Answers
The numeric value of the function f(x) at x = 5 is given as follows:
f(5) = 74.75.
How to obtain the function f(x)?The second derivative of the function f(x) is given as follows:
f''(x) = 2x + 6sin(x).
Integrating the second derivative, the first derivative of the function is given as follows:
f'(x) = x² - 6cos(x) + K.
When x = 0, y' = 2, hence the constant K is given as follows:
2 = -6 + K
K = 8.
Hence:
f'(x) = x² - 6cos(x) + 8.
Integrating the first derivative, the function is given as follows:
f(x) = x³/3 - 6sin(x) + 8x + K.
When x = 0, y = 4, hence the constant K is given as follows:
K = 4.
Then:
f(x) = x³/3 - 6sin(x) + 8x + 4.
The numeric value at x = 5 is given as follows:
f(5) = 5³/5 - 6sin(5) + 8(5) + 4
f(5) = 74.75.
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Related Questions
Quiz: Measures of Center and Spread
Question 1 of 10
If data set A has a larger standard deviation than data set B, data set A is more spread out than data set B.
A. True
B. False
Answers
The given statement "If data set A has a larger standard deviation than data set B, data set A is more spread out than data set B" is true.
The standard deviation is a measure of a data set's dispersion. It tells us how far the data values are from the mean.
A larger standard deviation means that the data points are more spread out, i.e., they are farther from the mean.
Therefore, if data set A has a standard deviation that is greater than data set B, it means that the values in data set A are more spread apart.
Hence, the given statement is true.
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I REALLY NEED THIS TO PASS SOMEONE PLEASE TRY AND HELP
solve this triangle. Round to the nearest tenth
Answers
Answer:
Im pretty sure its the third one
Step-by-step explanation:
It all depends on the square root to find the nearest tenth and rounding it all up.
given the expression (2^-3)(2^5)/2^7), select the three equivalent numerical expressions
Answers
The three equivalent numerical expressions are 1/32, 0.03125, 3.125 x 10^-2
How to simplify the numerical expressionsUsing the exponential rules, we can simplify the expressions as:
(2^-3)(2^5)/2^7)
= 2^(5-3)/2^7
= 2^2/2^7
= 1/2^(7-2)
= 1/2^5
= 1/32
Therefore, three equivalent numerical expressions for the given expression are: 1/32, 0.03125, 3.125 x 10^-2
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How would you describe what this transformation looks like when preformed on a coordinate plane
Answers
The description of function transformations and an example is highlighted below
Describing the transformation of the functionsTo describe the transformation of the functions, we need to identify the image and the preimage of the functions to be transformed
Take for instance the function is y = x² transformed to the function y = (x + 3)²
This means that the parent function is y = x²
When compared, we can see that
x in y = x² is x + 3 in y = (x + 3)²
This means that y = x² is shifted left by 3 units to form y = (x + 3)²
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13.5.6 Check Your Understanding Complete the statements. The graph of y = (x + 3)² is a [DROP DOWN 1] of the graph y = C with the graph of y = (x+3)2, it is shifted [DROP DOWN 2] 3 units. When building a table of values to 2 For the graph y = X to coincide model the function y = (x+3)2, this shift can be found by [DROP DOWN 3] 3 to/from each [DROP DOWN 4] for each corresponding [DROP DOWN 5].
Answers
The graph of y = (x + 3)² is a transformation of the graph y = x². It is shifted left 3 units.
Describing the transformation of the functionsThe equation of the function is given as
y = x²
The transformed function is
y = (x + 3)²
This means that the parent function is y = x²
When compared, we can see that
x in y = x² is x + 3 in y = (x + 3)²
This means that y = x² is shifted left by 3 units to form y = (x + 3)²
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can someone help me on number 1
Answers
The segments AB and CD on item 1 are classified as follows:
Perpendicular.
When are lines parallel, perpendicular or neither?The slope, given by change in y divided by change in x, determines if the lines are parallel, perpendicular, or neither, as follows:
If they are equal, the lines are parallel.If their multiplication is of -1, they are perpendicular.Otherwise, they are neither.The slope of segment AB is given as follows:
m = (3 - 13)/(0 - (-2))
m = -10/2
m = -5.
The slope of segment CB is given as follows:
m = (3 - 0)/(10 - (-5))
m = 3/15
m = 1/5.
The multiplication of these slopes is given as follows:
-5 x 1/5 = -1.
As the multiplication of the slopes is of -1, the segments are perpendicular.
