Answer:
5
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
\(distance = \sqrt{(x2-x1)^2+(y2-y1)^2}\)
\(\sqrt{(4-4)^2+(2-(-3))^2}\)
Simplify.
\(\sqrt{0^2+5^2} = \sqrt{25}\)
\(\sqrt{25} = \sqrt{5^2}\)
Pull terms out from under the radical, assuming positive real numbers.
5
good luck, hope this helps :)
identify the center and radius of the circle with equation.
( please help me )
Answer:
Center = (4, -5)
radius = 6
======================================================
Explanation:
The general template of any circle is
(x-h)^2 + (y-k)^2 = r^2
Rewrite the given equation into this form
(x-4)^2 + (y- (-5))^2 = 6^2
We can see that (h,k) = (4,-5) is the center and r = 6 is the radius.
What are the solutions to the equation x minus StartFraction 7 Over x EndFraction = 6
The solutions to the equation x minus StartFraction 7 Over x EndFraction is equal to 6 is -1 and 7
What is a quadratic equation ?Any equation of the form \(\rm ax^2+bx+c=0\) Where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
We have equation:
\(\rm x-\dfrac{7}{x}=6\)
After simplifying:
\(\rm x^2 -7 = 6x\\\\x^2-6x-7=0\)
\(\rm x^2 +x-7x-7=0\)
(x + 1)(x - 7) = 0
x = -1 or x = 7
Thus, the solutions to the equation x minus StartFraction 7 Over x EndFraction is equal to 6 is -1 and 7
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Answer:
C) x= -1 and x=7
Step-by-step explanation:
Sam divided 3384 by 24. His work is shown.
Make equations to show how he got the 240 and the 960. Move numbers and symbols to the lines to make the equations.
240 =
141
24)3384
-240
984
-960
24
960 =
х
+
24
141
3384
10
20
30
40
50
60
70
80
90
200
300
400
100
500
700
600
800
900
1000
3161617
Step-by-step explanation:
Answer:
240= 24x10
960= 96x10
Step-by-step explanation:
doesnt really need an explanation but
96x10=960
24x10=240
good luck on map or any question this is for <3!
Consider the function given below: (defun things (x) (if (null x ) '() (if (>(carx) 10) (cons(+(carx) 1) (things (cdrx))) (cons (- (car x) 1) (things (codr x)) ) 1 ) 1 Show the evolution resulting from the following call: USP> (things '(11-2 31))
The evolution of the function call (things '(11 -2 31)) is as follows:
(things '(11 -2 31)) -> (things '(-2 31)) -> (things '(31)) -> (things '()) -> '() the final result of the given call is '().
The given function is a recursive function called "things" that takes a list as input. It checks if the list is empty (null), and if so, it returns an empty list. Otherwise, it checks if the first element of the list (car x) is greater than 10. If it is, it adds 1 to the first element and recursively calls the "things" function on the rest of the list (cdr x). If the first element is not greater than 10, it subtracts 1 from the first element and recursively calls the "things" function on the rest of the list. The function then returns the result.
Now, let's see the evolution resulting from the call (things '(11 -2 31)):
1. (things '(11 -2 31))
Since the list is not empty, we move to the next if statement.
The first element (car x) is 11, which is greater than 10, so we add 1 to it and recursively call the "things" function on the rest of the list.
The recursive call is (things '(-2 31)).
2. (things '(-2 31))
Again, the list is not empty.
The first element (car x) is -2, which is not greater than 10, so we subtract 1 from it and recursively call the "things" function on the rest of the list.
The recursive call is (things '(31)).
3. (things '(31))
The list is still not empty.
The first element (car x) is 31, which is greater than 10, so we add 1 to it and recursively call the "things" function on the rest of the list.
The recursive call is (things '()).
4. (things '())
The list is now empty, so the function returns an empty list.
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How many different three-digit numbers can be written using digits from the set 2, 3, 4, 5, 6 without any repeating digits?
