Consider the following second order linear ODE y" - 5y + 6y = 0, where y' and y" are first and second order derivatives with respect to x. (a) Write this as a system of two first order ODEs and then write this system in matrix form. (b) Find the eigenvalues and eigenvectors of the system. (e) Write down the general solution to the second order ODE. (a) Using your result from part 3 (or otherwise) find the solution to the following equation. y' - 5y + y = 32
Answers
a. System in the matrix form is x' = Ax where A = \(\left[\begin{array}{ccc}0&1\\-5&6\end{array}\right]\) and x = [y, u].
b. The eigenvalues of the system are λ₁ = 5 and λ₂ = 1 and eigenvector are v₁ and v₂ = v₁, and v₁ is any non-zero value.
c. The general solution is equal to y(x) = c₁ × \(e^{(5x)\) × [v₁] + c₂× \(e^{(x)\)× [v₂].
a. Solution to the equation. y' - 5y + y = 32 is y(x) = c₁ × \(e^{(5x)\) + c₂ × \(e^{(x)\).
(a) To write the second order linear ODE as a system of two first order ODEs,
Introduce a new variable u = y'.
Then, we have,
u' = y'' - 5y + 6y
= -5y + 6u
Now, write this as a system of two first order ODEs,
y' = u
u' = -5y + 6u
To express this system in matrix form,
Define the vector x = [y, u] and the matrix A = \(\left[\begin{array}{ccc}0&1\\-5&6\end{array}\right]\)
The system can then be written as,
x' = Ax
(b) To find the eigenvalues and eigenvectors of matrix A, solve the characteristic equation,
|A - λI| = 0
where I is the identity matrix.
Substituting the values of A, we have,
\(|\left[\begin{array}{ccc}0&1\\-5&6\end{array}\right]\) \(-\lambda\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]|\) = 0
\(\left[\begin{array}{ccc}-\lambda&1\\-5&6-\lambda\end{array}\right]\) = 0
(-λ)(6-λ) - (-5)(1) = 0
λ²- 6λ + 5 = 0
Factoring the quadratic equation, we get,
(λ - 5)(λ - 1) = 0
So the eigenvalues are λ₁ = 5 and λ₂ = 1.
To find the corresponding eigenvectors,
solve the equation (A - λI)v = 0 for each eigenvalue.
Let us start with λ = 5
(A - 5I)v = 0
\(|\left[\begin{array}{ccc}1&1\\-5&6\end{array}\right]|\) v = 0
v₁ + v₂ = 0
-5v₁ + v₂ = 0
From the first equation, we get v₂ = -v₁.
Substituting this into the second equation, we have -5v₁ - v₁ = 0,
which simplifies to -6v₁ = 0.
This implies v₁ = 0, and consequently, v₂ = 0.
So, for λ = 5, the eigenvector is v₁ = 0 and v₂ = 0.
Now, let us find the eigenvector for λ = 1.
(A - I)v = 0
\(|\left[\begin{array}{ccc}-1&1\\-5&5\end{array}\right]\) v = 0
-v₁ + v₂ = 0
-5v₁ + 5v₂ = 0
From the first equation, we get v₂ = v₁.
Substituting this into the second equation, we have -5v₁ + 5v₁ = 0,
which simplifies to 0 = 0.
This implies that v₁ can be any non-zero value.
So, for λ = 1, the eigenvector is v₁ and v₂ = v₁, where v₁ is any non-zero value.
(e) The general solution to the second order ODE can be expressed using the eigenvalues and eigenvectors as follows,
y(x) = c₁ ×\(e^{(\lambda_{1} x)\) × v₁ + c₂ × \(e^{(\lambda_{2} x)\)× v₂
Plugging in the values we found earlier, the general solution becomes,
y(x) = c₁ × \(e^{(5x)\) × [v₁] + c₂× \(e^{(x)\)× [v₂]
where [v₁] and [v₂] are the eigenvectors corresponding to the eigenvalues λ₁ = 5 and λ₂ = 1 respectively.