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Answers
Answer:
The second scatterplot does not suggest a linear relationship between x and y.
A group of students was asked about the number of times they had been water-skiing. The data is shown in the histogram.
A histogram titled Water Skiing Trips. The x-axis is labeled Number of Times Water Skiing and has intervals of 1 to 5, 6 to 10, 11 to 15, 16 to 20, and 21 to 25. The y-axis is labeled Frequency and starts at 0 with tick marks every 1 units up to 6. There is a shaded bar for 6 to 10 that stops at 3, for 11 to 15 that stops at 5, for 16 to 20 that stops at 6, and for 21 to 25 that stops at 1. There is no shaded bar for the 1 to 5 interval.
Which of the following best describes the spread of the data?
Explain its meaning in this situation.
The data has a possible range of 19, which is a wide spread. This might mean that the most common number of water-skiing trips is 10.
The data has a possible range of 19, which is a wide spread. This might mean that there is a large difference in the number of water-skiing trips taken by the students.
The data has a possible range of 6, which is a narrow spread. This could mean that most of the students have taken a similar number of water-skiing trips.
The data has a range of 6, which is a narrow spread. This might mean that the most common number of water-skiing trips was 6.
Answers
Answer:
(b) The data has a possible range of 19, which is a wide spread. This might mean that there is a large difference in the number of water-skiing trips taken by the students.
Step-by-step explanation:
You want the best description of the spread of data shown in the histogram.
SpreadThe least data value that can be represented on the chart is 6. The greatest value the chart can represent is 25. This means the possible range of data values is ...
range = max - min = 25 -6 = 19
This possible spread of 19 might mean there is a large difference in the number of trips taken by students, choice B.
__
Additional comment
The range must be at least 21 -10 = 11 trips, not an answer choice. The most common number appears to be in the range 16-20, so will likely not be 10. (This is referred to as the "mode range", as we cannot tell from the grouped data what the actual mode is.)
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Which of the following choices is a linear function? NEED HELP ASAP!
Answers
Answer: f(x)=x-2
Step-by-step explanation:
Linear function means a straight line so graph each one to find which is a straight line
seventeen more than a number is negative twenty-three
Answers
The number that represents the phrase is -40.
Let's use algebra to solve the problem.
If we let "a number" be represented by the variable x, we can write the first part of the sentence as "Seventeen more than a number" which can be written as:
x + 17
The problem also says that this expression is equal to negative twenty-three.
We can write that as:
x + 17 = -23
To solve for x, we need to isolate it on one side of the equation. We can do this by subtracting 17 from both sides:
x + 17 - 17 = -23 - 17
x = -40
Therefore, the number is -40.
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The illustration represents the number 3. Which improper fraction does it also represent?
please help me its due in a little bit!!
Answers
a + b = 10 a - b = 2 Solve the system of equations. Responses
Answers
The solution to the given system of equations is a = 6, b = 4.
The system of equations is given as follows:
a + b = 10 .....(i)
a - b = 2 .....(ii)
To solve this system of equations, we can use the method of elimination.
Adding the two equations, we get:
(a + b) + (a - b) = 10 + 2
2a = 12
a = 6
Substituting a = 6 into one of the equations, we get:
6 - b = 2
b = 4
Therefore, the solution to the system of equations is:
a = 6, b = 4.
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Find (fog)(2).
f(x) = 3x + 2
g(x) = x²
(fog)(2)=
Answers
Answer:
(f·g)(2) = 14----------------------------
Find the composition of the functions f(x) and g(x), which is written as f(g(x)).
Given functions:
f(x) = 3x + 2,g(x) = x² .Find f(g(x)):
f(g(x)) = f(x²) = 3(x²) + 2Evaluate f(g(2)):
f(g(2)) = 3(2²) + 2 = 3(4) + 2 = 12 + 2 = 14So, (f·g)(2) = 14.
Which is NOT personally liable for any losses or damages? Group of answer choices Shareholders in a public corporation, Owner of a sole proprietorship, Shareholders in a corporation, Partners in a partnership
Answers
The option which is not personally liable for any losses or damages is Shareholders in a public corporation, the correct answer is A.
We are given that;
Four options of damages
Now,
Shareholders in a public corporation are not personally liable for any losses or damages caused by the corporation, because they have limited liability. This means that they can only lose the amount they invested in the corporation, and their personal assets are protected from creditors or lawsuits12.
