The particular solution of the differential equation f''(x) = sin(x) that satisfies the initial conditions f'(0) = 2, f(0) = 3 is : f(x) = -sin(x) + 3x + 3
To find the particular solution of the given differential equation, we first integrate both sides with respect to x:
f'(x) = ∫sin(x) dx = -cos(x) + C1
where C1 is the constant of integration.
Next, we integrate f'(x) again:
f(x) = ∫(-cos(x) + C1) dx = -sin(x) + C1x + C2
where C2 is the constant of integration.
To find the values of C1 and C2, we use the initial conditions:
f'(0) = -cos(0) + C1 = 2
C1 = 2 + cos(0) (Since, cos (0) = 1)
C1 = 2+1 = 3
f(0) = -sin(0) + C1(0) + C2
C2 = 0 + 0 + 3 (Since,sin(0) = 0 )
C2 = 3
Therefore, the particular solution of the differential equation that satisfies the initial conditions is:
f(x) = -sin(x) + 3x + 3
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What is inequality give answer?
An inequality is a mathematical statement that compares two expressions and expresses the relationship between them. It is represented by a symbol such as ">", "<", "≥", or "≤" and can be thought of as a generalization of an equation.
Unlike an equation, which has one unique solution, an inequality can have multiple solutions or no solution at all. The solutions of an inequality are the values that make the inequality true.
Inequalities are used to model real-world situations where there are constraints or limitations, such as determining the range of possible values for a variable. They are also used to describe relationships between variables, such as when one variable is greater than or less than another variable.
There are different types of inequalities, such as linear inequalities, quadratic inequalities, and absolute value inequalities, each with their own set of rules and methods for solving them.
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Peter own a total of one hundred and forty four prized baeball card. If he were to add 7 more American League player and three more national league player, hi collection of American to national would be in a ratio of nine five. Find out how many card of each league he ha currently
The total number of baseball cards that Peter owns is 154.
Mathematicians use the term "ratio" to compare two or more numbers. It serves as a comparison tool to show how big or tiny an amount is in relation to another.
Two amounts are compared using division in a ratio. In this case, the dividend is referred to as the "antecedent" and the divisor as the "consequent."
Given that,
Peter owns a total of one hundred and forty-four prized baseball cards.
He adds seven more American League players and three more national league players.
Total baseball cards he owns = 144+ 7+3 = 154
The ratio of American to national = 9:5 = 9/5 = 1.8
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Why is it called a prime number?
Prime numbers are called prime as they come multiplicative first and other numbers are multiples of prime numbers.
As given in the question,
Prime numbers are called prime:
Meaning of prime is known as first.Prime numbers are multiplicatively first numbers .All the other numbers are multiples of prime numbers other than one.'1' is neither a prime number nor a composite number.prime numbers represents such numbers which has only two factors one and the number itself.Example of prime numbers : 2, 3, 5, 7,.... so on.Other numbers : 4 = 2 × 2 , 12 = 2× 2 × 3 so on.Therefore, prime numbers are called prime as they are multiplicative first numbers other numbers are multiples of prime number other than one.
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please help quickly!
which of the following is the graph of y=|x+3|?
Answer:
It's D, because the point intercepts at (0, 3), which is 3 up from the y position. What the difference is from this graph and the others is that this graph has a y-intercept of positive 3, and starts at an x point of -3. The x and y values should be inverted in order for this to be correct, so that is why option D is correct.
Hope this helps!
The dog shelter has Labradors, Terriers, and Golden Retrievers available for adoption. If P(terriers) = 15%, interpret the likelihood of randomly selecting a terrier from the shelter. Likely Unlikely Equally likely and unlikely This value is not possible to represent probability of a chance event
If P(terriers) = 15%, the interpretation of the likelihood of randomly selecting a terrier from the shelter is; Unlikely
How to find the probability of selection?Probability of selection is one that defines the probability that a population unit is included in a sample generated by probability sampling.
For any population, the probability of any element within that population to be selected into a sample is calculated as the sample size divided by the population size.
