The value of μV is 40 cm³.
Given,The area of bottom of cylindrical container = 10 cm²The height of container = h = Mean height = 4 cm Standard deviation of height = σ = 0.2 cm We are supposed to find the mean volume of fluid in the container.In order to calculate the mean volume, first we need to calculate the volume of fluid in the container.Volume of a cylindrical container = πr²h Where, r is the radius of the base of the container.So, we need to calculate the value of r.The area of the bottom of the container is given as 10 cm².
We know that the area of the base of a cylinder is given as:Area of base of cylinder = πr² We are given that area of the base is 10 cm². So,10 = πr²r² = 10/πr = √(10/π) We can find the volume of fluid using the values we have.Volume of fluid = πr²h = π(√(10/π))² x 4 = 40 cm³We know that mean volume, μV is given as:μV = πr²μh So, we need to calculate the value of μh. We know that standard deviation σh is given as:σh = 0.2 cm So,μh = h = 4 cm So,μV = πr²μh = π(√(10/π))² x 4 = 40 cm³
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A circle with radius of 2 cm sits inside a circle with radius of 4 cm. What is the area of the shaded region? Round your final answer to the nearest hundredth. 2 cm CH 4 cm
the area of the shaded region is approximately 37.68 cm².
define area of circleThe area of a circle is the amount of space that is enclosed by the circle in a two-dimensional plane. It is defined as the product of the square of the radius (r) of the circle and the mathematical constant pi (π), which is approximately equal to 3.14159.
The area of the larger circle is:
A1 = π(4 cm)² = 16π cm²
The area of the smaller circle is:
A2 = π(2 cm)² = 4π cm²
To find the area of the shaded region, we subtract A2 from A1:
A1 - A2 = 16π cm²- 4π cm² = 12π cm²
To round the final answer to the nearest hundredth, we can use the approximation π ≈ 3.14:
12π cm² ≈ 12 × 3.14 cm² ≈ 37.68 cm²
Therefore, the area of the shaded region is approximately 37.68 square centimeters.
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If a first sample has a sample variance of 12 and a second sample has a sample variance of 22 , which of the following could be the value of the pooled sample variance? 1 10 16 25
The value of the pooled sample variance is 25 when the first sample has a sample variance of 12 and a second sample has a sample variance of 22.
If a first sample has a sample variance of 12 and a second sample has a sample variance of 22, then the possible values of the pooled sample variance are given by the formula below:
Formula:
pooled sample variance = [(n₁ - 1) s₁² + (n₂ - 1) s₂²] / (n₁ + n₂ - 2)
Where s₁ and s₂ are the sample standard deviations of the first and second samples,
n₁ and n₂ are the sample sizes of the first and second samples, respectively.
Thus, substituting the given values into the formula above, we have pooled sample variance:
= [(n₁ - 1) s₁² + (n₂ - 1) s₂²] / (n₁ + n₂ - 2)
= [(n₁ - 1) 12 + (n₂ - 1) 22] / (n₁ + n₂ - 2)
Checking each of the answer options:
If pooled sample variance is 1, then:
(n₁ - 1) 12 + (n₂ - 1) 22
= (n₁ + n₂ - 2)(1)
= 12n₁ + 22n₂ - 34
= (12n₁ - 12) + (22n₂ - 22)
= 12(n₁ - 1) + 22(n₂ - 1)
The expression on the right-hand side of the equation is a sum of multiples of 12 and 22, and therefore, the expression itself will be a multiple of the greatest common divisor of 12 and 22, which is 2.
Since 34 is not a multiple of 2, the equation cannot be true if the pooled sample variance is 1.
Thus, 1 is not a possible value of the pooled sample variance.
If pooled sample variance is 10, then:
(n₁ - 1) 12 + (n₂ - 1) 22
= (n₁ + n₂ - 2)(10)
= 12n₁ + 22n₂ - 34
= (12n₁ - 12) + (22n₂ - 22)
= 12(n₁ - 1) + 22(n₂ - 1)
The expression on the right-hand side of the equation is a sum of multiples of 12 and 22, and therefore, the expression itself will be a multiple of the greatest common divisor of 12 and 22, which is 2.
Since 34 is not a multiple of 2, the equation cannot be true if the pooled sample variance is 10.
Thus, 10 is not a possible value of the pooled sample variance.
