)dx = F(b) - F(a)\\\\= (\frac {b2}{2} + c) - (\frac{a2}{2} + c)\\\\= \frac{(b2 - a2)}{2}[/tex]
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How do you simplify 27^(3/4)?
By simplifying the above equation i.e 27^(3/4) we get, 9 x (3)^(1/4).
Simplification is the process of substituting a mathematical expression with a simpler (typically shorter) counterpart. A fraction is simplified to an irreducible fraction. In computer algebra, expressions are simplified.
In order to simplify the given equation we need to factorize the bases. You can see that in the following steps :
(a^b)^c=a^(bc)
a^(b+c)=a^b x a^c
By using this above equation, we can factorize the bases.
So, factorization would be equal to :
27 ^(3/4) = ((3^3) )^ (3/4)
= 3^(9/4)
= 3^ (2+1/4)
= 3^2 x 3^(1/4)
= 9 x 3^(1/4)
That’s how we simplified the given equation.
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Line A is perpendicular to the line represented by the equation 5x+4y=10.line a passes through the point (5,-4).which equation can be used to represent line A
?
The equation of the perpendicular line to the given line is, [tex]y = \frac{4}{5}x - 8[/tex].
What is perpendicular lines?
When two geometric objects intersect at a right angle, they are considered to be perpendicular in elementary geometry. By using the perpendicular symbol,, the condition of perpendicularity can be graphically represented. Between two lines, a line and a plane, or between two planes can be used to define it.
Consider the given equation of line
5x + 4y = 10
Convert it into the form y = mx + c
⇒ 4y = -5x + 10
y = -5/4x + 10/4
y = -5/4x + 5/2
Here the slope of line is, -5/4.
The slope of perpendicular line is negative reciprocal of the slope of given line.
So, the slope of perpendicular line is,
[tex]-\frac{1}{(-5/4)} = \frac{4}{5}[/tex]
Also the line passes through the point (5, -4).
By using the point slope form to find the equation of line
[tex]y-y_1 = m(x-x_1)\\y-(-4) = \frac{4}{5}(x-5)\\ y+4=\frac{4}{5}x - 4\\ y = \frac{4}{5}x - 4 - 4\\ y = \frac{4}{5}x - 8[/tex]
Hence, the equation of the perpendicular line to the given line is, [tex]y = \frac{4}{5}x - 8[/tex].
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if instead one quarter were apples and one quarter were oranges and there were also 4 bananas 3 pears and 3 plums how many would be apples show your work
The number of apples obtained from the product of the fraction represented by the apples and the total number of fruits is 5 apples.
What is a fraction?A fraction is a representation of the proportion or part of a whole quantity.
The fraction of the fruit that are apples = One quarter = 1/4
The fraction of the fruit that are oranges = One quarter of the number of fruits
The number of bananas = 4
Number of pear = 3
Number of plums = 3
The fraction of the whole fruit are represented by apples and oranges = (1/4) + (1/4) = 1/2
The fraction of the total number of fruits represented by the bananas, pear and plum = 1 - (1/4 + 1/4)) = 1/2
Therefore;
Half of the total number of fruits = 4 + 3 + 3 = 10 fruits
Half of the fruits = 10
The total number of fruits is therefore, n = 2 × 10 = 20
The number of fruits that are apples = (1/4) × The total number of fruits
Therefore, the number of apples = (1/4) × 20 = 5
The number of fruits that are apples are 5 fruits
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