In this case, we are told that the dog shelter has Labradors, Terriers, and Golden Retrievers available for adoption. There are three types of dogs.
We are given;
P(terriers) = 15%
This means the probability of randomly selection the other 2 dogs is way higher than that to select terriers.
Thus, we conclude that the probability of selecting terriers is unlikely due to its' low probability.
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Answer: B: Unlikely
Step-by-step explanation:
How many lines of longitude are there in total Class 6?
There are 180 lines of longitude in total.
Longitude is a geographic coordinate that specifies the east-west position of a point on the Earth's surface. Lines of longitude run in a north-south direction and measure the angular distance of a location east or west of the Prime Meridian, which is located at 0 degrees longitude. Lines of longitude are also known as meridians. Lines of longitude are drawn on the map and divided into 180 sections of exactly equal size. Each line of longitude is assigned a numerical value of 0 to 180 degrees east or west of the Prime Meridian. In total, there are 180 lines of longitude, which form a band around the Earth and divide it into eastern and western hemispheres. Lines of longitude are important for navigation, since they act as reference points for sailors and pilots, who use them to locate their position. They are also used to measure the time of day across different regions of the world.
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!!HELP!! evaluate using order of operations: A = L=50 W= 15 give your answer in simplest form
The numeric value of the expression A = LW, when L = 50 and W = 15, is given as follows:
A = 750.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The expression for this problem is defined as follows:
A = LW.
The input values of L and W are given as follows:
L = 50, W = 15.
Then the numeric value of the expression is found replacing the lone instance of L by 50 and the lone instance of W by 15, as follows:
A = 50 x 15
A = 750.
As there is only a single multiplication operation, precedence is not relevant for this problem.
Missing Information
The problem asks for the numeric value of the expression A = LW when L = 50 and W = 15.
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Jason is designing a new board game and is trying to figure out all the possible outcomes how many different possible outcomes are there if he spent a spinner with five equal sized labeled Monday, Tuesday Wednesday, Thursday Friday and spent a spinner with three equal sides section labeled walk when I stop
Answer:8
Step-by-step explanation:
Farmer Gepsil started with some dubbles on his farm. After 11 hours he had 88 dubbles. Every hour, he bought 6 more of them. Please help me make a table so I can graph this
The table for the farmer buying dubbles is given below.
What is a graph?
In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.
Let the time be represented by the variable = x.
Let the number of dubbles be represented by the variable = y.
At x = 11, the number of dubbles y = 88.
Every hour, the farmer bought 6 more of them.
So, at x = 12 the number of dubbles y = 88 + 6
So, the table will be of the formula (x,y+6).
Therefore, the table for the graph is obtained.
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For which sample size (n) and population parameter (p) can a normal curve be used to approximate the sampling distribution? O A. n = 30; p = 0.2 OB. n = 30; p = 0.3 O C. n = 40; p = 0.3 O D. n = 40; p = 0.2
The normal approximation to the binomial distribution is possible in the following case: C. n = 40; p= 0.3
When can we use the normal approximation to the binomial distribution?The binomial distribution is defined as the probability of x successes on n trials, with (p) probability of a success on each trial. It can be approximated to the normal distribution with the formula;
Mean; μ = np
Standard deviation; σ = √(np(1 - p)
The conditions are;
np ≥ 10
√(np(1 - p) ≥ 10
Looking at the given options, the only one that fits this conditions is Option C because;
np = 40 x 0.3 = 12.
n(1 - p) = 40 x 0.9 = 36
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HELP PLS
Sid has a baseball cap collection. 75% of his caps have sports team symbols. If 24 of the caps have the team symbols, how many total caps does Sid have?
Actually forget this answer
Find the solution to the system of equations.
The solution to the system of equations, x = 7y - 3 and x + 7y = 8, is: (5/2, 11/14).
How to Find the Solution tp a System of Equations?One way to solve a system of equations is to use substitution.
