The average four-digit number 7254 is the only one that is a multiple of another one, as it is composed of the digits 2, 4, 5 and 7 used exactly once.
To find the four-digit number that is a multiple of another one using the digits 2, 4, 5 and 7, we can list all the possible combinations of these digits:
2457, 2475, 2547, 2574, 2745, 2754, 4257, 4275, 4527, 4572, 4725, 4752, 5247, 5274, 5427, 5472, 5724, 5742, 7245, 7254, 7425, 7452, 7524, 7542. as it is composed of the digits 2, 4, 5 and 7 used exactly once.
Next, we can check to see which of these numbers is a multiple of another one. 7254 is the only one that is a multiple of another one, as it can be divided by 2, 4, 5 and 7. Therefore, the answer is 7254.
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Write a general expression for the electric potential V at any point on the y-axis inside the triangle in terms of Q,l , and y.
The electric potential V at any point on the y-axis inside the triangle can be expressed in terms of the charge Q, the length of the triangle l, and the distance y from the origin. The expression is V(y) = (Q/2l)y - (Q/2l)(2l-y) = (Q/l)(y - l).
The electric potential V at any point on the y-axis inside the triangle can be expressed in terms of the charge Q, the length of the triangle l, and the distance y from the origin. To find the expression, first note that the total charge of the triangle is Q, and the electric potential at the origin is 0. The distance from the origin to the top corner of the triangle is 2l. The electric potential at the top corner of the triangle is then equal to the total charge of the triangle divided by the length of the triangle, or Q/2l. The electric potential at any point on the y-axis is then equal to the total charge of the triangle divided by the length of the triangle times the distance from the origin to the point, minus the total charge of the triangle divided by the length of the triangle times the distance from the top corner of the triangle to the point. This gives the expression V(y) = (Q/2l)y - (Q/2l)(2l-y) = (Q/l)(y - l).
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An EMT sees himself as a bit of a rebel, but is highly sociable and is able to keep calm in an emergency. This person would likely score in the lower range of which of the following traits? (A) Psychoticism (B) Neuroticism (C) Extraversion (D) Conscientiousness
The correct answer is option D, extraversion, neuroticism, and psychoticism
Eysenck's theory of personality is based on three logical attributes namely:
a) introversion vs. extroversion – Extroversion leads to sociable life , while introversion causes need of being alone and limited interactions
b) neuroticism vs. stability – Neuroticism leads to anxiousness and overactive sympathetic nervous system while stability leads to emotional stability
c) psychoticism vs. socialization. - psychoticism leads to independent thinking, and hostility. While socialization leads to co-operative and conventional behaviour.
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Need answer how many hrs week=
Please
A week has three days, monday \stuesday \swednesday \sthursday \sfriday \ssaturday \ssunday.
The length of a week is ____ days. How many days are there in a week?A week can be any period of time with 7 days; it is not required to be from Monday through Sunday. Example: The days of Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday, and Monday all add up to a week.
T stands for Tuesday in the alphabetical list of days of the week. W stands for Wednesday. R stands for Thursday. F is for Friday. Saturday is denoted by the letter S.
You're correct about yesterday, today, and tomorrow.
The word "short" is a five-letter phrase that becomes "shorter" when we add the two letters "e,r."
A week has three days, monday \stuesday \swednesday \sthursday \sfriday \ssaturday \ssunday.
The complete question is?
A week has how many ts?
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A graph the shows y= -3/2x - 2
The graph of the given equation is given at end.
A graph is a graphic depiction or diagram that displays data in an organized manner. The points on a graph are typically used to depict the relationships between two or more things.
Determine the slope and y-intercept first, then put the equation in y-intercept (y=mx+b) form to get the equation of a graphed line. The y-to-x change ratio is known as the slope. The two locations you locate on the line should be connected by a sloping triangle.
Common graph types include line graphs, bar graphs, pie charts, scatter plots, and histograms. Graphs are an excellent tool for visualizing data and presenting statistics. An example of displaying numerical data is with a bar graph or chart.
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instructions: complete the following table, columns c and d. use the information from the assigned module readings on the revenue cycle components to explain the tasks and roles of each revenue cycle component listed in columns a and b.