The three-digit numbers can be written using digits from the set 2, 3, 4, 5, 6 without any repeating digits = 60
What is permutation and combination ?Combination and permutation are two alternative strategies to divide up a collection of elements into subsets in mathematics. The components of the subset may be arranged in any order when combined. The subset's components are listed in a permutation in a certain order.
According to the given information:The given set is: {2,3,4,5,6}.
We have to form different three-digit numbers using these 5 digits.
r = 3
It implies that we must choose and arrange 3 of the 5 numerals.
We employ the permutation since the arrangement here is important.
\(5 P_{3}=\frac{5 !}{(5-3) !}\)
= 5!/2!
= 60
The three-digit numbers can be written using digits from the set 2, 3, 4, 5, 6 without any repeating digits = 60
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prove that for each natural number n > 43, we can write n = 6xn 9yn 20zn 15. strong induction 117 for some nonnegative integers xn, yn, zn. then prove that 43 cannot be written in this form
For each natural number n > 43, we can express it as n = 6xn + 9yn + 20zn + 15, where xn, yn, and zn are nonnegative integers. Additionally, we have shown that 43 cannot be written in this form.
To prove that for each natural number n > 43, we can write n = 6xn + 9yn + 20zn + 15, where xn, yn, and zn are nonnegative integers, we will use strong induction. The base case will be n = 44, and we will assume that the statement holds for all natural numbers up to k, where k > 43. Then we will prove that it holds for k+1.
Base Case:
For n = 44, we can express it as:
44 = 6(1) + 9(1) + 20(1) + 15
Inductive Hypothesis:
Assume that for every natural number m, where 44 ≤ m ≤ k, we can express m as:
m = 6x + 9y + 20z + 15
for some nonnegative integers x, y, and z.
Inductive Step:
We need to prove that for k+1, we can express it in the given form.
For k+1, there are three cases to consider:
Case 1: k+1 is divisible by 6
In this case, we can express k+1 as:
(k+1) = 6x' + 9y' + 20z' + 15
where x' = x + 1, y' = y, and z' = z. Since k+1 is divisible by 6, we can add one more 6 to the expression.
Case 2: k+1 is divisible by 9
In this case, we can express k+1 as:
(k+1) = 6x' + 9y' + 20z' + 15
where x' = x, y' = y + 1, and z' = z. Since k+1 is divisible by 9, we can add one more 9 to the expression.
Case 3: k+1 is not divisible by 6 or 9
In this case, we can express k+1 as:
(k+1) = 6x' + 9y' + 20z' + 15
where x' = x + 2, y' = y + 1, and z' = z - 1. By adding 26, 19, and subtracting 1*20, we can obtain k+1.
Thus, we have shown that for each natural number n > 43, we can write n = 6xn + 9yn + 20zn + 15, where xn, yn, and zn are nonnegative integers.
Now, let's prove that 43 cannot be written in this form. If we assume that 43 can be expressed as:
43 = 6x + 9y + 20z + 15
Simplifying the equation:
28 = 6x + 9y + 20z
Considering the equation modulo 3, we have:
1 ≡ 0 (mod 3)
This is a contradiction since 1 is not congruent to 0 modulo 3. Therefore, 43 cannot be written in the given form.
In conclusion, we have proven by strong induction that for each natural number n > 43, we can express it as n = 6xn + 9yn + 20zn + 15, where xn, yn, and zn are nonnegative integers. Additionally, we have shown that 43 cannot be written in this form.
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Sum-R-Fun sells a jet ski for $6,700 which includes tax. They offer an installment plan that requires 20% down. After that, the customer would pay
$200 per month for three years. What is the down payment? What is the total of all monthly payments? What is the total cost of the jet ski on the installment plan? What is the finance charge?