(a) To find the solution to the equation y' - 5y + y = 32,
Use the general solution obtained above.
Comparing the equation with the standard form y' - 5y + 6y = 0,
The equation corresponds to the case where λ₂ = 1.
Substitute λ = 1, v₁ = 1, and v₂ = 1 into the general solution.
y(x) = c₁ × \(e^{(5x)\) × [1] + c₂ × \(e^{(x)\) × [1]
Simplifying this expression, we have,
y(x) = c₁ × \(e^{(5x)\) + c₂ × \(e^{(x)\)
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Related Questions
Which expression is equivalent to the expression below? startfraction 6 c squared 3 c over negative 4 c 2 endfraction divided by startfraction 2 c 1 over 4 c minus 2 endfraction startfraction 3 c (2 c minus 1) over 2 c 1 endfraction startfraction negative 3 c (2 c 1) squared over 4 (2 c minus 1) squared endfraction 3c –3c
Answers
The expression that is equivalent to the expression [(6c² + 3c)/(-4c + 2)] ÷ [(2c + 1)/(4c - 2)] is; -3c
What is a simplification of fractions?Simplification of fractions is the process of reducing fractions that involves making the fraction as simple as feasible.
We achieve this by dividing the numerator and denominator by the greatest integer that divides perfectly into both numbers.
The given expression is;
\(\frac{[(6c^2 + 3c)(-4c + 2)] }{[(2c + 1)/(4c - 2)]}\)
On Simplifying the fraction equation by factorization we obtained ;
\(\frac{[3c(2c + 1)/(-2(2c - 1))]}{[(2c + 1)/(2(2c - 1)]}\)
\(\frac{[3c(2c + 1) }{(-2(2c - 1))] \times [(2(2c - 1)/(2c + 1)]}\)
\(-3c\)
Hence he expression that is equivalent to the expression [(6c² + 3c)/(-4c + 2)] ÷ [(2c + 1)/(4c - 2)] is; -3c
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A person invests 6500 dollars in a bank. The bank pays 6. 75% interest compounded
semi-annually. To the nearest tenth of a year, how long must the person leave the
money in the bank until it reaches
15700 dollars?
A = P(1 + -]nt
n
Answers
In order to get $15700 the person has to leave the money in the bank for approximately 7.1 years.
Given: A person invests $6500 in a bank The bank pays 6.75% interest compounded semi-annually. The formula for compound interest is given by: A = P(1 + r/n)nt Where, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, t is the number of years, and A is the amount of money at the end of the investment period.
In this case, P = $6500, r = 6.75% = 0.0675, n = 2 (semi-annually compounded), A = $15700.Now, we need to find t. To do that, let's rearrange the formula as follows: t = ln(A/P) / n ln(1 + r/n)Putting the values, we get: t = ln(15700/6500) / 2 ln(1 + 0.0675/2)t ≈ 7.1 years (rounded to the nearest tenth of a year)Therefore, the person must leave the money in the bank for approximately 7.1 years until it reaches $15700.
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you have 20 bags of mulch. You plan to spread the mulch from all the bags to make a rectangular layer that is 3 inches thick.
Answers
the 20 bags of mulch will cover an area of 17,280 square inches when spread in a rectangular layer that is 3 inches thick.
To determine how much area the mulch will cover, you need to know the volume of mulch you have. Assuming each bag of mulch contains the same amount, you can find the total volume by multiplying the volume of one bag by the number of bags:
Total volume = volume of one bag x number of bags
To find the volume of one bag, you need to know the dimensions of the bag. Assuming the bag is roughly rectangular in shape, you can measure its length, width, and height, and then use the formula for the volume of a rectangular prism:
Volume of one bag = length x width x height
Let's say that the dimensions of one bag are 2 feet by 1.5 feet by 0.5 feet. Converting to inches, we get:Length = 2 x 12 = 24 inches
Width = 1.5 x 12 = 18 inches
Height = 0.5 x 12 = 6 inches
Volume of one bag = 24 x 18 x 6 = 2,592 cubic inches
If you have 20 bags of mulch, then the total volume is:
Total volume = 2,592 x 20 = 51,840 cubic inches
To find the area the mulch will cover, you need to know the area of the rectangle that will be covered by the mulch layer. Assuming the layer will be a uniform thickness of 3 inches, you can use the formula for the volume of a rectangular prism to find the area:
Volume = length x width x height
In this case, the height is the thickness of the layer, which is 3 inches. Solving for the area:
Area = Volume / Height
Area = (51,840 cubic inches) / (3 inches)
Area = 17,280 square inches
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Answer it pls :)
Which values of m and b will create a system of equations with no solution? Select two options.