The revenue cycle is the process of generating revenue by providing a product or service to a customer.
It begins with the pre-service phase, when a customer inquires about the product or service, and ends with the post-service phase, when the customer is invoiced and payment is received.
The four components of the revenue cycle are pre-service, service, billing, and post-service.
Pre-service: The pre-service phase involves obtaining the necessary information from the customer, including insurance information and eligibility, to ensure proper billing and payment.
Service: During the service phase, the product or service is provided to the customer.
Billing: In the billing phase, the appropriate charges are calculated and a bill is generated and sent to the customer.
Post-service: In the post-service phase, the customer's payment is received and the revenue is recorded in the organization's accounting system.
The formula for calculating revenue is: Revenue = Price x Quantity. This formula can be used to calculate the total revenue generated from a sale of a product or service. For example, if a company sells 100 items at a price of $5 each, the formula would be: Revenue = $5 x 100 = $500.
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A rectangular prism measures 7” x 7” x 4” what is the surface area?
The surface area of a rectangular prism is calculated by adding up the area of all its faces. To calculate the surface area of a rectangular prism, you can use the formula: 2(lw + lh + wh) where l represents the length, w represents the width and h represents the height.
In this case, the rectangular prism measures 7" x 7" x 4", so the surface area can be calculated as: 2(7" x 7" + 7" x 4" + 4" x 7") = 2(49" + 28" + 28") = 2(105") = 210 square inches.
It is important to note that the surface area is a measure of the total area of all the faces of a three-dimensional object, and it is always a positive value. Also, it is measured in squared units, in this case square inches, since all the measurements provided are in inches.
I hope this helps :)
Answer:
210 square
Step-by-step explanation:
just because
Select the correct answer.
Choose the system of inequalities that best matches the graph below.
y
O B.
O А. У <
um All rights reserved
C
4
-2-10
4 5 6
4
y > 42 - 4
y ≤ 4
y ≤ x +4
The set of inequality that most closely resembles the graph below is called [tex]$y \leq \frac{2}{3} x-3$[/tex] , [tex]$y < -x$[/tex] .
What is the system of inequality ?Two or more inequalities in one or more variables make up a system of inequalities. When a problem has a variety of possible solutions and those solutions are subject to several constraints, systems of inequalities are used. Inequality in income, gender, health care, and social class are some of the most prominent examples of social inequality.
At position five, there is an open circle with a right arrow. As a result, the compound inequality can be solved, for instance, by the numbers 0 and 6, but not by the number 4. An expression that doesn't contain the equals sign (=) is called an inequality. ,, >, and are the most widely used inequality symbols. Addition, subtraction, multiplication, and division are the four operations kinds that are performed on linear inequalities.
Therefore the correct answer is option B ) [tex]$y \leq \frac{2}{3} x-3$[/tex] , [tex]$y < -x$[/tex] .
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determine whether the triangles are similar by angle-angle similarity. if yes, write a similarity statement.
Congruency is said to be defined on two triangles when they have exact same length of sides and equal angles between them. The shape and size are supposed to be the same even after rotation or flipping of triangles for them to remain congruent.
There are 4 criteria to test the congruency of the triangle and they are as follows:
SAS - This proves congruency when two sides and the angle between them are the same w.r.t both trianglesSSS - Two triangles are congruent if all three sides of both of them are equal w.r.t to each otherAAS- When Two pairs of corresponding angles and one pair of corresponding sides (not between the angles) are equal then this is trueASA- When Two pairs of corresponding angles and one pair of corresponding sides between the angles are equal then this is trueTo know more about Congruency visit:
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consider the case of a binary classification problem in which the response is sampled froma. non-linear complex function which of the following algorithms has the potential to perform the best
It is used to perform binary classification with a high level of accuracy.
Support Vector Machines (SVMs) is a powerful algorithm with the potential to perform best in a binary classification problem with a non-linear complex function. SVMs are based on the concept of maximizing the margin between two classes of data points in the feature space. This is done by solving the optimization problem, which is formulated as a quadratic programming problem.
The formulation of the optimization problem for an SVM model is given by:
minimize W,b
subject to
y_i(w^T x_i + b) ≥ 1, i = 1,2,…,n
where W is the weight vector, b is the bias, x_i is the ith feature vector, and y_i is the ith class label.
