Where the above conditions are given then, F(x) = -10x⁻¹ + (9/4)x⁻⁴ + 31 /4.
This is the antiderivative F( x) of f(x) with F( 1 ) = 0.
To find the antiderivative F x) of f( x)
integrate the function f( x) with respect to x
Seperate the terms ....
f(x) = 10/x² - 9/x⁵
= 10x⁻² - 9x⁻⁵
Integrating each term separately....
∫10 x⁻² dx = -10x ⁻¹ + C 1
∫-9 x⁵ dx = (9/4 )x⁴ + C2
where C1 and C2 are constants of integration.
So the antiderivative F( x) of f( x) is:
F( x) = -10x⁻¹+ (9 /4) x⁻⁴ + C
where C is the constant of integration that we need to solve for using the given initial condition F(1) = 0:
F(1 ) = -10 (1 )⁻¹ + (9/ 4)( 1)⁻⁴ + C = 0
Simplifying this equation:
-10 + (9/4) + C = 0
C = 10 - (9/4)
C = 31/4
So we can conclude that the antiderivative F(x) of f(x) with F(1) = 0 is
F(x) = -10x⁻¹ + ( 9 /4)x⁻⁴ + 31 /4
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Find the area of the shaded region. Round your answer to the nearest hundredth.
I need a detailed way to solve the solution.
Quick as possible!
Answer:
4.56
Step-by-step explanation:
i see a sector hosting 2 semi circles.
this sector area will be .25 of area of circle with radius 4ft.
area of sector = .25*π*16= 4π ft^2
area of semi circle of radius 2ft = .5π*4= 2πft^2
area of 2 semicircles = 4π
the total area of sector = area of 2 semicircles - intersection area + area not covered by semi circles
4π = 4π - intersection area+area not covered by semi circles
intersection area = area not covered by semi circles
now draw a square starting from the intersection point of 2 semi circles at their upper portion. the side will be 2ft
the area of intersection will be covered in the square.
area of intersection = 2*quarter area of circle of radius 2ft - area of square
= 2*(.25π4) - 4
2π-4 = 2.28
area of intersection = area not covered by semicircle
so area of shaded region = 4.56
Zendaya needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 4.25 hours and charged her $59 for parts. The total was $377.75. What was the cost of labor, per hour?
This is oddly the funniest question I've seen so far. But never fear, I guess I'm here? :\
Honestly, I'm kinda lost but your answer should be $88.88. Even though it would say $88.88 multiplied by total hours, which is 4 hours and 25 minutes is $377.74, that answer is determined by a thousandth of a number. If you want it the other way, it's 88.8824.
Definitely hope this helped. [Pretty much, the answer is $88.88.]
The cost of labor per hour is $75.
It is required to find the cost of labor per hour.
What is arithmetic?Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.
Given:
The total amount that the technician charged her is the sum of the cost for the total hours worked and the costs of the parts.
Total charge = cost of total hours worked + cost of parts
$377.75 = $59 + cost of total hours worked
Cost of total hours worked = $377.75 - $59
Cost of total hours worked = $318.75
In order to determine the cost per hour of labor, divide the total cost of total hours worked by the hours worked.
$318.75 / 4.25 = $75.
Therefore, the cost of labor per hour is $75.
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I need a help with this hw
The values of the trigonometric ratios are: a) - 7/5, b) -75 c ) -1/5 d ) -25/12
What is trigonometric ratio?
Trigonometric ratios are measurements of the lengths of two sides of a triangle. There are three basic trigonometric ratios: sine, cosine, and tangent. Sine ratios are the ratios of the length of the side opposite the angle they represent over the hypotenuse
the give parameters are:
tanα = -4/3 where π/2 <α<π and sinβ = √3/2, 0<β<π/2
a) sin(α+β)
Using the trig ratios tan = opp/adj
but from pyth. rule, 4² + 3² = h²
16+9 = h²
h = √25 = 5
Now from trig Sin(α+β)
4/5 + 3/5
=- 7/5
b) cos(α+β)
cos = ad/hypo
4/5 + 3/5
= -7/5
c) Sin(α-β)
4/5 - 3/5
-1/5
d) tan(α-β)
= -4/3 - 3/4
= (-16 - 9)/ 12
-25/12
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How do you tell if a function is a power function?