Owner of a sole proprietorship, shareholders in a private corporation, and partners in a partnership are all personally liable for any losses or damages caused by their business activities, unless they have some form of liability insurance or protection12. This means that they can be sued for their personal assets if the business cannot pay its debts or obligations.
Therefore, by unitary method the answer will be Shareholders in a public corporation
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Anwer fast due tomorrow show work
Answers
Answer:45.3 miles/h
Step-by-step explanation
let 'x' be the speed of the car.
60 × 2/3 = 120/3 = 40
30 × 1/5 = 151/5
151/5 /40 = x / 60
151 / 200 = x / 60
=> x = (151×60) / 200
=> x = 45.3
A ribbon is lining the outside of a circular object. If the object has a radius of 7 cm, then how long should the ribbon be?
Answers
Answer:
Length= 43.98 cm
Step-by-step explanation:
Circumference=2πr
r=7cm
C=2π(7)
C=43.98 cm
circumference is equal to the length of ribbon along the outside of the circular object
Which of the following points represents a striking deviation in the box plot above?
A.
P
B.
R
C.
S
D.
Q
Answers
A point that represent a striking deviation in the box plot above include the following: C. P.
What is a box-and-whisker plot?In Mathematics and Statistics, a box plot can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.
Based on the information provided about the data set, the five-number summary for the given data set include the following:
Minimum (Min) = 24.First quartile (Q₁) = 26.Median (Med) = 28.Third quartile (Q₃) = 29.Maximum (Max) = 30.In conclusion, we can logically deduce that point P represent a striking deviation in the box plot because it is an outlier (it is significantly far from all of the other data points).
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Calculate the area of the square
Answers
The area of the given rectangle is 83.6cm²
How to find the area of the shape?We know that the area of a rectangle is equal to the product between the dimensions, here we can see that:
b = 11cm
h = 7.6cm
The formula for the area is:
A = b*h
Replacing the values we will get:
A = 11cm*7.6cm = 83.6cm²
that is the area.
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14 minus 25% algebraic expression
Answers
The value of the expression is 13. 75
What is an algebraic expression?An algebraic expression is described as an expression that is known to consist of certain variables, terms, their coefficients, factors and also their constants.
Algebraic expressions are also known to be made up of some arithmetic operations such as;
BracketParenthesesDivisionMultiplicationSubtractionAdditionFrom the information given, we have that;
14 minus 25%
This is represented as;
14 - 25%
Find the percent
14 - 25/100
Divide the values
14 - 0.25
13. 75
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A cube has volume 3375 cubic inches. Determine the area of one face of the cube.
Answers
The area of one face of the cube that has a volume of 3375 cubic inches is: 225 square inches.
What is the Volume of a Cube?A cube has equal edge length, and therefore has faces with the same area. The formula for finding the volume of a cube is given as:
Volume of cube = s³, where s is the side length of the cube.
Also, to find the area of one face of a cube, we would use the formula below:
Area of one face of a cube = s².
Given the following:
Volume of a cube = 3375 cubic inches
Find s as shown below:
s = ∛3375
s = 15 inches.
Therefore, we have:
Area of one face of a cube = 15² = 225 square inches.
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the diamter is 37 m find its nearest whole number
Answers
The area and the circumference of the circle is 1074.6 m² and 116.18 m respectively.
Given that a circle has a diameter of 37 m, we will find the circumference of and the area of the circle,
Radius = diameter /2
Radius = 18.5 m
Circumference = π × diameter
= 3.14 × 37
= 116.18 m
Area = π × radius²
= 3.14 × 18.5²
= 1074.6 m²
Hence, the area and the circumference of the circle is 1074.6 m² and 116.18 m respectively.
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Answer choices
Only child
Have chores
Have a sibling
Does not have chores
Answers
Answer:
only child
Step-by-step explanation:
MODELING REAL LIFE A hemisphere-shaped mole has a diameter of 5.7 millimeters and a surface area of about
51 square millimeters. The radius of the mole doubles. Estimate the new surface area of the mole. Round your
answer to the nearest whole number.
The new surface area is square millimeters.
Answers
The new surface area of the hemisphere-shaped mole would be = 102mm².
How to calculate the new surface area for the hemisphere-shaped mole?A hemisphere-shaped mole has a shape that has one surface that is curved and the other surface a flat circular base.
Since the surface area of one hemisphere has been given, the second hemisphere can be determined.