The goal of the optimization problem is to find the weight vector W and bias b such that the distance between the two classes is maximized. This is done by minimizing the objective function, which is the sum of the weight vector. By solving this optimization problem, we can obtain an optimal hyperplane that separates the two classes. SVMs are powerful algorithms capable of dealing with non-linear complex functions, and can thus be used to perform binary classification with a high level of accuracy.
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f(x+1)=3x2+4x-2 find the function
how many different numbers can be represented in a 4 byte integer. (note that this is not the same as the above question.)
The range, based on the solution, is between -2,147,483,648 and 2,147,483,647.
Describe range:When the sample maximum as well as minimum are subtracted, the range of a collection of data seems to be the difference between the greatest and lowest values. It uses the same units as the data to express itself.
Why is math range?The distance between the greatest and smallest data sets in some kind of a set of numerical data is known as the range. The average of the greatest and smallest data points is the middle.
According to the given information:1 byte has 8 bits,
so 4 bytes have 32 bits.
Each bit can have 2 distinct states, so we have 2³² distinct combinations of bits (in 4 bytes) which correspond to 2³² distinct whole numbers.
Normally,
the range is 0 to 4,294,967,295 but if you want to allow negatives,
the range is -2,147,483,648 to 2,147,483,647
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if trace of a matrix is postive and determinant is positive does it mean eigen values are all positive?
To have the determinant negative, at least one Eigenvalue has to be negative but the reverse of this statement may or may not be true.
If we add all the diagonal elements of the square matrix, we get the trace of the given matrix.
Eigenvalues is a scalar that associates with a set linear equation described as -
(A - λ I) X = 0
If we take the product of all the eigenvalues of a matrix, we'll get the determinant of the matrix. If we consider a case in which the trace of the matrix is +ve, and its determinant is -ve, then at least one or an odd no. of Eigenvalues must be negative, since their product has to be positive when we solve for the determinant of the matrix
Therefore, to have the determinant negative, at least one Eigenvalue has to be negative but reverse may or may not be true.
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What is the value of x?
Enter your answer in the box.
X =
72 cm
9 cm
bd Reading Of
3x-20
56 cm
Next
Answer:
9
Step-by-step explanation:
72/9 =8
by the same ratio
56/8 = 7
so 3x-20 = 7
so x = 27/3 = 9
Gabriel is deciding between two landscaping companies for his place of business. Company A charges $45 per hour and a $250 equipment fee. Company B charges $55 per hour and a $200 equipment fee. Let AA represent the amount Company A would charge for tt hours of landscaping, and let BB represent the amount Company B would charge for tt hours of landscaping. Write an equation for each situation, in terms of t,t, and determine the interval of hours, t,t, for which Company A is cheaper than Company B.
The linear functions for each situation are given as follows:
Company A: 45x + 250.Company B: 55x + 200.The interval of hours for which Company A is cheaper than Company B is given as follows:
x > 5.
How to model the linear functions?The linear functions are modeled in slope-intercept format, as follows:
y = mx + b.
In which:
The slope m represents the cost per hour.The intercept b represents the equipment fee.Hence the functions are defined as follows:
Company A: 45x + 250.Company B: 55x + 200.Company A will be cheaper when:
45x + 250 < 55x + 200
10x > 50
x > 5.
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the polynomial 1-x x^2-x^3 \ x^{16}-x^{17} may be written in the form a 0 a 1y a 2y^2 \a {16}y^{16} a {17}y^{17}, where y
The polynomial[tex]1-x x^2-x^3 \ x^{16}-x^{17}[/tex] can be written in the form [tex]a0 + a1(x+1) + a2(x+1)^2 + ... + a16(x+1)^{16} + a17(x+1)^{17}[/tex] where y = x + 1 and a1's are constants.
a polynomial can be written in the form
[tex]a0 + a1x + a2x^2 + a3x^3 + ... + anx^n[/tex]
where a0, a1, a2, ..., an are constants (also known as coefficients) and x is the variable.
In this case, we are given a polynomial in the form [tex]1-x x^2-x^3 \ x^{16}-x^{17}[/tex] and we want to express it in the form [tex]a0 + a1y + a2y^2 + ... + a17y^{17}[/tex], where y = x + 1 and a1's are constants.