y = mx + b
y = -2x + 3/2
Answers
Answer:
first one because the second one is solvable through graphing
Step-by-step explanation: y = mx +b could be anything
Use one of the triangles to approximate PQ in the triangle below
choices:
A) 4.5 units
B) 5.4 units
C) 9.1 units
D) 10.9 units
Answers
The approximate value of PQ in the right angle triangle is 5.4 units.
What is the Right angle triangle?A right-angle triangle has one of its angles at 90 degrees. Therefore, the sides can be found by trigonometric ratios.
Hence,
sin 50 = opposite / hypotenuse
sin 50 = PQ / 7
cross multiply
PQ = 7 sin 50°
PQ = 7 × 0.76604444311
PQ = 5.36231110183
PQ = 5.4 units
hence, the approximate value of PQ in the right angle triangle is 5.4 units.
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Mrs Mabaspacked , prudence's mom packed a cooler box bag for the day of the painting . Two six pack cans fit exactly on top of each other in the cooler bag. A can has a diameter of 6 cm and a height of 8,84 cm 0:41 EZ07/67/90 dy the information given in the information above and answer the questions that follow. 2.1 2.2 2.3 2.4 Calculate the volume in ml of one can of cold drink, rounded to the nearest whole number. Determine the height of the cooler bag, rounded to the nearest whole number. Determine the volume in ml of the cooler bag if the breadth of the bag is 12 cm and the length 18 cm. Each can have a label on them as shown by the image below Piesse Circumference of the can NEW Diet, Soda 0 Calories! Calculate the length of the lable. CALORIES PER SERVING Nutrition Fac Hight of the can (3) (2) (3) (2) 27 [10]
Answers
2.1 The volume in ml of one can of cold drink is 83 ml.
2.2 The height of the cooler bag is 18 cm.
2.3 The volume in ml of the cooler bag if the breadth of the bag is 12 cm and the length 18 cm is 3,888 ml.
2.4 The circumference of the can is 18.84 cm.
How to calculate the volume of a cylindrical can?In Mathematics and Geometry, the volume of a cylinder can be calculated by using this formula:
Volume of a cylinder, V = πr²h
Where:
V represents the volume of a cylinder.h represents the height or length of a cylinder.r represents the radius of a cylinder.By substituting the given side lengths into the volume of a cylinder formula, we have the following;
Volume of can = 3.14 × (6/2)² × 8.84
Volume of can = 83.27 cm³.
Note: 1 cm³ = 1 ml
Volume of can in ml = 83.27 ≈ 83 ml.
Part 2.2.
For the height of the cooler bag, we have:
Height of cooler bag = 2 × height of can
Height of cooler bag = 2 × 8.84
Height of cooler bag = 17.68 ≈ 18 cm.
Part 2.3
Volume of cooler bag = length × breadth × height
Volume of cooler bag = 18 × 12 × 18
Volume of cooler bag = 3,888 ml.
Part 2.4
The circumference of the can is given by:
Circumference of circle = 2πr
Circumference of can = 2 × 3.14 × 3
Circumference of can = 18.84 cm.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
if [2+3] [1+x]=25 what is x?
Answers
\(\boxed{\underline{\bf \: ANSWER}}\)
\((2 + 3)(1 + x) = 25 \\ 5(1 + x) = 25 \\ 1 + x = 25 \div 5 \\ 1 + x = 5 \\ x = 5 - 1 \\ \boxed{x = 4}\)
Note :-
Image is attached.