Using the formula f(x)=kxⁿ, we can tell whether the given function is a power function or not. Here, k and n should be a real number.
A polynomial function having a single term that is the product of a real number, a coefficient, and a variable raised to a fixed real number is called a power function. The power function is given by the formula f(x)=kxⁿ. Here, k is the constant of proportionality, and n is the power or real number.
To find out whether the given function is a power function, first convert the given function into a standard form.
Then, look for the constants of proportionality and power value. If we are able to find these two, then the function will be a power function.
For example, y=3x² is a power function because here 3 is the constant of proportionality, and 2 is the power.
Another example, y=7ˣ is not a power function because here the power is a variable (x) not a constant.
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Write the percent as a fraction and as a decimal.
2%
_
4
What is the fraction equivalent?
What is the total square inches
Square Area = side x side = 3x3 = 9
Rectangle Area = side x side= 7x3= 21
9 + 21 = 30 square inches
Answer:
30 square inches
Step-by-step explanation:
\(\boxed{\text{\bf Area of rectangle = length *width}}\)
Rectangle1:
Area = 6 * 3
= 18 square inches
Rectangle2:
Area = 4 * 3
= 12 square inches
Area of the figure = area of rectangle1 + area of rectangle2
= 18 + 12
= 30 square inches
Please look at the pic and help!!
Answer:
4x² + 22x - 12
Step-by-step explanation:
A = bh/2
A = (4x - 2)(2x + 12)/2
A = (8x² + 48x - 4x - 24)/2
A = (8x² + 44x - 24)/2
A = 4x² + 22x - 12
What is the value of x, the side length of the smallest square (please show work) Thanks!
Answer:
8 cm
Step-by-step explanation:
Ok lets on the biggest square we have 17 cm
17cm is the hypotenuse for the right triangle
The second largest's area is 225 cm^2
Sq root of 225 cm^2, is 15
To find x, lets plug the info we have to the pythagorean theorom
\(a^2 + b^2 = c^2\\a^2 + 15^2 = 17^2\\a^2 + 225 = 289\\\\289 - 225 = a^2\\64=a^2\\a = 8 cm\)
The side length of the smallest Square is 8 cm
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
43,761 rounded to the nearest thousands
Answer:
44,000
Step-by-step explanation:
The number 43,761 rounded to its nearest thousands is 4400.
What is place value?The place value of a number is given as:
Example:
1234.567
1 = thousand place value
2 = hundred place value
3 = tens place value
4 = ones place value
5 = tenths place value
6 = hundredths place value
7 = thousandths place value
We have,
43,761
3 is in the thousand place.
So,
We will round 3761 to its nearest thousand value.
There are two options:
3000 or 4000
If It is greater than 3499 it will round to 4000.
If it is less than 3500 it will round to 3000.
Now,
3761 > 3499.
So,
The number is rounded to 4000.
Thus,
43,761 is rounded to 4400.
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The U.S. Weather Bureau has a station on Mauna Loa in Hawaii that has measured carbon dioxide levels
since 1959. At that time, there were 313 parts per million of carbon dioxide in the atmosphere. In 2005,
the figure was 374 parts per million. Find the increase in carbon dioxide levels and the percent of increase.
Round to the nearest tenth of a percent.
Increase carbon dioxide levels:
Percent increase:
196
Submit Question
parts per million
Question Help: Video Message instructor
Answer: The U.S. Weather Bureau has a station on Mauna Loa in Hawaii that has measured carbon dioxide levels since 1959. At that time, there were 313 parts per million of carbon dioxide in the atmosphere. In 2005, the figure was 383 parts per million.
Step-by-step explanation:
Ambar and Cole are engaged. Ambar works at the pharmacy and Cole works at the Library. In a few months, they will move to an apartment that is located at a point that is collinear to the locations of the pharmacy and the library, and partitions the line segment into a ratio of 2:3 coming from the pharmacy. If each grid in the graph represents 500 meters, then how far is the apartment from both Cole's and Ambar's current places?