If pooled sample variance is 16, then:
(n₁ - 1) 12 + (n₂ - 1) 22
= (n₁ + n₂ - 2)(16)
= 12n₁ + 22n₂ - 34
= (12n₁ - 12) + (22n₂ - 22)
= 12(n₁ - 1) + 22(n₂ - 1)
The expression on the right-hand side of the equation is a sum of multiples of 12 and 22, and therefore, the expression itself will be a multiple of the greatest common divisor of 12 and 22, which is 2.
Since 34 is not a multiple of 2, the equation cannot be true if the pooled sample variance is 16.
Thus, 16 is not a possible value of the pooled sample variance.
If pooled sample variance is 25, then:
(n₁ - 1) 12 + (n₂ - 1) 22
= (n₁ + n₂ - 2)(25)
= 12n₁ + 22n₂ - 34
= (12n₁ - 12) + (22n₂ - 22)
= 12(n₁ - 1) + 22(n₂ - 1)
The expression on the right-hand side of the equation is a sum of multiples of 12 and 22, and therefore, the expression itself will be a multiple of the greatest common divisor of 12 and 22, which is 2.
Since 46 is a multiple of 2, the equation can be true if the pooled sample variance is 25.
Thus, 25 is a possible value of the pooled sample variance.
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In a candy factory, each bag of candy contains 300 pieces. The bag can be off by 10 pieces.
Write an absolute value inequality that displays the possible number of candy pieces that a bag contains.
Answer:
[tex] |x - 300| \leqslant 10[/tex]
help!! i really can't do this pls help me with this inquality question
Explanation:
2n is greater than 20, so 2n > 20. This solves to n > 10 after dividing both sides by 2. That inequality is the same as 10 < n.
5n is less than 60. It leads to 5n < 60. That solves to n < 12 after dividing both sides by 5.
To summarize:
"2n is greater than 20" leads to n > 10, aka 10 < n."5n is less than 60" leads to n < 12Combine 10 < n with n < 12 to write a compound inequality:
10 < n < 12
The value n is between 10 and 12. We exclude each endpoint.
The only possible whole number that works here is n = 11
Please look at the photo and let me know the three answers ASAP!! Thank you!
Answer:
(a) $ 67.1
(b) $98.60
(c) $ 1.26
Step-by-step explanation:
Given equation is
[tex]y\:=\:-1.26x\:+\:98.6[/tex]
where x is the temperature in °F and y is the heating cost in $
To find heating cost for a specific temperature just substitute the value of x (temperature) in the equation
Part (a)
For x = 25 we get
y = -1.26(25)+ 98.6 = $ 67.1
Part (b)
For x = 0 we get
y = -1.26(0) + 98.6 = 0 + 98.6 = $98.60
Part (c)
For a 1 degree increase in temperature, the predicted decrease is the slope of the line
Slope of line = coefficient of x = -1.26
So decrease in cost for 1 degree increase in temperature = $1.26
in a group of 100 students 50 like online class and 70 loke physical class .represent in venn diagram and how many students like bith type pf classes
Answer:
Step-by-step explanation:
100 students all together.
50+70=120....so 20 must like both.
Write the equation of a line that is perpendicular to y=-2/7+9 and that passes through the point (4,-6)
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{2}{7}}x+9\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{-2}{7}} ~\hfill \stackrel{reciprocal}{\cfrac{7}{-2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{7}{-2} \implies \cfrac{7}{ 2 }}}[/tex]
so we're really looking for the equation of a line whose slope is 7/2 and it passes through (4 , -6)
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{-6})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{7}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-6)}=\stackrel{m}{ \cfrac{7}{2}}(x-\stackrel{x_1}{4}) \implies y +6= \cfrac{7}{2} (x -4) \\\\\\ y+6=\cfrac{7}{2}x-14\implies {\Large \begin{array}{llll} y=\cfrac{7}{2}x-20 \end{array}}[/tex]
The length of a rectangle is nine more than twice the width. If the perimeter is 120 inches, find the dimensions.