Hope it helps!
꧁✿ ᴿᴬᴵᴺᴮᴼᵂˢᴬᴸᵀ2222 ✬꧂
![if [2+3] [1+x]=25 what is x?](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/oJbrK1u2kVyb6OPQgOW1bAXGU4SwIWLz.jpeg)
Answer:
4
Step-by-step explanation:
2+3=5
5*(1+4)
1+4=5
5*5=25
(ii) Show that the equation x(x−2)2=3 can be expressed as x3−4x2+4x−3=0 The polynomial p(x) is given by p(x)=x3−4x2+4x−3. (i) Find the remainder when p(x) is divided by x+1. (ii) Use the Factor Theorem to show that x−3 is a factor of p(x). (iii) Express p(x) in the form (x−3)(x2+bx+c), where b and c are integers. c) Hence show that the equation x(x−2)2=3 has only one real root and state the value of this root.
Answers
(i) The remainder is -12.
(ii) Concluded that x - 3 is a factor of p(x).
(iii) It can be express p(x) as (x - 3)(x² - x + 1).
c) The equation x(x - 2)² = 3 has only one real root, which is x = 3.
(i) To find the remainder when p(x) = x³ - 4x² + 4x - 3 is divided by x + 1, we can use synthetic division, which is shown in the attached image.
Here, the remainder is -12.
(ii) According to the Factor Theorem, if (x - a) is a factor of a polynomial p(x), then p(a) = 0.
Substitute x = 3 into p(x) to verify if x - 3 is a factor:
p(3) = 3³ - 4(3)² + 4(3) - 3
= 27 - 36 + 12 - 3
= 0
Since p(3) = 0, we can conclude that x - 3 is a factor of p(x).
(iii) Using the factor we found in part (ii), we can divide p(x) by (x - 3) using long division or synthetic division:
We obtain a quotient of x² - x + 1 and no remainder.
Therefore, we can express p(x) as (x - 3)(x² - x + 1).
(c) Now let's consider the original equation x(x - 2)² = 3.
We know that x = 3 is a root of p(x) = x³ - 4x² + 4x - 3, which means it satisfies the equation p(x) = 0.
Hence, x = 3 is a solution to the equation x(x - 2)² = 3.
Since (x - 3) is a factor of p(x) and the quadratic factor (x² - x + 1) does not have any real roots, the equation x(x - 2)² = 3 has only one real root, which is x = 3.
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what is the difference (7² + 8² + 9²) - (6² + 5² + 4²)
Answers
Answer:
199
Step-by-step explanation:
49 + 64 + 81 - 36 +25+16
194 - 36 +25 + 16
-36 + 25 + 16
= -11 + 16 = 5
194 + 5 = 199
Solve -3y(y-8)(2y+1)=0
Answers
Answer: I think it's 0
please help me answer it
Answers
Answer:
Yes, I think. I could be wrong but hopefully not!
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
it follows a pattern so it is a function. I am pretty sure about this because I learned about functions and non functions a few classes ago.
The equation of the line is ___
Answers
Answer:
Since the slope is -2 and y-int. is 3 the slope-intercept form is y = -2x + 3 which in standard form is 2x + y = 3.
Answer:
y = -2x + 3
Step-by-step explanation:
→ We know the slope so we can automatically plug that into the y = mx + c formula so,
y = -2x + c
→ Now we substitute in the coordinates (0,3) to find the c value and therefore complete the equation
y = -2x + c
3 = ( -2 × 0 ) + c ⇔ 3 = 0 + c ⇔ c = 3
y = -2x + 3
Hannah is instructed to write down a positive, 4-digit integer. What is the probability that Hannah's number is an even number that is also a palindrome (a number that reads the same forward and backward)
Answers
The probability that Hannah's number is an even palindrome is 1/45.
What is the chance of Hannah writing a 4-digit even palindrome number?There are 45 even palindrome numbers between 1000 and 9999, out of a total of 4500 possible 4-digit numbers.
So, the probability of Hannah writing an even palindrome number is 1/45.