The ratio is 2:3
Let
Coles place be 2xAmbars place=3x\(\\ \sf{:}\!\implies 2x+3x=500\)
\(\\ \sf{:}\!\implies 5x=500\)
\(\\ \sf{:}\!\implies x=\dfrac{500}{5}\)
\(\\ \sf{:}\!\implies x=100\)
2x=2(100)=2003x=3(100)=300Solve the equation. 14 + 6d = -4 A. d = -1 B. d = 5 C. d = -4 D. d = -3
Answer:
D. d = -3
Step-by-step explanation:
14 + 6d = -4
14 + 6(-3) = -4
14 -18 = -4?
Correct :)
what is the answer for d?
Your ability to borrow money at lower rates improves as
OA. you save more
OB. you earn more
OC. your debt ratio increases
OD. your credit score increases
Your ability to borrow money at lower rates improves as your credit score increases. Option D.
What is a credit score?Your ability to borrow money at lower rates improves as your credit score increases.
A higher credit score indicates to lenders that you have a strong credit history, responsible financial behavior, and a lower risk of defaulting on loans.
Lenders view borrowers with higher credit scores as more reliable and trustworthy, making them more likely to offer lower interest rates and better loan terms.
While saving more and earning more can indirectly contribute to improving your credit score by positively impacting your financial stability and ability to manage debt, they are not direct factors that lenders consider when determining interest rates.
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Simplify this expression:2x + 3 – (5 – 6x).
Answer:
8x - 2
Step-by-step explanation:
2x + 3 - (5 - 6x) ← distribute parenthesis by - 1
= 2x + 3 - 5 + 6x ← collect like terms
= (2x + 6x) + (3 - 5)
= 8x + (- 2)
= 8x - 2
If s(x) = 2-x2 and t(x) = 3x, which value is equivalent to (s° f)(-7)?
Answer:
-439
Step-by-step explanation:
Think of the question as s(f(-7))
First replace x with -7 in the equation f(x)= 3x
s(-7) = 3*(-7)
s(-7) = -21
now it is s(-21)
we substitute -21 into the s(x) equation to get \(2-(-21)^2\)
That gives you 2-441 = -439
Find the surface area
of the figure below:
19 cm
30 cm.
The surface area of the figure is approximately 997.5π cm².
We have,
The figure has two shapes:
Cone and a semicircle
Now,
The surface area of a cone:
= πr (r + l)
where r is the radius of the base and l is the slant height.
Given that
r = 15 cm and l = 19 cm, we can substitute these values into the formula:
= π(15)(15 + 19) = 885π cm² (rounded to the nearest whole number)
The surface area of a semicircle:
= (πr²) / 2
Given that r = 15 cm, we can substitute this value into the formula:
= (π(15)²) / 2
= 112.5π cm² (rounded to one decimal place)
The surface area of the figure:
To find the total surface area of the figure, we add the surface area of the cone and the surface area of the semicircle:
Now,
Total surface area
= 885π + 112.5π
= 997.5π cm² (rounded to one decimal place)
Therefore,
The surface area of the figure is approximately 997.5π cm².
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How many zeros are in the product?
(2 x 9) x 10
Answer:
1
Step-by-step explanation:
(2x9)= 18
18x10=180
there is 1 zero in 180
Emergency rooms have reason to suspect that visits increase on the weekends. A recent report indicates that Monday through Thursday represent 10% per day of the weekly total visits while Friday accounts for 15%, Saturday 25% and Sunday 20%. If your ER has the following pattern, Monday, 120, Tuesday, 130, Wednesday 110, Thursday 95, Friday 160, Saturday 280 and Sunday 105. Does your facility have the same pattern as the recent report at the 10% level
Answer:
No the facility dose not have the same pattern as the recent report at the 10% level
Step-by-step explanation:
To determine if the Facility have the same pattern ; Perform Chi squared test for Goodness of fit
state the hypothesis
H0 : μ = same pattern
Ha : μ ≠ same pattern
expected frequency ( E ) = proportion * summation of frequency
summation of frequency = 1000
degree of freedom = 7 - 1 = 6
Next : Calculate the expected frequency (E) , (O-E)²/E. given that the observed frequency and expected proportion is given
For Monday
expected frequency = proportion * frequency = 0.1 * 1000 = 100
(O-E)²/E. = ( 120 - 100 )^2 / 100 = 4.0.