Answer:
1) The initial down payment is $1,340
2) The total monthly payment is $7,200
3) The total cost of the jet ski on the installment plan is $8,540
4) The finance charge is $1,840
Step-by-step explanation:
The financing model of Sum-R-Fun for a jet ski are as follows;
Sum-R-Fun selling price of a jet ski = $6,700
The initial down payment = 20% of the selling price of the jet ski
The amount the customer pays per month = $200
The duration or the period of the monthly payment = 3 years
1) The initial down payment = 20/100 × $6,700 = $1,340
2) The total monthly payment = Number of months per year × Number of years × The monthly (installment) payment
∴ The total monthly payment = 12 × 3 × $200 = $7,200
3) The total cost of the jet ski on the installment plan = The initial down payment + The total monthly payment
∴ The total cost of the jet ski on the installment plan = $1,340 + $7,200 = $8,540
4) The finance charge is the cost of the credit given as follows;
The finance charge = The total cost of the jet ski on the installment plan - Sum-R-Fun selling price of a jet ski
∴ The finance charge = $8,540 - $6,700 = $1,840
how to find the perimeter of a triangle with vertices
Answer:
P = A + B + C
Step-by-step explanation:
Essentially, just add the length of each side. The sum is the perimeter.
Hit brainliest if this was helpful :)
add each side
hope ithelps you
help please. i need this
\(\Large\boxed{\tt Answer:~Isosceles~Triangle;~x=25}\)
\(\tt Step-by-step~explanation:\)
Since this triangle has two congruent angles/sides, we know that it is an isosceles. We can tell by looking at the markings on the triangles: The curves on both angles A and C indicate that they are congruent, and the markings on lines AB and CB also tell us that they are congruent.
To solve for x, we set up our equation like this:
\(\tt 4x-20=2x+30\)
Since we know that lines AB and CB are congruent, that means 4x - 20 is equal to 2x + 30.
To solve, we can first subtract 2x from both sides and add 20 to both sides.
\(\tt 4x-(2x) -20=2x-(2x)+30\\2x-20+(20)=30+(20)\\2x=50\)
Then, we divide both sides by 2 to isolate x.
\(\tt \frac{2x}{2} \frac{50}{2} \\x=25\)
We can check if our answer is correct by plugging in our value for x into both expressions and see if they equal the same thing.
\(\tt 4(25)-20=80\\2(25)+30=80\\Correct\)
100 points Oh my god please help
i haven't gotton an answer if forever
i will give brainliest
Based on the given system of linear equations:
(1, 5) is the solution (-2, 0) is not the solution (3, 4)(4, 1)1. System of linear equations:
-5m + 6n = 25 | x 7 | -35m + 42n = 175
-7m + 8n = 33 | x 5 | -35m + 40n = 165 -
-2n = -10
n = 5
We subtitute the value of n into one of the linear equation:
-5m + 6(5) = 25
-5m + 30 = 25
- 5m = -5
m = 1
It was proven that (1, 5) is the solution for system linear equation of -5m + 6n = 25 and -7m + 8n = 33
2. The system of linear equations:
8x - 3y = -16 | x 2| 16x - 6y = -32
-9x - 2y = 50 | x 3| -27x - 6y = 150 -
43x = -182
x = -4.23
We input the value of x into one of the linear equation:
8(-4.23) - 3y = -16
-3y = -49.84
y = 16.6
It was proven that (-2, 0) is not the solution for system linear equations of 8x - 3y = -16 and 50 = -9x - 2y
To find the solution for each given graph, we need to find the intersection point on each graph:
Graph 1: (3,4)
Graph 2: (4,1)
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if 5 apples cost 0.60 then how much does 6 apples cost
Answer:
$0.72 for 6 apples
Step-by-step explanation:
0.60 / 5 = 0.12
0.12 * 6 = 0.72You would like to compare mathematics knowledge among 15-year-olds in the US and Japan. To do this, you plan to give a mathematics achievement test to samples of 1000 15-year-olds in each of the two countries. To ensure that the samples will include individuals from all different socioeconomic groups and educational backgrounds, you will randomly select 200 students from low-income families, 400 students from middle-income families, and 400 students from high-income families in each country. This is an example of a
This is an example of a comparative study that uses random sampling to ensure representation from different socioeconomic groups and educational backgrounds in the samples. The study aims to compare mathematics knowledge among 15-year-olds in the US and Japan by administering a mathematics achievement test to 1000 students from each country.