A palindrome number is the same when read from left to right or right to left. There are 90 possible 2-digit palindrome numbers (11, 22, 33, etc.), and 9 possible 1-digit palindrome numbers (1, 2, 3, etc.), making a total of 99 palindrome numbers from 1 to 999. In a 4-digit number, the first and last digits must be the same for it to be a palindrome.
Therefore, the first digit has 9 choices (1-9), and the last digit also has 9 choices. The second digit can be any of the 10 digits (0-9), and the third digit can be any of the 5 remaining even digits (0, 2, 4, 6, 8).
Thus, there are 45 even palindrome numbers between 1000 and 9999.
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If f(x) = {x and g(x)=x? - 8, simplify the expressions (fog)(4), (f of)(8), (gof)(x), and (fog)(x). (fog)(4)=0 (f of)(8)= (gof)(x)= (fog)(x) = 0
Answers
For given functions, f(g(4)) = 2, f(f(8)) = ∛2 and f(g(x)) = ∛ ( x² - 8 ).
Describe a function.A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range and a co-domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).
In math, various function types exist. Among the crucial kinds are:
When there is a mapping for a range for each domain between two sets, this is known as an injective function or one to one function.
When more than one element is mapped from domain to range, the function is said to be surjective or to be an onto function.
a polynomial function is a function made by of polynomials
Now,
For functions f(x) = ∛ x and g(x) = x²-8
f(g(x)) = ∛ (x²-8)
f(f(x)) = ∛ ∛ x
g(f(x)) = ( ∛ x ) ² - 8
Therefore,
f(g(4))=∛4²-8= ∛16 - 8
= ∛8 = 2
f(f(8)) = ∛ ∛ 8 = ∛2
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Right function are
f(x)=∛x and g(x)=x^2-8
Please please please IM BEGGING
Answers
Answer:
1. D.)28.26 m^2
2.) A.)377 mm
4.) 615.75 square inches^3
Step-by-step explanation:
1.) Formula: π(r)^2
(3)^2=9
9π=28.27
2.) Formula for circumference: 2πr
D=120
Half the diameter is the radius: 60
60(2)=120
120(π)= 376.99
376.99 is close to 377
4.) Formula: (r)^2(pi)
D=28
R=14
14^2=196
196(pi)
615.75 square inches^3
Keep in mind, I used the symbol pi and not 3.14 so it's mostly accurate and a bit slightly off.
Hope this helps! :)
Can you put this into intercept form
Answers
Answer:
whats the equation
Step-by-step explanation:
work out the area of a rectangle with base, b = 20mm and perimeter, p = 50mm.
Answers
Answer:
100
Step-by-step explanation:
If the base is 20, then 2 of the sides must have a length of 20. This means that the TOTAL length of the remaining sides is 10. (20*2) + (10) = 50. If we divide that in half, we get 5. That is the side length of the remaining 2 sides. This means that 20 * 5 will give us the area (b*h).
Given,
base, b = 20mm &
perimeter, p = 50mm.
the area of the rectangle : (50 – 20 × 2) ÷ 2 = 5. 5 × 20 = 100 \(mm^{2}\).
Perimeter and area are two important and basic mathematical subjects. They help quantify the physical space and also provide a more advanced foundation of mathematics in algebra, trigonometry, and calculus. Perimeter is a measure of the distance around a shape, and area indicates how much area the shape covers.
The perimeter of a 2D shape is the distance around the shape. You can imagine wrapping a string around a triangle. The length of this cord is around the triangle. Or, if you're traveling outside the park, take a route that goes around the edge of the park.
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Last week you worked 24 hours, and earned $216
What is your hourly pay rate?
$ (per hour)
Give your answer in dollars and cents
Answers
216 divided by 24 = 9
Your hourly pay rate is $9.00
I hope this helps good luck :)
Answer:
9$
Step-by-step explanation:
hours worked in a week = 24
money earned = $216
hourly earning = 216/24
= 9
Please solve quickly! Qestion: c - 1.5 = 7
Answers
Answer:
8.5
Step-by-step explanation:
c = 8.5
hope this helps
Answer:8.5
Step-by-step explanation:
Add 7 and 1.5
what value of aa would indicate no association between gender and voting pattern for the people in the sample?