observed frequency ( O ) , expected frequency ( E )
For Tuesday
E = 0.1 * 1000 = 100
(O-E)²/E = ( 130 - 100 )^2 / 100 = 9.0
Repeat same calculations for Wednesday through Sunday
Then perform Chi-squared test
X² = Σ(O-E)²/E = 63.642
∝ = 0.1
df = 6
hence P-value = 0.000 ( =chisq.dist.rt(test-stat,df)
since P-value < ∝ ; we will fail to reject Ha hence we reject H0
on spirit day 63 fewer 7th graders wore green and white then 8th grade. the total number of students wearing green and white was 561. find the number of 7th and 8th graders who wore green and white
I got the answer of 505 students
During a single day at the radio station WMZH, the probability that a particular song is played is 1/6. What is the probability that this song will be played on exactly 6 days out of 7 days? Round your answer to the nearest thousandth.
Around 0.000125 or 0.0125% of the time, the song will be played exactly six out of seven days.
Every day represents a trial in this binomial probability issue, and there are only two potential results:
either the music is played (a success), or it is not (failure). We're looking for the likelihood that exactly 6 out of 7 trials will be successful.
The likelihood of success (performing the song) is 1/6, while the likelihood of failure (not playing the song) is 1 - 1/6 = 5/6, on any given day.
We can use the binomial probability formula to find the probability of exactly 6 successes in 7 trials:
P(6 successes) = (7 choose 6) * (1/6)⁶ * (5/6)¹
where (7 choose 6) is the number of ways to choose 6 days out of 7 to play the song, and is calculated as:
(7 choose 6) = 7! / (6! * 1!) = 7
Plugging in the values, we get:
P(6 successes) = 7 * (1/6)⁶ * (5/6)¹
P(6 successes) ≈0.00012502
Therefore, the probability that the song will be played on exactly 6 days out of 7 is approximately 0.000125 or 0.0125%.
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A zip wire runs between two posts, 25m apart. The zip wire is at an angle of 10 degrees to the horizontal. Calculate the length of the zip wire.
∘
to the horizontal. Calculate the length of the zip wire
The length of the zip wire, with a 10-degree angle to the horizontal and a distance of 25 meters between the posts, is approximately 25.35 meters.
To calculate the length of the zip wire, we can use trigonometry. Let's consider the triangle formed by the zip wire, where the horizontal distance between the two posts is 25 meters and the angle between the zip wire and the horizontal is 10 degrees.
Using trigonometric functions, we can determine the length of the zip wire. In this case, we'll use the sine function because we have the opposite side (the vertical distance) and we want to find the hypotenuse (the length of the zip wire).
The formula for sine is:
sin(angle) = opposite / hypotenuse
Rearranging the formula, we have:
hypotenuse = opposite / sin(angle)
In this case, the opposite side is the vertical distance, which is h.
So, the formula becomes:
hypotenuse = h / sin(angle)
To find h, we can use the formula for the length of the zip wire:
h = 25 * tan(angle)
Substituting this into the previous formula, we get:
hypotenuse = (25 * tan(angle)) / sin(angle)
Calculating the value, we have:
hypotenuse = (25 * tan(10°)) / sin(10°)
Using a calculator, we find:
tan(10°) ≈ 0.1763
sin(10°) ≈ 0.1736
Substituting these values, we can calculate the length of the zip wire:
hypotenuse ≈ (25 * 0.1763) / 0.1736 ≈ 25.35 meters
Therefore, the length of the zip wire is approximately 25.35 meters.
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Which of these expressions is equivalent to log(15/7)
A. 15 • log (7)
B. log (15)• log (7)
C. log (15) - log (7)
D. log (15) + log (7)
Answer:
C
Step-by-step explanation:
using the rule of logarithms
log a - log b = log (\(\frac{a}{b}\) ) , then
log (\(\frac{15}{7}\) ) = log 15 - log 7
Find an equation for the line with slope
m=5 and which goes through the point (8,−9).