By substituting y = x + 1 into the polynomial, we get:
[tex]1 - (x + 1) + (x + 1)^2 - (x + 1)^3 + ... + (x + 1)^{16} - (x + 1)^{17}[/tex]
Each term in this polynomial is a function of y, which is in turn a function of x.
We can then match the coefficients a0, a1, a2, ..., a17 with the corresponding powers of y in the polynomial, i.e, a0 = 1, a1 = -1, a2 = -1, a3 = 0, ..., a16 = -1, a17 = -1, and we get the polynomial
It's important to note that the value of a1's are constants, meaning that they are not dependent on the variable x.
Did you mean: The polynomial [tex]1-x x^2-x^3 \ x^{16}-x^{17}[/tex] may be written in the form [tex]a 0 a 1y a 2y^2 \a {16}y^{16} a {17}y^{17}[/tex], where y = x + 1 and a1's are constants?
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[tex]-\frac{11}{48} +\frac{1}{72} -\frac{3}{16}[/tex]
Answer:
[tex]\frac{-29}{72}[/tex]
Step-by-step explanation:
use a calculator
Here are the weights (in pounds) of a sample of 13 male eleventh graders.
148, 140, 159, 141, 151, 156, 173, 167, 160, 159, 146, 174, 170
Send data to calculator
Find the median weight of these students.?
pounds
S
Weight of the 13 male eleventh graders is 157.23 pounds. Median is the number in the middle, ranked from least to greatest.
Median weight = 148+140+159+141+151+156+173+167+160+159+146+174+170
= 2044/13
= 157.23
Median :
The value that separates the upper half of a population, a data sample, or a probability distribution from the lower half is known as the median. It could be referred to as "the middle" value for a data set. The value in the middle of a data set is called the median. This means that 50% of the data points have values that are smaller than or equal to the median, and 50% of the data points have values that are higher than or equal to the median. First, you count the number of data points (n) and arrange them in ascending order for a small data set.
How is the Median Calculated?The middle value in a set of data is called the median. First, arrange the data in ascending order from smallest to largest. Divide the total number of observations by two to get the midpoint value. Round that number up if there are an odd number of observations, and the value in that position is the median. Take the average of the values found above and below that position if the number of observations is even.
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Correct the error in solving system of linear equations
x is 6 and y is 0 are the only solutions to the given pair of linear equations.
What are the linear equations?It is possible to write the given pair as x-3y 6=0. and 2x−3y−12=0
Here, a 1 = 1, b 1 = 3, c 1 = 6, and a 2 = 2, b 2 = 3, c 2 = 12, and eq2 a 2.
a1 = 2
b1 , b2
b 1 = −6
3 = −2 1
therefore a 2
a 1= b 2 b 1.
The given pair of equations is therefore consistent.
In order to solve them graphically, we've
Take x-3y=6=0, x=0y=2, and x=3y=1 into consideration.
Draw a line to connect the points.
Think about 2x3y12=0 x=0y=4 x=3y=2.
Create a line connecting the two points.
x=6 and y=0 are the only solutions to the given pair of linear equations.
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If we know that a 3 by 3 matrix B is known to have eigenvalues 0, 1 and 2, find each of the following, or explain why more information is needed to find the answer: (a) The rank of B. (b) The determinant of BTB. (c) The eigenvalues of BTB. (d) The eigenvalues of (B?+1)-!
a) The rank of B can be determined by looking at the eigenvalues of B. Since the eigenvalues of B are 0, 1, and 2, the rank of B is 3.
b) The determinant of BTB can be found by multiplying the eigenvalues of B together. Since the eigenvalues are 0, 1, and 2, the determinant of BTB is 0.
c) The eigenvalues of BTB can be found by taking the square of the eigenvalues of B. Since the eigenvalues of B are 0, 1, and 2, the eigenvalues of BTB are 0, 1, and 4.
d) More information is needed to find the eigenvalues of (B?+1)-!. We need to know the components of B in order to solve this equation.
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Order the side lengths EF, FG, and GE from least to greatest.
(Note that the figure is not drawn to scale.)