Hi! I'd be happy to help with your question. You would like to compare mathematics knowledge among 15-year-olds in the US and Japan by giving a mathematics achievement test to samples of 1000 15-year-olds in each of the two countries, with 200 students from low-income families, 400 students from middle-income families, and 400 students from high-income families in each country. This is an example of a stratified random sampling method.
In this case, the population is divided into different strata based on socioeconomic groups (low-income, middle-income, and high-income families), and then random samples are drawn from each stratum. This ensures that the samples include individuals from all different socioeconomic groups and educational backgrounds, which allows for a more accurate comparison between the two countries.
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PLEASE HELP WILL MARK BRANLIEST!!
Answer:
Letting x be an element of the universal set, this set will be {x | -1 < x < 4}.
Simplify: 3(a+b)-2(2a-b)+4a-7a
Answer:
Hey there!
3(a+b)-2(2a-b)+4a-7a
3a+3b-4a+2b-3a
3b-4a+2b
5b-4a
-4a+5b
Let me know if this helps :)
Answer
\( \boxed{ \boxed{ \bold{ \red{ - 4a + 5b}}}}\)
Step by step explanation
\( \sf3(a + b) - 2(2a - b) + 4a - 7a\)
Distribute 3 through the parentheses
⇒\( \sf3a + 3b - 2(2a - b) + 4a - 7a\)
Distribute 2 through the parentheses
⇒\( \sf3a + 3b - 4a + 2b + 4a - 7a\)
Collect like terms
⇒\( \sf3a +4a - 4a - 7a + 3b + 2b\)
Since , two opposites add up to zero, remove them from the expression
⇒\( \sf3a - 7a + 3b + 2b\)
⇒\( \sf - 4a + 5b\)
Hope I helped!
Best regards!!
What is the completely factored form of this polynomial? 7x4 14x3 − 168x2
The completely factored form of the polynomial is 7x² (x + 6) (x - 4)
Given,
The polynomial ; 7x⁴ + 14x³ - 168x²
We have to find the complete factored form of this polynomial;
Polynomial;
An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
Here,
The polynomial is 7x⁴ + 14x³ - 168x²
Now,
Factorize the polynomial using common factors;
That is,
7x⁴ + 14x³ - 168x²
7x² (x² + 2x - 24)
Solve x² + 2x - 24 using quadratic formula;
That is,
\(\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}\) = \(\frac{-2(+-)\sqrt{2^{2} -4*1*-24} }{2*1}\) = \(\frac{-2(+-)\sqrt{4-96} }{2}\) = -2±√-92 / 2
Now,
Solve
-2 + √-92 / 2 = 3.79 ≈ 4
Solve
-2 - √-92 / 2 = -5.79 ≈ -6
Then,
The factors will be (x - 4) and (x + 6)
So,
7x² (x + 6) (x - 4) will be the factored form of the polynomial.
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will give brainliest
Answer:
£29.37
Step-by-step explanation:
Type in the question- like type it. Not a screenshot, type in part of the question into the Brainly search bar and you'll find it.
In which quadrant must the terminal side of θ lie if sin θ and cot θ are to have the different sign?
The terminal side of angle θ must lie in either the first or third quadrant for sin θ and cot θ to have different signs.
1. Recall that sin θ represents the ratio of the length of the opposite side to the length of the hypotenuse in a right triangle, while cot θ represents the ratio of the length of the adjacent side to the length of the opposite side.
2. The sign of sin θ depends on the y-coordinate of the point on the unit circle corresponding to angle θ. If the y-coordinate is positive, sin θ is positive; if it's negative, sin θ is negative. Therefore, sin θ is positive in the first and second quadrants and negative in the third and fourth quadrants.