Answer:
Width = 17 inches
Length = 43 inches
Step-by-step explanation:
Framing and solving algebraic equation:Let the width of the rectangle = x inches
Length = 2*width +9
= (2x + 9) cm
[tex]\boxed{\bf Perimeter \ of \ rectangle = 2* (length + width)}[/tex]
2* (length + width) = 120 inches
2* (2x + 9 + x) = 120
2* (3x + 9) = 120
Use Distributive property,
2 * 3x + 2*9 = 120
6x + 18 = 120
Subtract 18 from both sides,
6x = 120 - 18
6x = 102
Divide both sides by 6,
x = 102 ÷ 6
x = 17
Width = 17 inches
Length = 2*17 +9
= 34 + 9
= 43 inches
the six trigonometric functions are not invertible what has to be done make them invertible
Can you post the image in your question.
3. The length of one leg of a 45-45-90 triangle is 7 m. What is the length of the other leg and the length of the hypotenuse?
The other leg is 7 m, and the hypotenuse is 7 m.
The other leg is 7 m, and the hypotenuse is 14 m.
O The other leg is 7√2 m, and the hypotenuse is 7 m.
The other leg is 7 m, and the hypotenuse is 7√2 m.
Answer: The other leg is 7 m, and the hypotenuse is 7√2 m.
Step-by-step explanation:
This is just a rule that in all cases, the two legs are equal and the hypotenuse is equal to the length of a leg times the square root of 2.
Hope this helps :)
sarah is trying to decide what combination of cups and plates to buy. her budget is $18. plates cost $6 each and cups cost $3 each. the numbers in the table represent total utility. given her budget, which combination will maximize total utility?
Answer:- Hence, the combination will maximize total utility is [tex]12.[/tex]
Step-By-Step-Explanation:-
What is cost?
Cost is the amount of money you spent to make the product or service. Price is what you will charge for it.
Here given that,
The cups and plates budget is [tex]$18 (3 plates x $6 each + 6 cups x $3 each)[/tex]
Then the utility for the combination is [tex]12 (3 plates x 4 utility each + 6 cups x 2 utility each).[/tex]
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are these equivalent
10-2x -2x10
At the age of 30, Jasmine started a retirement account with $50,000 which compounded interest semi-annually with an interest rate of 1. 75%. She made no further deposits. After 25 years, she decided to withdraw 50% of what had accumulated in the account so that she could con- tribute towards her grandchild's college education. She had to pay a 10% penalty on the early withdrawal. What was her penalty?
Jasmine's penalty for the early withdrawal from her retirement account was approximately $3,702.50.
The formula to calculate the compound interest is:
[tex]A = P(1 + r/n)^{n \times t}[/tex]
Where:
A = the final amount after t years
P = the principal amount (initial investment) ($50,000 in this case)
r = the annual interest rate (1.75% in decimal form, so 0.0175)
n = the number of times interest is compounded per year (semi-annually, so 2)
t = the number of years (25 years in this case)
Let's calculate the final amount accumulated in the account:
[tex]A = 50000 \times (1 + 0.0175/2)^{2\times 25}[/tex]
[tex]A = 50000 \times (1.00875)^{50}[/tex]
A = 50000 × 1.481
A = $74,050
After 25 years, Jasmine has approximately $74,050 in her retirement account.
Now, she decides to withdraw 50% of that amount:
Withdrawal Amount = 0.5 × $74,050
Withdrawal Amount = $37,025
Finally, she had to pay a 10% penalty on the early withdrawal:
Penalty = 0.10×$37,025
Penalty = $3,702.50
So, Jasmine's penalty for the early withdrawal from her retirement account was approximately $3,702.50.
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The following table represents the highest educational attainment of all adult
residents in a certain town. If a resident who is 40 or older is chosen at random, what
is the probability that they have only completed high school? Round your answer to
the nearest thousandth.
High school only
Some college
Bachelor's degree
Master's degree
Total
Age 20-29 Age 30-39 Age 40-49 Age 50 & over Total
1567
1078
5664
718
5026
1324
430
3550
1713
900
969
5149
1077
615
1108
525
3325
1942
1980
2062
513
6497
5394
2437
18521
The probability that a person chosen at random at age 40 or older has only completed high school is 0.2912.
What is probability?Probability is the chance or likelihood that something will occur. It is quantified using numbers, ranging from 0 (no chance) to 1 (certainty). It also helps us to draw conclusions about the chances of something happening based on the available data.
The total number of people who have only completed high school
=(5394)
the total number of people in the age group 40 and over =(18521)
By dividing both the data, we get
5394/18521= 0.2912
From the given data in the table, we can calculate the probability that a person chosen at random at age 40 or older has only completed high school.