G
72°
F
66°
0 < 0 < 0
E
Order of the side lengths EF, FG, and GE from least to greatest is EF < FG < GE.
Give a brief account on Law of Coslnes?When the lengths of two sides and the size of the included angle are known (SAS) or when the lengths of all three sides are known (SSS), the Law of Cosines can be used to determine the remaining components of an oblique (non-right) triangle. We are unable to establish a solvable percentage in either of these scenarios, making it impossible to apply the Law of Sines.
According to the Law of Cosines:
c² = a² + b² - 2ab * cos(C)
With the exception of the third component, which equals zero if C is a straight angle and the Pythagorean Theorem results, this is similar to the Pythagorean Theorem. As a result, the Law of Cosines is a specific case of the Pythagorean Theorem.
Using the Law of Cosines
In the given triangle, we are given the measure of angle G and the length of side FG, so we can use the Law of Cosines to find the lengths of the other sides. The Law of Cosines states that for a triangle with sides a, b, and c and angle C opposite side c, the relationship between the sides and the angle is:
c² = a² + b² - 2ab * cos(C)
Given: angle G = 72°, FG = 6
We can use the Law of Cosines to find the lengths of the other sides:
EF² = FG² + GE² - 2FG * GE * cos(G)
EF = √(6² + GE² - 2 * 6 * GE * cos(72))
FG² = EF² + GE² - 2EF * GE * cos(F)
FG = √(EF² + GE² - 2 * EF * GE * cos(66))
As we don't have any value for GE, we can't calculate the exact values, but as we know that the side opposite to the largest angle is the longest side of a triangle, so we can order the sides as follows:
EF < FG < GE
It means that side GE is the longest side of the triangle, followed by side FG, and side EF is the shortest side of the triangle.
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which of the following sampling strategies makes it difficult to discern what sub-population the sample represents?
Convenience sampling represents the sub-population of the sample strategies.
Convenience sampling is defined as a type of non-probability sampling that involves the sample being drawn from that part of the population that is close to hand and is a type of sampling that is most useful for pilot testing.
Convenience sampling can be used by almost anyone and has been around for generations. One of the reasons that it is most often used is due to the numerous advantages it provides
Expedited data collection, Ease of research, Ready availability, Cost-effectiveness.
Bias, Power is the disadvantages of convenience sampling.
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at times, the relationship between a dependent and an independent variable is expressed as a logarithmic equation. given the two equations below, what is the relationship between x and y? equation 1: log36
The relationship between x and y as a logarithmic equation is: y = log_36 9 = 2.
The relationship between x and y can be expressed as a logarithmic equation. Let's take a look at the two equations:
Equation 1: log36
To calculate the relationship between x and y, we will use the logarithmic property: logb(x) = y ⇔ b^y = x
From equation 1, we can solve for y:
log36 = y
⇒ 36^y = 36
⇒ y = 1
Therefore, the relationship between x and y is: x = 36^1 = 36.
To verify this, we can plug x = 36 into equation 2 and see if it is true:
Equation 2: y = log_x 9
Plugging in x = 36, we have:
y = log_36 9
⇒ y = log_36 3^2
⇒ y = 2
Therefore, the relationship between x and y is: y = log_36 9 = 2.
This confirms that the relationship between x and y is x = 36 and y = 2.
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The picture shows two ladders propped against
facing walls. The end of the first ladder is 5m
above the base of the second wall. The second
ladder is 5m above the base of the first wall.
5m
Can you work out at what height the
ladders cross?
Are you surprised that we don't need to know
the distance between the two walls?
5m
5m
10m
By using Triangles ABC and ADC given in image, Ladders will cross at 10/3 m above the ground.
What are triangles?
Triangles are polygons in geometry that have three sides and three vertices. This figure is two-dimensional and has three straight sides. A triangle is a three-sided polygon. A triangle's three angles added together equals 180°. A single plane contains the triangle. The triangle is classified into six forms based on its sides and angles.
A triangle is categorized into three categories based on its sides, namely:
Scalene Triangle - Each side has a distinct length.
Isosceles Triangle - A triangle with two sides of equal length and one side of a different length.
Equilateral Triangle - A triangle has three sides that are of the same length.