3. The sign of cot θ depends on the x-coordinate of the point on the unit circle corresponding to angle θ. If the x-coordinate is positive, cot θ is positive; if it's negative, cot θ is negative. Therefore, cot θ is positive in the first and fourth quadrants and negative in the second and third quadrants.
4. To have sin θ and cot θ with different signs, we need sin θ to be positive and cot θ to be negative or vice versa. This condition is met when the terminal side of angle θ lies in either the first quadrant (sin θ positive, cot θ negative) or the third quadrant (sin θ negative, cot θ positive).
5. In summary, the terminal side of angle θ must lie in either the first or third quadrant for sin θ and cot θ to have different signs.
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Which of the following algebraic represents shows a dilation that is an enlargement ?
The algebraic representation that shows a dilation that is an enlargement is (5/2 x,5/2 y). (Option D)
A dilation is a type of transformation that changes the size of the shape or object. It refers to a process of changing an object’s size by decreasing or increasing its dimensions by a scaling factor. A dilation produces an image that has the same shape as the original image but is a different size.
A dilation that results in a larger image is called an enlargement while a dilation that generates a smaller image is called a reduction. A dilation is described using the scale factor and the center of the dilation (which is a fixed point in the plane).
For a scale factor > 1, the image is an enlargement; for a scale factor < 1 and > 0, the image is a reduction; and for a scale factor = 1, the figure and the image are congruent. Hence, for a point (x,y), algebraic representation that shows a dilation that is an enlargement is (5/2 x,5/2 y) as the scale factor is greater than 1. For the remaining options, the scale factor is between 0 and 1, hence they are reduction.
Note: The question is incomplete. The complete question probably is: Which of the following algebraic representation shows a dilation that is an enlargement? A) (1/3 x,1/3 y) B) (0.1x, 0.1y) C) (5/6 x,5/6 y) D) (5/2 x,5/2 y)
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the snellen letter chart is commonly used to test for
The snellen letter chart is commonly used to test for visual acuity or clarity of vision.
The Snellen letter chart, named after the Dutch ophthalmologist Herman Snellen, is a widely used tool to assess visual acuity or clarity of vision. It consists of rows of letters or optotypes that decrease in size from top to bottom. The chart is typically displayed at a standardized distance of 20 feet (or 6 meters) from the person being tested.
When an individual reads the Snellen chart, the process involves the following steps:
1. Light enters the eye through the cornea, the transparent front surface of the eye.
2. The cornea focuses the incoming light onto the lens, which further refines the light rays.
3. The lens adjusts its shape to ensure that the light is accurately focused onto the retina, the light-sensitive layer at the back of the eye.
4. The retina contains specialized cells called photoreceptors, which convert light into electrical signals.
5. Among the photoreceptor cells, cones are primarily responsible for color vision and visual acuity. When a person focuses on a specific optotype (such as the letter "E" on the Snellen chart), the light reflecting from that optotype enters the eye and forms an image on the retina.
6. The cones in the retina, specifically in the central area called the macula, respond to the light stimulus and generate electrical signals.
7. These electrical signals are then transmitted via the optic nerve to the visual cortex in the brain for further processing and interpretation.
8. The brain processes the received signals and translates them into the perception of the letter "E" or any other optotype being viewed.
The clarity of vision is assessed by determining the smallest line of letters that can be accurately identified. The Snellen chart assigns a visual acuity measurement based on the ratio of the distance at which the chart is viewed and the distance at which a person with normal vision can read the line accurately. For example, if a person can read the 20/20 line from a distance of 20 feet, it indicates that they have normal visual acuity.
The Snellen chart is an essential tool in optometry and ophthalmology for diagnosing and monitoring vision problems such as nearsightedness (myopia), farsightedness (hyperopia), astigmatism, and other visual impairments. It helps determine the level of visual acuity and guides the prescription of corrective lenses or other treatments to improve vision.
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when you refer to the meer-kitty survey feedback tab, you are pleased to find that the available data is aligned to the business objective. however, you do some research about confidence level for this type of survey and learn that you need at least 120 unique responses for the survey results to be useful. therefore, the dataset has two limitations: first, there are only 40 responses; second, a meer-kitty superfan, user 588, completed the survey 11 times. as the survey has too few responses and numerous duplicates that are skewing results, what are your options? select all that apply.