We can start by substituting the first equation into the second equation:
x + 7y = 8
(7y - 3) + 7y = 8
7y + 7y - 3 = 8
14y - 3 = 8
14y = 11
y = 11/14
Now that we know the value of y, we can substitute it back into the first equation to find x:
x = 7y - 3
x = 7(11/14) - 3
x = 11/2 - 3/2
x = 8/2 - 3/2
x = 5/2
So the solution to the system of equations is (x, y) = (5/2, 11/14)
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mala walk her dog 3 times a day each walk is 3/4 mile. which expression tell how many mile mala walks her dog each day
3×3/4 is the expression which gives the 2.25 miles mala walks her dog each day.
What is Expression?An expression is combination of variables, numbers and operators.
Given that mala walk her dog 3 times a day
Each walk is 3/4 mile.
We have to find the expression tell how many mile mala walks her dog each day.
The miles walk by Mala and her dog=3×3/4
=9/4
=2.25 miles.
Hence, 3×3/4 is the expression which gives the 2.25 miles mala walks her dog each day.
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Given △abc ~ △xyz, what is the value of cos(z)? five-thirteenths five-twelfths twelve-thirteenths twelve-fifths
The value of cos(Z) is 12/13.
Since both triangles are similar, △ABC ~ △XYZ, the corresponding angles are congruent. It means:
m∠C = m∠Z, and
cos C = cos Z
The ratio for cosine is adjacent/hypotenuse. In a right triangle, the hypotenuse is the longest side, while an opposite side is the one across from a given angle, and an adjacent side is the one next to a given angle.
Since the side marked 12 is adjacent to angle C and 13 is the hypotenuse of this triangle; so, we know that:
cos C = 12/13
Thus, because of the angles and cosines for C and Z will be the same, it makes:
cos Z = cos C = 12/13
Hence, the value of cos(Z) is 12/13.
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If polygons are similar then what do you know about the corresponding sides and the corresponding angles ?
Answer:
Step-by-step explanation:
In Similar polygons, the corresponding angles are congruent, but the corresponding sides are proportional. So, similar polygons have the same shape, whereas their sizes are different. There would be certain uniform ratios in similar polygons.
Can a triangle be constructed with sides 2.5 cm 3.0 cm and 6.5 cm give reason?
We cannot construct a triangle with side lengths 2.5 cm, 3.0 cm and 6.5 cm as they don't follow the Triangle Inequality Theorem.
It is not possible to construct a triangle using the given side lengths of 2.5 cm, 3.0 cm, and 6.5 cm. This is because of the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, if we take 2.5 cm and 3.0 cm as two sides, the sum of their lengths is 5.5 cm. But the length of the third side (6.5 cm) is greater than 5.5 cm, so these three side lengths cannot form a triangle.
It is important to note that this theorem applies to any triangle, whether it is acute, right or obtuse-angled triangle. It is also important to note that this theorem is necessary for the formation of a triangle, and without it, it would not be possible to form a triangle.
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Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan. Click the trashcan to clear all your answers.
Add the following polynomials, then place the answer in the proper location on the grid. Write answer in descending
powers of x.
Add: x5-4x4+7x³ + 8, 9x³ +7x2-10, and -2x 5 +7x4-3x + 8.
The simplified exponential notation of the given expression is 9[tex]a^{2}b[/tex].The following polynomials, then put the resolution in the right spot.
what is expression ?A mathematical expression is a sentence with at least two variables or integers and one mathematical action. Addition, subtraction, multiplication, or division are all possible outcomes of this mathematical process. The following are the fundamental parts of an expression: Expression: (Math Operator, Number/Variable, Math Operator). A statement that has a least two numbers or variables, at least one mathematical operation, and is called a mathematical expression. Let's get acquainted with expressive writing. A number is 6 more than half of another number, which is known as x. This statement is written as x/2 + 6 in a mathematical expression.
given
the expression as:
=[tex](\frac{18}{2})( \frac{a^{3} }{a})(\frac{b^{2} }{b})[/tex]
know [tex]\frac{a^{m} }{a^{n} } = a^{m - n}[/tex]
So, =[tex](\frac{18}{2})( \frac{a^{3} }{a})(\frac{b^{2} }{b})[/tex] = 9[tex]a^{2}b[/tex].