A triangle is categorized into three categories based on its angles, namely:
Acute Angle Triangle - A triangle with all of its angles smaller than 90°.
Obtuse Angle Triangle - A triangle with one of its angles larger than 90°.
Triangle with a Right Angle - A triangle with one of its angles equal to 90°.
Now,
As shown in image that the angles ∠BAD and ∠ADC are alternate angles, and therefore equal. Likewise, angles ∠ABC and BCD are also alternate and therefore equal.
∠BEA and ∠CED are opposite, which means that they are equal. You can see these equal angles in the image.
This means that the triangles ABE and DCE have the same angles as each other, and are therefore similar.
This means:
AE/ED=AB/DC=5m/10m=1/2
Therefore AE=1/3AD
This means E is 1/3 of the way up from the floor to D, so is at a height of 10/3m=3 1/3m
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Solve the following system of equations. Enter the y coordinate of the solution. Round your answer to the nearest tenth. 5x+ 27= 21 -2x+6y=-34
The solution to the system of equations is x = ( -6/5 ) and y = -6.1
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the first equation be represented as A
Let the second equation be represented as B
Now , the value of A is
5x + 27 = 21 be equation (1)
Now , the value of B is
-2x + 6y = -34 be equation (2)
On simplifying the equations , we get
Subtracting 27 on both sides of the equation , we get
5x = -6
Divide by 5 on both sides of the equation , we get
x = -6/5
Substitute the value of x in equation (2) , we get
-2 ( -6/5 ) + 6y = -34
12/5 + 6y = -34
Subtracting 12/5 on both sides of the equation , we get
6y = -34 - 2.4
6y = -36.4
Divide by 6 on both sides of the equation , we get
y = -6.067
y = -6.1
Hence , the value of y is -6.1
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Find the volume of the solid of revolution generated when the region in the first quadrant bounded by the graphs of y = x2 +1, y = 5, and the y-axis is revolved about the line x = -3. a. 8πb.12πc. 20π d. 40π
When the area in the first quadrant bordered by x=0, y=1, x=y4, and y=10 is rotated about the line y=10, the solid's volume is 11π/3
What is meant by volume?Every three-dimensional item takes up space in some way. The volume of this area is what is used to describe it. The area occupied within an object's three-dimensional bounds is referred to as its volume. The object's capacity is another name for it. Volume is a mathematical term that describes how much space in three dimensions is occupied by an object or a closed surface. The measurement of volume is done in cubic units, like m3, cm3, in3, etc.Volume is a measurement of how much room a thing occupies. To put it another way, just as height and width are terms used to describe size, volume is a measurement of the size of an object.We using,
V = π ∫|(f(x) - d) 2 - (g (x) - d) 2|dx Integrating from a to b
For this case, a = 0, b = 1, g(x) = 1, f(x) = x1/4
Simplifying the equation,
V = π∫|(x1/4 - 10) 2 - (1 - 10) 2dx = π∫|x1/2 - 20x1/4 + 100 - 81|dx
= π[(2/3) x 3/2 - 20(4/5) x 5/4 + 19x] evaluated from at 1 and 0
= π|(2/3 -16 +19) = 11π/3
The complete question is?
find the volume of the solid obtained by rotating the region in the first quadrant bounded by x=0, y=1, x=y^4 about the line y=10
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sketch the vector field f. (select update graph to see your response plotted on the screen. select the submit button to grade your response.) f(x, y, z)At(-2,-2,-2) the vector is ___
The vector field f is defined as f(x, y, z) = (-2, -2, -2).
This means that at any point (x, y, z), the vector is (-2, -2, -2). For example, if the point is (1, 2, 3) then the vector is (-2, -2, -2). This can be represented mathematically as f(1, 2, 3) = (-2, -2, -2). At the point (-2, -2, -2), the vector field is (-6, -6, -6). This can be calculated by substituting the given point into the formula. The x-coordinate of the vector is x+y+z = -2+(-2)+(-2) = -6. Similarly, the y-coordinate of the vector is x-y-2z = -2+(-2)-2(-2) = -6, and the z-coordinate of the vector is -2x+y+z = -2(-2)+(-2)+(-2) = -6.The vector field f is constant in all directions, meaning that the same vector is found at any point (x, y, z). This is why the vector field is sometimes referred to as a constant vector field.