Write your answer in the form y=mx+b
An equation of line with slope m = 5 and which goes through the point (8, -9) is y = 5x - 49
In this question, we have been given a slope of the line and a point (8, -9)
We need to find an equation of the line with slope m = 5 and which goes through the point (8, -9)
Let (x1, y1) = (8, -9)
Using the slope-point form of the line,
y - y1 = m(x - x1)
y - (-9) = 5(x - 8)
y + 9= 5x - 40
y = 5x - 40 - 9
y = 5x - 49
Therefore, an equation of line with slope m = 5 and which goes through the point (8, -9) is y = 5x - 49
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Point C has the same y-coordinate as point B and the distance between point B and point C is equal to the distance between point C and the y-axis. Point A has the same x-coordinate as point C and the distance between point A and point C is twice the distance between point B and point C. What is one possible location of point A? How many possible locations are there for point A?
The possible location of point A is (x, y), which is the same as the location of point B and point C, there is only one possible location for point A, and it is the same as the location of point B and point C.
Let's solve this step by step.
First, let's consider the information given:
Point C has the same y-coordinate as point B.
The distance between point B and point C is equal to the distance between point C and the y-axis.
Point A has the same x-coordinate as point C.
The distance between point A and point C is twice the distance between point B and point C.
Let's denote the coordinates of point B as (x, y), and we'll let y be the y-coordinate of point B.
From point 2, we know that the distance between point B and point C is equal to the distance between point C and the y-axis. This implies that point C lies on the vertical line passing through point B. So, the x-coordinate of point C is the same as that of point B, which is x.
From point 1, we know that point C has the same y-coordinate as point B, so the coordinates of point C are (x, y).
From point 4, we know that the distance between point A and point C is twice the distance between point B and point C. Since the distance between two points can be calculated using the distance formula, let's write the equations based on the given information:
Distance between point B and point C = Distance between point C and y-axis
√((x - x)² + (y - y)²) = √(x² + y²)
Simplifying the equation:
0 = √(x² + y²) - √(x² + y²)
This implies that the distance between point B and point C is 0, which means point B and point C coincide. Therefore, point A and point C also coincide since they have the same x-coordinate.
In summary, the possible location of point A is (x, y), which is the same as the location of point B and point C. So, there is only one possible location for point A, and it is the same as the location of point B and point C.
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1. |x - 7] + 8 < 11
How do u solve
The solution of the given inequality |x - 7| + 8 < 11 is 4 < x < 10.
What is meant by the term inequality?In mathematics, an inequality is an interaction between two expressions as well as values which are not equitable to each other. Inequality results from a lack of balance.
Rule 1: Once inequalities are linked, they can be crossed. As a result, if an is greater than b and b is greater than c, a will indeed be greater than c as well.If a > b > c, a > c, we can skip b and get to the relationship between a and c directly.Rule 2: When you swap the values, this same sign reverses.If p > q, then q < pIf p < q, then q > pAs per the given relation;
|x - 7| + 8 < 11
Subtract both side by -8.
|x - 7| + 8 - 8 < 11 - 8
|x - 7| < 3
Removing modulus will give the relation as;
- 3 < x - 7 < 3
Add 7 on both side.
- 3 + 7 < x - 7 + 7 < 3 + 7
4 < x < 10
Thus, the solution of the x lied between 4 and 10 with the condition that;
4 < x < 10.
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Solve the following system of linear equations by addition. Indicate whether the given system of linear equations has one solution, hasno solution, or has an infinite number of solutions. If the system has one solution, find the solution.- 2x + y = 7- 2x + y = -6
Answer:
Explanations:
Given the system of equations:
- 2x + y = 7 .................................... 1
- 2x + y = -6 .................................. 2
Subtract both equations from each other to have;
-2x-(-2x) + (y-y) = 7 - (-6)
0x = 7 + 6
0x = 13
Divide both sides by 0
0x/0 = 13/0
x = 13/0
x = ∞
This shows that the system of equations has no solution
Help me please !?...........<3
Step-by-step explanation:
1. DOB & COA, COB& AOD
2. 20 :)
sorry lol my answer needs to be 20 characters long
Which graph is defined by the function given below? y = (x + 2)(x + 8)
Answer:
x^2+8x+2x+16
=x^2+10x+16
=x(x+8)+2(x+8)
=(x+8)(x+2)
=ans.(-8,-2)
Step-by-step explanation:
hope it is helpful to you
A boy walks 5km due north and then 4km due east. Find the bearing of his current position from the starting point, how far is the boy now from the starting point