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A grocer has two kinds of candy: one sells for 90 cents per pound, and the other sells for 40 cents per pound. How many pounds of each kind must he use to make 50 pounds that he can sell of 85 cents per pound?
The grocer must use 45 pounds of each kind of candy
How to calculate the number of pounds that the grocer requires?A grocer has two kinds of candy
The first type of candy sells for 90 cents per pound
The second type of candy sells for 40 cents per pound
The number of pounds needed to make each kind of candy if he uses 50 pounds can be calculated as follows
The first step is to multiply 50 by 85%
50(85/100)
= 50(0.85)
= 42.5
Let y represent the unknown
y(90/100) + (50-y)(40/100)
0.9y + 0.4(50-y)
0.9y + 20-0.4y
0.9y-0.4y+20
0.5y+20(equate this value with 42.5)
0.5y+20= 42.5
collect the like terms
0.5y= 42.5-20
0.5y= 22.5
y= 22.5/0.5
y= 45
Hence the grocer needs 45 pounds for each kind of candy
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find the standard form of the parabola equation: 2x^(2)-8x-3y+11=0
The standard form of the parabola with the equation 2x² - 8x - 3y + 11 = 0 is y = 2/3x² - 8/3x + 11/3
Calculating the standard form of the parabola
Given that
2x² - 8x - 3y + 11 = 0
To put the given equation in standard form, we need to isolate the y term on one side of the equation.
Here's how to do it:
2x² - 8x - 3y + 11 = 0
Isolate 3y
This gives
3y = 2x² - 8x + 11
Divide through by 3
y = 2/3x² - 8/3x + 11/3
Hence, the standard form is y = 2/3x² - 8/3x + 11/3
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What is the meaning of logarithm in math?
In mathematics, a logarithm is a mathematical operation that determines how many times a given number (known as the base) must be multiplied by itself to produce another given number.
Logarithms are used to simplify complex calculations involving exponents and to convert between exponential and logarithmic expressions.
The logarithm of a number x to a given base b is represented as logb(x). For example, log10(100) = 2 because 10 multiplied by itself twice equals 100.
Logarithms have a wide range of applications in various fields, including mathematics, physics, engineering, finance, and computer science. They are particularly useful in scientific calculations involving large numbers, where working with exponents can become cumbersome. Logarithms are also used in the study of exponential growth and decay, as well as in the analysis of data sets with a wide range of values.
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I NEED HELP BADLY PLEASE HELP
Answer: 0.11
Step-by-step explanation:
5/45=0.11
Calculate the area of this trapezium.
6 cm
4 cm
5 cm
8 cm
Answer: 28cm²
Step-by-step explanation: To calculate the area of the trapezium, we can use the formula:
Area = (1/2) x (sum of parallel sides) x (height)
In this case, the two parallel sides are 6 cm and 8 cm, and the height is 4 cm.
Plugging in the values, we get:
Area = (1/2) x (6 cm + 8 cm) x 4 cm
Area = (1/2) x 14 cm x 4 cm
Area = 28 cm²
mathematics 3 and 4 grapgh mwehhh pleaseee
The answers of the question number 3 and 4 are given below respectively.
What is graph?A graph is a visual representation of data or mathematical relationships.
It typically involves plotting points on a coordinate plane and connecting them with lines or curves.
Graphs can help to illustrate patterns, trends, and relationships in data and make it easier to understand complex information.
3.Assuming that the sale of bracelets and necklaces are represented by the variables B and N respectively, the total sale would be represented by the mathematical statement:
Total sale = B + N
Graph of Total Sale = B + N
The x-axis represents the number of bracelets sold (B), and the y-axis represents the number of necklaces sold (N).
4.To represent Nimfa's goal of achieving a total sale of at least Php 15,000, we can use the inequality:
Total sale ≥ Php 15,000
or, using the expression from the previous question:
2B + N ≥ Php 15,000
Graph of Total Sale ≥ Php 15,000
The shaded area above the plane represents all the combinations of sales of bracelets and necklaces that result in a total sale of at least Php 15,000. Any point above the plane is a valid combination of sales that meet Nimfa's goal.
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3. The x-axis represents the number of bracelets sold (B), and the y-axis represents the number of necklaces sold (N).