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Find the area of the figure.
The area of the figure would be 40 square mm.
What is the area of a figure?
The area of a figure is a measure of the amount of space inside a two-dimensional shape. The area of a figure is typically represented by the symbol A, and is usually measured in square units, such as square inches or square centimeters.
In the given figure, there are four triangles.
Two of them have the same area and other two have the same area
Area of one triangle = 1/2 * height * breadth
= 1/2 * 4 * 6
= 12
Area of other triangle = 1/2 * height * breadth
= 1/2 * 4 * 4
= 8
Area of figure = 2 * 12 + 2 * 8
= 24 + 16
= 40 square mm.
Hence, the area of the figure would be 40 square mm.
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The diagram shows four angles round a point.
a Write an inequality for x.
b Solve the inequality.
c Explain why the angle labelled xº cannot be a right angle.
For the given figure, The value angle x is 55 ° . A) x + x + 30 + 2x < 360; x < 82.5°.
C) The figure does not permit any right angles of 90 degrees that correspond to the mathematical norms involving opposite angles and angles of a turn. This means that x is not a right angle.
1) Interpreting the question we'll be asking:
In the diagram, a point is surrounded by four angles.
A) Construct a difference for x.
B) Addressing the inequality
C) Describe the reasons why the angle x° is not a straight angle.
2) In response to each query, we shall have:
A) x + x + 30 + 2x < 360
4x < 360 - 30
4x < 330
x < 82.5,
B) x + 2x + x + 30 + 2x = 360
6x = 360 - 30
6x = 330
x = 55
C) A right angle is one that measures 90 degrees; in the problem at hand, x cannot be straight because, in that case, the total of the values shown in the figure would exceed 360, which would be an incorrect representation of the mathematical principles governing opposite angles and angles of a turn.
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what value will make 7x +ky =35 parallel to 5x-3y+44=0
The value of k that makes the line 7x + ky = 35 parallel to the line 5x - 3y + 44 = 0 is k = -21/5.
How to solve the parallel equation?Two lines are parallel only if their slopes are the same. The slope of a line of the form y = mx + b (where m is the slope and b is the y-intercept) is m. The slope of a straight line of the form ax + by + c = 0 can be found using the formula: The calculation formula for the slope cutting shape will change.
So to find the value of k that makes the line 7x + ky = 35 parallel to the line 5x - 3y + 44 = 0, we need to find the slope of the line 5x - 3y + 44 = 0. To do this, we rearrange the equation into slope-intercept form.
5x - 3y + 44 = 0
-3y = -5x + 44
y = (5/3)x - 14.67
The straight line 5x - 3y + 44 = 0 has a slope of 5/3. In order for the 7x + ky = 35 line to be parallel to this line, the slope of 7x + ky = 35 must also be 5/3. To find the slope of 7x + ky = 35, rearrange the formula into slope-intercept form.
7x+ky=35
y = -(7/k)x + 35/k
Setting the slope of the line 7x + ky = 35 equal to the slope of the line 5x - 3y + 44 = 0 gives:
-(7/k) = 5/3
-7/k = 5/3
-7 * 3 = 5 * k
-21 = 5k
k = -21/5
Therefore, the value of k that makes the line 7x + ky = 35 parallel to the line 5x - 3y + 44 = 0 is k = -21/5.
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PLEASE HELP! Find the slope of the secant line between x= 3 and x= 8 for the function f(x) = [tex]\sqrt{16x-47}[/tex]. (Enter your answer in either exact notation of round to four decimal places.
The slope of the secant line between x = 3 and x = 8 for the function [tex]f(x) = \sqrt{16x - 47}[/tex] is given as follows:
8/5.
How to obtain the slope of the secant line?The secant line intersects the function f(x) at the coordinates x = 3 and x = 8.
The numeric value for the function at each of these points is given as follows:
x = 3: [tex]f(x) = \sqrt{48 - 47} = 1[/tex].x = 8: [tex]f(x) = \sqrt{128 - 47} = \sqrt{81} = 9[/tex]Given two points, the slope of a line is calculated as the change in y divided by the change in x, hence:
m = (9 - 1)/(8 - 3)
m = 8/5.
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