To calculate the new surface area of the hemisphere-shaped moles the following is carried out;
Radius of the initial mole = 5.7/2 = 2.85 mm
If 2.85mm radius = 51 mm²
2(2.85mm) radius = x
Make X the subject of formula;
X = 2×2.85 × 51/2.85
= 102 mm²
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solution to the system of equations y = 2x -1 and y = x + 3
Answers
The solution to the system of equations, y = 2x -1 and y = x + 3 is: x = 4 and y = 7.
How to Find the Solution to a System of Equations?Given the system of equations as:
y = 2x - 1 ---> eqn. 1
y = x + 3 --> eqn. 2
Substitute y for (x + 3) into equation 1:
x + 3 = 2x - 1
Combine like terms:
x - 2x = -3 - 1
-x = -4
x = 4
Substitute x = 4 into equation 1:
y = 4 + 3
y = 7
The solution is: x = 4 and y = 7.
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Evelyn has 36 m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. (The fourth side of the enclosure would be the river.) The area of the land is 154 square meters. List each set of possible dimensions (length and width) of the field.
Answers
The possible dimensions (length and width) of the field which is rectangle are (26m, 5m) or (5m, 26m) and (28m, 4m) or (4m, 28m)
Let's assume the length of the rectangle be L and the width be W.
We know that we have three sides of the rectangle to fence, so the total length of the fence will be L+2W = 36m.
Also, we know the area of the rectangle = L×W = 154 sq.m
Using the two equations above, we can solve for L and W as follows:
L = 36 - 2W (from the first equation)
Substituting this value of L in the second equation:
(36 - 2W)W = 154
2W² - 18W + 77 = 0
We get two possible values of width: W = 5 or W = 4
For W = 5, L = 26
For W = 4, L = 28
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i need help with this, please anyone I am so scared of failing. Please explain throughly,
thank you so much.
Answers
Check the picture below.
[tex]\stackrel{ \textit{\LARGE Areas} }{\stackrel{ triangle }{\cfrac{1}{2}(26)(17)}~~ + ~~\stackrel{ rectangle }{(26)(9)}}\implies 221+234\implies \text{\LARGE 455}[/tex]
Danielle deposited $300.00 into a new savings account that earns interest compounded continuously. After 8 years, the balance in the account
was $907.00. What was the interest rate on the account?
O 13.8%
O 12.5%
O 14.5%
O 10.1%
Answers
In this case, A = $907, P = $300, and t = 8 years. We need to find r.
907 = 300 * e^(8r)
Now, we'll solve for r:
(907/300) = e^(8r)
3.0233 = e^(8r)
To isolate r, take the natural logarithm of both sides:
ln(3.0233) = 8r
Now, divide by 8:
(ln(3.0233))/8 = r
r ≈ 0.125
To express the interest rate as a percentage, multiply by 100:
0.125 * 100 = 12.5%
So, the interest rate on the account is approximately 12.5%.
Which is a Function or
Not a function
Answers
The relation that is not a function is relation 3, and the other 3 are functions.
Which are functions and which aren't?A relation is a function if each point on its domain is mapped into a single point in the range.
So if you see an input that is mapped into two different outputs, then it is not a function.
Then the relation 3 is not a function, because h is mapped to different things, meaning that we have the same input being mapped to different outpouts. While the other 3 relations are all functions.
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Help me, please my friends. I need the assistance
Answers
The area of a rectangle is 14x² + 19x - 3 square units.
The degree of 4x² + 3y - 6x⁴y + 4 is 5.
The number of terms of 4x² + 3y - 6x⁴y + 4 is 4.
Adding, subtraction or multiplying two polynomials always results in another polynomial.
How to calculate the area of a rectangle?In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:
A = LB
Where:
A represent the area of a rectangle.B represent the breadth of a rectangle.L represent the length of a rectangle.By substituting the given parameters into the formula for the area of a rectangle, we have the following;
Area of rectangle = (7x - 1) × (2x + 3)
Area of rectangle = 14x² + 21x - 2x - 3
Area of rectangle = 14x² + 19x - 3 square units.
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A student said that to
write a percent as a fraction, write the
number that comes before the percent
symbol over a denominator of 100. Is the
student correct? Justify your conclusion.
Answers
Answer:
Step-by-step explanation:
Yes, the student is correct. To write a percent as a fraction, we can write the number before the percent symbol as the numerator and 100 as the denominator. For example, 25% can be written as 25/100, which can be simplified to 1/4. This is because percent means "per hundred," so 25% means 25 per hundred, which can be expressed as a fraction with a denominator of 100.