The simplified exponential notation of the given expression is 9[tex]a^{2}b[/tex].The following polynomials, then put the resolution in the right spot.
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What is the mean of the values below (48,59,70,27,61)
please help me with this question thank you very much
today fever is 100.7 F, today is 2.5 higher than yesterday
yesterday is 2.5 lower than today.
x = temperature of yesterday
x + 2.5 = 100.7
x = 98.2 F
Answer:
B) Let x = yesterday's body temperature
x + 2.5° = 100.7 °F
x = 98.2 °F
Step-by-step explanation:
We want to determine Dud's body temperature yesterday. Therefore, the unknown variable is:
Let x = yesterday's body temperatureIf Dud's body temperature today is 2.5° higher than yesterday's body temperature, then his body temperature today is the sum of yesterday's body temperature and the increase:
x + 2.5° = 100.7 °FTo solve the equation, subtract 2.5° from both sides of the equation:
x + 2.5° - 2.5° = 100.7 °F - 2.5°x = 98.2 °FTherefore, Dud's body temperature yesterday was 98.2 °F.
Someone help me pleaseeeee
The polygons are similar, but not necessarily drawn to scale. Find the value of x.
Answer:
Summary: The polygons are similar but not necessarily drawn to scale, the value of x is 13 units.
Step-by-step explanation:
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please answer this question and I will give you a brainlist!
The coordinate of point A are (-2,1), Point B are (-4,-2), Point C are (-4,-6), and Point D are (-1,-3).
What is a coordinate of a graph?A coordinate of a graph is defined as the point where the line of X axis and y axis meets to form a location on the graph.
To find the coordinates of a point in the coordinate system, you do the opposite. Start at one point and follow the vertical axis vertically up or down. You have x-coordinates. Then do the same thing, but with a horizontal line to find the y-coordinate.
Thus, the coordinates of the following points include the following:
Point A: (-2,1)
Point B: (-4,-2)
Point C: (-4,-6)
Point D: (-1,-3)
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Which of the following is an advantage of a lossless compression algorithm over a lossy compression algorithm
A lossless compression algorithm preserves all of the original data, while a lossy compression algorithm may discard some of the original data.
A lossless compression algorithm is a type of data compression algorithm that preserves all of the original data without any loss. This means that when the original data is uncompressed, it is exactly the same as when it was compressed. On the other hand, a lossy compression algorithm is a type of data compression algorithm that discards some of the original data in order to reduce the size of the file. This means that when the original data is uncompressed, it may not be exactly the same as when it was compressed.
The advantage of a lossless compression algorithm over a lossy compression algorithm is that it preserves all of the original data, while a lossy compression algorithm may discard some of the original data.
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Please help!!! 30+ points! Thank you so much! :)
Answer:
8/5, -5/8
Step-by-step explanation:
[tex]5x+8y=-8 \\ \\ 8y=-5x-8 \\ \\ y=-\frac{5}{8}x-1[/tex]
So, the slope of the given line is -5/8.
Perpendicular lines have slopes that are negative reciprocals of each other, so the answer for the first question is 8/5.Parallel lines have the same slope, so the answer to the second question is -5/8.Pill bluethooth Speaker conit two emiphere and cyclinder. The diameter of the cylinder and emiphere i 2 inche. The height of the cylinder i a foot. The According to the Statement pleae fill in the blank. Pleae anwer the following in inch format and round it to
The Volume of the Bluetooth speaker is 0.36cm³
The capacity of the Bluetooth speaker = Volume of both the hemispherical parts + Volume of the cylindrical part
Given that,
The volume of a hemisphere of radius 'r' = 2/3πr³
The volume of a cylindrical = πr²h where r is
the radius of the base of the cylinder and h is the height.