4. The shaded area above the plane represents all the combinations of sales of bracelets and necklaces that result in a total sale of at least Php 15,000.
What is graph?A graph is a visual representation of data or mathematical relationships.
It typically involves plotting points on a coordinate plane and connecting them with lines or curves.
Graphs can help to illustrate patterns, trends, and relationships in data and make it easier to understand complex information.
3.Assuming that the sale of bracelets and necklaces are represented by the variables B and N respectively, the total sale would be represented by the mathematical statement:
Total sale = B + N
Graph of Total Sale = B + N
4.To represent Nimfa's goal of achieving a total sale of at least Php 15,000, we can use the inequality:
Total sale ≥ Php 15,000
or, using the expression from the previous question:
2B + N ≥ Php 15,000
Graph of Total Sale ≥ Php 15,000
The shaded area above the plane represents all the combinations of sales of bracelets and necklaces that result in a total sale of at least Php 15,000. Any point above the plane is a valid combination of sales that meet Nimfa's goal.
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ling makes bracelets and necklaces and salesman a different crafts fairs the table shows how much is string is used to make each item
bracelet 7 1/2
small necklace 15
large necklace 19 1/4
ling plans to make at least 20 bracelets
write and solve an inequality to determine the minimum length of string that she needs to buy.
What is the least number of inches of string ling will need
According to the given information Ling has enough string to produce at least 20 bracelets.
What is a number and what are its many types?Numbers serve the purpose of counting, measuring, organising, indexing, and other purposes. Natural numbers, whole numbers, rational and irrational numbers, integers, actual values, complex numbers, even and odd numbers, and so on are all distinct forms of numbers.
What exactly is a number?A number is really a numerical value that is used to express quantity. As a consequence, a number seems to be a mathematical idea that may be used to count, measure, and name objects. As little more than a result, numbers are the foundation of mathematics. Here is one butterfly, and here are four butterflies.
Each bracelet requires 7 1/2 inches of string. So, the total length of string required to make 20 bracelets is:
20 × 7 1/2 = 150 inches
Therefore, Ling needs to buy at least 150 inches of string.
We can write the inequality to represent this situation as:
length of string ≥ 150
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3gh2x4g3h3 help me please
Answer:
Step-by-step explanation:
To find the product
Its gonna be
12g^4h^5
This shape is made up of one half-circle attached to an equilateral triangle with side lengths 20 inches. You can use 3. 14 as an approximation for π
If the shape is made up of one half-circle attached to an equilateral triangle with side lengths 20 inches then, the perimeter of the shape is 91.4 inches.
To find the perimeter of the shape, we need to know the length of the curved boundary (the circumference of the half-circle) and the length of the straight boundary (the perimeter of the equilateral triangle).
The radius of the half-circle is half the length of the side of the equilateral triangle, which is 10 inches. Therefore, the circumference of the half-circle is:
C = πr = π(10) = 31.4 inches.
The perimeter of the equilateral triangle is 3 times the length of one side, which is 20 inches. Therefore, the perimeter of the triangle is:
P = 3s = 3(20) = 60 inches
Finally, the perimeter of the entire shape is the sum of the lengths of the curved and straight boundaries:
Perimeter = C + P = 31.4 + 60 = 91.4 inches.
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Complete Question
This shape is made up of one half-circle attached to a square with side lengths 11 inches. Find the perimeter of the shape.
You can use 3.14 as an approximation for π. help i don't know it.
Help me help me help me help me help me
Answer: cab
Step-by-step explanation:
you start with the last point and move up
1.3. The Dow Jones average (a stock market share index) dropped from 12 837 to 12 503 in one week in July 2012. 1.3.1. Calculate the drop in the share index. 1.3.2. If the price continued to drop at the same rate, calculate the Dow Jones average after 4 more weeks.
The Dow Jones average after 4 more weeks of the same rate of drop would be 11,167.
What is average?
Average, also known as mean, is a measure of central tendency that represents the typical or common value in a set of data. It is calculated by adding up all the values in a data set and then dividing the sum by the total number of values.
To calculate the drop in the Dow Jones average, we subtract the initial value from the final value:
Drop = Final Value - Initial Value
Drop = 12,503 - 12,837
Drop = -334
So the Dow Jones average dropped by 334 points in one week.