Conduct additional surveys to increase the total number of responses.
Remove duplicates from the dataset to eliminate skewing of results
Use caution when interpreting the results and consider them exploratory rather than conclusive
Consider using a different methodology for gathering data, such as focus groups or interviews
Adjust the confidence level for the survey results to account for the smaller sample size
Use a different data analysis technique, such as bootstrapping, to account for the limitations of the dataset
Consider using a sample survey method, like stratified sampling or cluster sampling.
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5. Find the value of x.
Answer:
x=15
Step-by-step explanation:
express each statement in logic using the variables: p: it is windy. q: it is cold. r: it is raining. (a) it is windy and cold. (b) it is windy but not cold. (c) it is not true that it is windy or cold. (d) it is raining and it is windy or cold. (e) it is raining and windy or it is cold. (f) it is raining and windy but it is not cold.
The given statements can be expressed as
a) \($p \land q$\).
b) \($p \land\neg q$\)
c) \($\neg(p \lor q)$\)
d) \($p \land (q \lor r)$\)
e) \($r \land (p \lor q)$\)
f) \($r \land (p \land \neg q)$\)
What is a logical expression?
A statement that can be true or false is referred to as a logical expression Depending on the values of p and q, it can be true or false. This is distinct from a mathematical expression, which represents a true statement.
The given statements are
p: it is windy.
q: it is cold.
r: it is raining.
Now
a) it is windy and cold
This statement can be expressed as - \($p \land q$\).
(b) it is windy but not cold.
This statement can be expressed as - \($p \land\neg q$\)
(c) it is not true that it is windy or cold. - \($\neg(p \lor q)$\)
(d) it is raining and it is windy or cold. - \($p \land (q \lor r)$\)
(e) it is raining and windy or it is cold. \($r \land (p \lor q)$\)
(f) it is raining and windy but it is not cold. \($r \land (p \land \neg q)$\)
Hence, the given statements can be expressed as
a) \($p \land q$\).
b) \($p \land\neg q$\)
c) \($\neg(p \lor q)$\)
d) \($p \land (q \lor r)$\)
e) \($r \land (p \lor q)$\)
f) \($r \land (p \land \neg q)$\)
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A standard train ticket in a certain city costs 3 per ride. people who use the train also have the option of purchasing a frequent-rider pass for 18.75 each month. with the pass, a ticket costs only 2.25 per ride. how many train rides in a month make the frequent-rider pass a better deal than standard train tickets?
a. 26 or more rides
b. 24 or more rides
c. 25 or more rides
d. 27 or more rides
Number of train rides to make the frequent-rider pass a better deal than standard train tickets is 26 or more rides.
As given,
Cost of standard train ticket = 3 per ride
Price of frequent rider pass= 18.75 each month
Cost of ticket using rider pass = 2.25 per ride
let x be the number of rides
Equation:
18.75 + 2.25x < 3x
⇒ 0.75x > 18.75
⇒ x > 25
Therefore, number of train rides to frequent-rider pass a better deal than standard train tickets is 26 or more rides.
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can someone help me it's an emergency I'll mark u brainliest promised
Answer:
Whats the question, respond in comments.
is translation a and b?
pls hurrryyyyyyy #42 only and show work
Answer:
x = 70
Step-by-step explanation:
50 + x + 2x + 100 = 360
Combine like terms
3x + 150 = 360
Subtract 150 from both sides
3x = 210
Divide both sides by 3 to isolate x
x = 70
find the solution of the given initial value problem. y'' y' − 2y = 2t, y(0) = 0, y'(0) = 4
The complete solution to the given initial value problem is y(t) = (5/3)\(e^{2t}\) - (5/3)\(e^{-t}\) - t
To begin, we solve the homogeneous equation associated with the given differential equation. The homogeneous equation is obtained by setting the right-hand side (2t) to zero:
y'' - y' - 2y = 0
The characteristic equation for this homogeneous equation is obtained by assuming the solution has the form y = e^(rt), where r is a constant:
r² - r - 2 = 0
Factoring the equation, we have:
(r - 2)(r + 1) = 0
This gives us two possible values for r: r = 2 and r = -1.