Answers
The value of ' a 'indicating no association between gender and voting pattern for the people in the sample is 500.
What is sample?A sample is a result of a random experiment. We sample a random variable when we select a specific value from among its possible possibilities. A exact value is that of a sample. The potential values and likelihood of each are determined by the random variable's probability distribution. They should be picked at random from a broader group or population in order to assist you understand more about the population as a whole. Samples are employed in statistical testing when population sizes are too big for all prospective participants or observations to be included in the test.
Here,
Considering Split ticket,
a + b = 600 ---(1)
Considering No Split ticket,
c + d = 400 ---(2)
Considering Men,
a + c = 800 ---(3)
Considering Women,
b + d = 200 ---(4)
Applying (1) - (4),
a + b - b - d= 600 - 200
a - d = 400 ---- (5)
Applying (2) - (4),
c + d - b - d = 400- 200
c - b = 200 ----(6)
a - c = 200 --- (7)
Applying (3) + (7)
2a = 1000
a = 500
For those in the sample, the value of "a" showing there is no correlation between gender and voting behavior is 500.
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Rosie needs to solve the systems of equations below. She is deciding
between the substitution and elimination method. Which method would
be best to solve with?
Answers
Answer:
Elimination method
Step-by-step explanation:
Both x values have a coefficient with the exact value of three. This would make it easy to eliminate to solve for y.
How would you find the slope and the y-intercept for the equation y=2.50x+2.50?
Answers
Answer:
Slope = m = 2.50
Y-intercept = b = 2.50
Step-by-step explanation:
Given equation is:
\(y=2.50x+2.50\)
Comparing it with slope-intercept form of equation \(y = mx+b\), where m is slope and b is y-intercept, we get:
Slope = m = 2.50
Y-intercept = b = 2.50
\(\rule[225]{225}{2}\)
Hope this helped!
~AH1807The diameter of a cylindrical construction pipe is 6 ft, and the length is 29 ft.a) Find the exact volume of the pipe. Write you answer in terms of π.b) Using a calculator, approximate the volume of the pipe.To do the approximation, use your answer to part (a) and the π button on the calculator. Round your answer to the nearest 100th.
Answers
We get that the radius is 3 ft and the length is 29 ft so the volume is
\(V=\pi\cdot3^2\cdot29=261\pi^{}\)the approximate value is:
\(819.96ft^3\)Now answer the following questions with respect to your perceived diversity.What are your feelings about being different?Which elements of diversity are you proud of? Why?____________________________________________________________________________________________________________________________________________________________What element would you like to change to be less diverse? Why?How do your differences contribute to a student team or work organization?
Answers
I don't have personal feelings, emotions, or diversity elements. However, I can provide you with a general explanation of how diversity can impact an individual and their role in a team or organization.
1. Feelings about being different: People's feelings about being different can vary. Some may feel proud and empowered by their unique experiences, while others may feel isolated or misunderstood. Embracing and celebrating one's differences can lead to increased self-esteem and personal growth.
2. Elements of diversity to be proud of: Individuals might be proud of their cultural background, language, traditions, or unique talents and skills. These elements can bring a wealth of knowledge and experience to a team or organization, fostering creativity and innovation.
3. Changing an element to be less diverse: While diversity is generally beneficial, an individual might wish to change an element to be less diverse in order to fit in or avoid discrimination. It's important to recognize that everyone's experiences and perspectives are valuable, and true progress comes from embracing diversity rather than trying to suppress it.
4. How differences contribute to a team or organization: Diverse perspectives and experiences can lead to better problem-solving, innovation, and understanding of different customer needs. Diversity also fosters a more inclusive and welcoming environment, attracting a wider range of talent and promoting employee satisfaction and retention.
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Help Please?