If the price continued to drop at the same rate for 4 more weeks, then the total drop after 5 weeks would be:
Total Drop = 5 x Drop
Total Drop = 5 x (-334)
Total Drop = -1670
To calculate the Dow Jones average after 4 more weeks, we need to subtract the total drop from the initial value:
New Dow Jones Average = Initial Value - Total Drop
New Dow Jones Average = 12,837 - 1,670
New Dow Jones Average = 11,167
Therefore, the Dow Jones average after 4 more weeks of the same rate of drop would be 11,167.
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simplest form please
hmmm what we do is firstly make the recurring part a variable, then we multiply it such that, the recurring digits move over from the decimal point to the left, so we'd multiply it by some power of 10, in this case power of 3, because we have three digits to move, 246, so let's do all that
[tex]0.\overline{246}\hspace{5em}x=0.\overline{246}\hspace{5em} \begin{array}{llll} 1000x&=&246.\overline{246}\\\\ &&246+0.\overline{246}\\\\ &&246+x \end{array} \\\\[-0.35em] ~\dotfill\\\\ 1000x=246+x\implies 999x=246\implies x=\cfrac{246}{999}\implies x=\cfrac{82}{333}[/tex]
The given family of functions is the general solution of the differential equation on the indicated interval. Find a member of the family that is a solution of the initial-value problem. y = c1ex + c2e−x, (−[infinity], [infinity]); y'' − y = 0, y(0) = 0, y'(0) = 5
The given family of functions is y = c1ex + c2e−x which is the general solution of the differential equation y'' − y = 0 on the indicated interval which is (−∞, ∞).
Now, we are required to find a member of the family that is a solution to the initial-value problem which is
y(0) = 0 and y′(0) = 5.
The differential equation is y'' − y = 0
The characteristic equation is r2 − 1 = 0r2 = 1r1 = 1 and r2 = −1
The general solution of the differential equation is y = c1ex + c2e−x
Let us solve for the constants by using the given initial conditions:
At x = 0,y(0) = c1e0 + c2e0 = 0 + 0 = 0y(0) = 0
means c1 + c2 = 0or c1 = -c2At x = 0, y′(0) = c1ex |x=0 + c2e−x |x=0(d/dx)(c1ex + c2e−x) |x=0y′(0) = c1 - c2 = 5c1 - c2 = 5c1 - (-c1) = 5c1 + c1 = 5c1 = 5/2c1 = 5/2
Let's replace c1 = 5/2 in c1 = -c2, c2 = -5/2
The solution of the initial-value problem y = (5/2)ex − (5/2)e−x is a member of the family y = c1ex + c2e−x that is a solution of the initial-value problem y(0) = 0 and y′(0) = 5.
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Problem 13.3 Use the power method to determine the lowest eigenvalue and corresponding eigenvector for the system from Prob. 13.2. Problem 13.2 Use the power method to determine the highest eigenvalue and corresponding eigenvector for |2-x 8 10|
|8 4-x 5 |
|10 5 7-x|
In problem 13.2, we can use the power method to determine the highest eigenvalue and corresponding eigenvector for the matrix:
|2-x 8 10|
| 8 4-x 5 |
|10 5 7-x|
We start by assuming a random initial vector, say v0, and then repeatedly multiplying it by the matrix A and normalizing the resulting vector, until the vector converges to the eigenvector corresponding to the highest eigenvalue.
For problem 13.3, we can use a similar approach to determine the lowest eigenvalue and corresponding eigenvector. However, instead of multiplying by A, we multiply by A^-1. This is because the lowest eigenvalue is the reciprocal of the highest eigenvalue, and the corresponding eigenvector remains the same.
Both problems require us to perform the power method until the resulting vector converges to the desired eigenvector. The number of iterations required for convergence depends on the matrix A and the initial vector v0.
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find the values of a and b such that
x^2- +5=(x-a)^2+b
The value οf a = 1/2 and b = 19/4 in the equatiοn x² - x + 5 = (x-a)² + b.
What dο yοu mean by algebra?The part οf mathematics in which letters and οther general symbοls are used tο represent numbers and quantities in fοrmulae and equatiοn is called algebra.
x² - x + 5 = (x-a)² + b
x² - x + 5 = x² + a² - 2xa + b
-x + 5 = -2xa + a² + b
By matching cοrrespοnding terms,
2a = 1 and a²+ b = 5
a= 1/2 and a²+ b = 5
Substituting value οf "a"
(1/2)² + b = 5
1/4 + b = 5
b = 5- 1/4
b = 19/4
Thus, a = 1/2 and b = 19/4.