The hemisphere and the cylinder will have the same radius r =0.25cm
Since the total length of the toy is 2 cm, the length of the conical part
will be 2−0.25−0.25=1.5cm
Hence, the Volume of the bluetooth speaker =2×( 2/3*22/7 *0.25³) + (22/7 *0.25²*1.5) = 0.36cm³
Correct question: A BlueTooth speaker is in the shape of a cylinder of diameter 0.5 cm with two hemispheres stuck to each of its ends. The length of the entire capsule is 2 cm The capacity of the Bluetooth speaker is?
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evaluate the integral (2 to 1)( v5 + v6) / 4 dv
If we evaluate the ∫(2to1)(v^6+v^5)/4 dv the answer would be 7.16
An integral gives numerical values to functions to represent concepts like volume, area, and displacement that result from combining infinite small amounts of data. Integration is the action of locating integrals.
The signed area of the region in the plane that is circumscribed by the graph of a specific function between two points on the real line can be used to represent definitive integrals.
Traditionally, portions above the plane's horizontal axis are positive, and those below it are negative.
First, calculate the corresponding indefinite integral.
∫(v^6+v^5)/4 dv= v^6(6v+7)/168
According to the Fundamental Theorem of Calculus, ∫(b to a) F(x)dx=f(b)−f(a), so just evaluate the integral at the endpoints
(v^6(6v+7)/168)at (v=2)=152/21.
(v^6(6v+7)/168)at (v=1)=13/168
∫(2to1)(v^6+v^5)/4 dv= (v^6(6v+7)/168)at (v=2) - (v^6(6v+7)/168)at (v=1) = 401/56 = 7.16
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a furniture store is having a sale where everything is 40% off. write a function that represents the amount of amount of discount d on an item with a regular price of p
d = 0.4 p, where the sales price of the bookshelf is $51, is the function that depicts the percentage off of a regular price.
What is the amount of discount ?When an item's price is lowered, it is said to be on sale. Multiplying the cost of an item by the % discount will give you the discount's value.
Discount = Original Price × Percentage Discount
$85 × 40%
$85 × 0.4 = $34.
Original cost less any discounts equals sales price.
$85 - $34 = $51.
The discount is the amount that separates an item's selling price from its marked (or list) price. Discount is therefore calculated as follows: Discount=List price – Selling price. Take advantage of deals like the buy one, get one free promotion or 15% off shirts, for instance. On an item with a price per hundred displayed, you have a percentage discount. An item that was previously priced at Rs. 1,000 is now being offered for Rs. 900 thanks to a 10% percentage discount.
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If p is inversely proportional to the square of q, and p is 20 when q is 7, determine p when q is equal to 2.
The requried value of the proportional value of p when q = 2 is given as 245.
What is proportionality?proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
here,
p ∝ 1 / q²
So,
p₁/p₂ = q₂² / q₁²
Substitute value in the above equation,
20/p = 2²/7²
20 ×49 / 4 = p
p = 245
Thus, the requried value of p when q = 2 is given as 245.
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Determine which representation has the greatest rate of change.
The representation that has the greatest rate of change is y = 2 + 3.5x
How to find the representation that has the greatest rate of changeThe rate of change in the expression y = 2 + 3.5x is 3.5. This is compared with the equation y = mx + c where m is the rate of change
For the table the rate of change is calculated as follows
m = change in y / change in x
m = (20 - 8) / (5 - 1)
m = 12 / 6
m = 2
For the graph the slope is calculated using the points (2, -1) and (3, -4)
m = (-1 + 4) / (2 - 3)
m = 3 / -2
m = -1.5
The slope of 3.5 from the equation is the greatest
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If AB=6 A B = 6 and BC=11 B C = 11 ,what is the length of AC A C ?
The length of the third side can be in range of [1, 17].
What are triangles?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane
Given is that in triangle ABC, AB = 6 and BC = 11.
In a triangle, the sum of two sides of a triangle is always greater than the third side. This means -
AB + BC > AC
(6 + 11) > AC
AC < 17
Therefore, the length of the third side can be in range of [1, 17].
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