Florence buys a model railroad set priced at $57. Shipping and handling are an additional 30% of the price. How much shipping and handling will Florence pay? $
Answers
Answer:
\(74.1\)$
Step-by-step explanation:
\( \frac{x}{57} = \frac{30}{100} \)
\((x)100 = (30)57\)
\((x)100 = 1710\)
\( \frac{(x)100}{100} = \frac{1710}{100} \)
\(x = \frac{1710}{100} \)
\(x = 17.1\)
\(57 + 17.1 = 74.1\)
\(74.1\)$
I need help. Find the surface area.
Answers
Answer:
253.5π
Step-by-step explanation:
Surface area of cylinder: 2πrh+2πr^2
Height: 13, Radius: 6.5
A = 2π6.5(13)+2π6.5^2
A = 169π + 84.5π
A = 253.5π
Answer ASAP, will give brainliest
Answers
Answer:
Step-by-step explanation:
1) Diagonal bisect the angles of Rhombus
∠CAB = ∠CAD
∠CAB = 71
2) ∠DAB = ∠CAB + ∠CAD
∠DAB = 71 + 71 = 142
In Rhombus, adjacent angles are supplementary
∠DAB + ∠ABC = 180
142 + ∠ABC = 180
∠ABC = 180 - 142
∠ABC = 38
3) In rhombus, opposite angles are congruent
∠ADC = ∠ABC
∠ABC = 38
In rhombus, diagonal bisect angles
∠BDC = (1/2)*∠ADC
∠BDC= 38/2
∠BDC = 19
4) Diagonals bisect each other at 90
∠DEC = 90
5) Diagonals bisect each other
BE = DE
BE + DE = DB
7x -2 +7x -2 =24 {add like terms}
14x - 4 =24
14x = 24+4
14x = 28
x = 28/14
x = 2 m
6) AB = 13m
BE = 7x - 2 = 7*2 -2 = 14 -2 = 12 m
In right angle ΔAEB, {use Pythagorean theorem}
AE² + BE² = AB²
AE² + 12² = 13²
AE² + 144 = 169
AE² = 169 - 144
AE² = 25
AE = √25
AE = 5 m
Diagonals bisect each other
AE = EC
AC = 2*5
AC = 10 m
7)Side = 13 m
Perimeter = 4*side
= 4*13
Perimeter = 52 m
8) d1 = AC = 10 m
d2 = DB = 24 m
Area = \(\frac{d_{1}*d_{2}}{2}\)
\(=\frac{10*24}{2}\\\)
= 10 *12
= 120 m²
Given the following declarations, what is stored in ans as a result of the arithmetic expression?
int ans = 0, v1 = 5, v2 = 8;
ans = v2 % v1++;
1.3333
1.6
2
3
Answers
Given the following declarations, the value of the arithmetic expression is 7.
int ans;int a = 3, b = 4;ans = a + b / 2;In the arithmetic expression ans = a + b / 2, the division will be carried out first and the result will be 2. Then, the addition will be performed with the value of a, which is 3. Thus, the value of ans will be 7. In other words, ans will store the value 7.
Arithmetic terms are combined by arithmetic procedures to form arithmetic expressions.
Arithmetic terms like x, x2, xy, or 3xy2 are coupled with arithmetic operations like addition, subtraction, multiplication, and division to form an equation.
Mathematical connections, like equality and inequality, can contain arithmetic expressions. Expressions in mathematics can be either linear (like x z + 3y) or nonlinear (like x z2 + y*z + 3y). Over integer decision variables, the CP Optimizer provides arithmetic constraints. Integer or numerical (floating-point) expressions are also supported.
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Express 9 hours as a percentage of 3 days
Answers
total hours in 3 days= 72
total %= 9/72*100
= 100/8
= 12.5% ans.... HOPE IT HELPS
Answer:
total hours in 3 days= 72
total %= 9/72*100
= 100/8
= 12.5% ans.... HOPE IT HELPS =D
HURRY!
What system of linear inequalities is shown in the graph?
Enter your answers in the boxes
Answers
1/2x -1 (less than or equal to) y
See photo