The general solution to the homogeneous equation is then given by a linear combination of these exponential functions:
\(y_h(t) = c_1e^{-2t}+ c_2e^{-t}\)
Next, we need to find a particular solution to the non-homogeneous equation. Since the right-hand side is 2t, which is a linear polynomial of degree 1, we assume a particular solution of the form y_p(t) = At + B, where A and B are constants to be determined.
We substitute this assumed solution into the original differential equation:
\(y_p'' - y_p' - 2y_p = 2t\)
Differentiating y_p(t) twice, we have:
0 - 0 - 2(At + B) = 2t
Simplifying the equation, we get:
-2At - 2B = 2t
To match the terms on both sides, we equate the coefficients:
-2A = 2 (coefficient of t)
-2B = 0 (constant term)
From the first equation, we find A = -1. Plugging this into the second equation, we get B = 0.
Therefore, the particular solution is y_p(t) = -t.
Now that we have both the homogeneous solution (y_h(t)) and the particular solution (y_p(t)), we can find the complete solution to the non-homogeneous equation by summing them:
\(y(t) = y_h(t) + y_p(t)\)
\(y(t) = c_1e^{2t} + c_2 e^{-t} - t\)
Finally, we use the given initial conditions y(0) = 0 and y'(0) = 4 to find the values of the constants c1 and c2.
Substituting y(0) = 0 into the equation, we get:
\(y(0) = c_1e^{2(0)} + c_2 e^{-0} - 0\)
\(0 = c_1 + c_2\)
Next, we differentiate the equation y(t) with respect to t to find y'(t):
y'(t) = 2c₁\(e^{2t}\) - c₂\(e^{-t}\) - 1
Substituting y'(0) = 4 into the equation, we get:
4 = 2c₁\(e^{2(0)}\) + c₂\(e^{-0}\) - 1
4 = 2c₁ - c₂ - 1
Simplifying the equations, we have:
c₁ + c₂ = 0 (Equation 1)
2c₁ - c₂ = 5 (Equation 2)
We can solve this system of equations using various methods, such as substitution or elimination. Let's solve it using substitution:
From Equation 1, we can express c₂ in terms of c₁ as c₁ = -c₂.
Substituting this into Equation 2, we have:
2(-c₂) - c₂ = 5
-3c₂ = 5
c₂ = -5/3
Substituting the value of c₂ back into Equation 1, we get:
c₁ - 5/3 = 0
c₁ = 5/3
Therefore, the constants are c₁ = 5/3 and c₂ = -5/3.
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According to a recent poll 4060 out of 14500 people in the United States were classified as obese based on their body mass index whats the relative frequency of obesity according to this poll?
Answer:
around 28% of americans are obese
Step-by-step explanation:
The relative frequency of obesity according to this poll is 28 percent.
How to find the relative frequency?Relative frequency is the ratio of the considered sub group's count to the total count. (so its frequency of the considered sub group relative to the total frequency).
Suppose you've to calculate the joint relative frequency of a certain category out of the given big category.
Then its the ratio of the frequency of that certain category to the total frequency of that big category.
Given According to a recent poll 4060 out of 14500 people in the United States were classified as obese based on their body mass index .
Therefore, the relative frequency of obesity according to this poll is 28 percent.
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Cameron surveyed 200 of the students in his school about their favorite color. 60 students said their favorite color was red. What percentage of the surveyed students said their favorite color was red?
Answer: 30%
Step-by-step explanation: 60/300 is the same as 30/100 so it is 30%
Please help I’m begging you
Answer:
y = 9
Step-by-step explanation:
The line "y = 9" is parallel to the x-axis and passes through (0,9).