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pleaseee im begging anyone for the steps of these questions i need them so urgently right now, i have the answer but not the steps pls anyone
Answer:
3. 79.9 mm²
4. 6.4 in
5. 177.5 mi²
6. 60.3°
Step-by-step explanation:
Given various quadrilaterals and their dimensions, you want to find missing dimensions.
Trig relationsIn all cases, one or more area formulas and trig relations are involved. The trig relations are summarized by the mnemonic SOH CAH TOA. The relevant relation for these problems is ...
Tan = Opposite/Adjacent
It is also useful to know that 1/tan(x) = tan(90°-x).
Area formulasThe formula for the area of a trapezoid is ...
A = 1/2(b1 +b2)h
The relevant formula here for the area of a parallelogram is ...
A = bs·sin(α) . . . . . where α is the angle between sides of length b and s
3. Parallelogram areaUsing the area formula above, we find the area to be ...
A = (21 mm)(9 mm)·sin(155°) ≈ 79.9 mm²
The area is about 79.9 square mm.
4. Trapezoid base 2The given figure shows two unknowns. We can write equations for these using the area formula and using a trig relation.
If we draw a vertical line through the vertex of the marked angle, the base of the triangle to the right of it is (b2-4). The acute angle at the top of that right triangle is (121°-90°) = 31°. The tangent relation tells us ...
tan(31°) = (b2 -4)/h ⇒ h = (b2 -4)/tan(31°)
Using the area formula we have ...
A = 1/2(b2 +4)h
and substituting for A and h, we get ...
20.8 = 1/2(b2 +4)(b2 -4)/tan(31°)
2·tan(31°)·20.8 = (b2 +4)(b2 -4) = (b2)² -16 . . . . . multiply by 2tan(31°)
(b2)² = 2·tan(31°)·20.8 +16 . . . . . . . add 16
b2 = √(2·tan(31°)·20.8 +16) ≈ 6.4 . . . . . . take the square root
Base 2 of the trapezoid is about 6.4 inches.
5. Trapezoid areaTo find the area, we need to know the height of the trapezoid. To find the height we can solve a triangle problem.
If we draw a diagonal line parallel to the right side through the left end of the top base, we divide the figure into a triangle on the left and a parallelogram on the right. The triangle has a base width of 10 mi, and base angles of 60° and 75°.
Drawing a vertical line through the top vertex of this triangle divides it into two right triangles of height h. The top angle is divided into two angles, one being 90°-60° = 30°, and the other being 90°-75° = 15°. The bases of these right triangles are now ...
h·tan(30°)h·tan(15°)and their sum is 10 mi.
The height h can now be found to be ...
h·tan(30°) +h·tan(15°) = 10
h = 10/(tan(30°) +tan(15°))
Back to our formula for the area of the trapezoid, we find it to be ...
A = 1/2(b1 +b2)h = 1/2(20 +10)(10/(tan(30°) +tan(15°)) ≈ 177.5
The area of the trapezoid is about 177.5 square miles.
6. Base angleThe final formula we used for problem 5 can be used for problem 6 by changing the dimensions appropriately.
A = 1/2(b1 +b2)(b1 -b2)/(tan(90-x) +tan(90-x))
112 = 1/2(20+12)(20-12)/(2·tan(90-x)) = (20² -12²)·tan(x)/4
tan(x) = 4·112/(20² -12²)
x = arctan(4·112/(20² -12²)) = arctan(7/4) ≈ 60.3°
Angle x° in the trapezoid is about 60.3°.
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Additional comment
There is no set "step by step" for solving problems like these. In general, you work from what you know toward what you don't know. You make use of area and trig relations as required to create equations you can solve for the missing values. There are generally a number of ways you can go at these.
A nice scientific calculator has been used in the attachment for showing the calculations. A graphing calculator can be useful for solving any system of equations you might write.
The second attachment shows a graphing calculator solution to problem 5, where we let y = area, and x = the portion of the bottom base that is to the left of the top base. Area/15 represents the height of the trapezoid. This solution also gives an area of 177.5 square miles.