To find the temperature in Reigate, which is halfway between St. Petersburg and Rome, we need to find the average of the two temperatures.
Average = (Temperature1 + Temperature2) / 2
Average = (-7 + 15) / 2 = 8 / 2 = 4
So, the temperature in Reigate was 4°C.
Answer:
4°C
Step-by-step explanation:
Try drawing it on a number line and counting 11 from -7° C and 11 from 15°C you'll end up with 4°C as the middle
On a line segment, U is between T and V. If TU = 11x − 15, UV = 10x, and TV = 20x − 3, what is TU?
The value of TU is 117.
What is a line segment?
A line segment in geometry is a section of a straight line that is enclosed by two clearly defined endpoints and contains all of the points on the line that lies inside those endpoints. The Euclidean distance between two ends of a line segment determines its length.
Here, we have
Given: U is between T and V. If TU = 11x − 15, UV = 10x, and TV = 20x − 3.
We have to find the value of TU.
TV = TU + UV
20x − 3 = 11x − 15 + 10x
20x − 3 = 21x - 15
-3 + 15 = 21x - 20x
12 = x
Now, we have TU = 11x − 15.
We put the value of x on TU and we get
TU = 11x − 15
TU = 11(12) - 15
TU = 132 - 15
TU = 117
Hence, the value of TU is 117.
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the questions for quiz 2 will include all 6 trig functions with angles on the unit circle in the interval [0, 2pi], given in radians or degrees.
Trigonometry is the study of relationships between angles and sides of a triangle.
The six trigonometric functions—sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot)—are used to describe the relationships between the angles and sides of any triangle.
The unit circle is a circle of radius one centered at the origin of a Cartesian coordinate system. When we determine the coordinates of points on the unit circle, we are using the six trigonometric functions. The unit circle is used to find the values of the trigonometric functions for angles of measures 0°, 30°, 45°, 60°, and 90°.
In the interval [0, 2π], we can use the unit circle to calculate the trigonometric functions of the angles in both degrees and radians. For example, sin 0° = 0, cos 0° = 1, tan 0° = 0, csc 0° = undefined, sec 0° = 1, cot 0° = undefined. The corresponding values in radians are sin 0 = 0, cos 0 = 1, tan 0 = 0, csc 0 = undefined, sec 0 = 1, cot 0 = undefined.
By using the unit circle, we can find the value of all six trigonometric functions for any angle in the interval [0, 2π], given in degrees or radians. We can also use the unit circle to find the trigonometric functions for any angle in any interval.
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Evaluate the expression 3s - 4q - m² where m= 4, q= -3, and s = -24.
We can substitute the given values into the expression to find the result:
3s - 4q - m² = 3(-24) - 4(-3) - 4² = 72 + 12 - 16 = 60.
So the expression equals 60 when m= 4, q= -3, and s = -24.
On 21/04 the service fee for depositing the amount of R2239.10 was 31.74. Determine the service fee as a percentage of the deposited amount
To determine the service fee as a percentage of the deposited amount, we can use the following formula:
What does math's % mean?
In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).
Service fee percentage = (Service fee / Deposited amount) x 100
In this case:
Service fee percentage = (31.74 / 2239.10) x 100 = 1.41%
So, the service fee for depositing the amount of R2239.10 was 1.41% of the deposited amount.
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A text message plan costs $6 per month plus $0.43 per text. Find the monthly cost for x text messages The monthly cost of x messages is dollars.
The monthly cost of x messages is 0.43x + 6 dollars.
What is an expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows:
Expression: (Math Operator, Number/Variable, Math Operator)
Given
Cost of message plan for one month = $6
cost for each text = $0.43
The monthly cost is calculated by adding the price of the message plan for one month to the cost of each text message multiplied by the number of messages sent in a month.
Total number of messages sent in a month = x
monthly cost for x text messages = (0.43 * x) + 6
Monthly cost for x text messages = 0.43x + 6 dollars
Hence the cost is 0.43x + 6 dollars.
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the sum of two consecutive integers is 65. find the two numbers
Answer:
x=32
x+1=33
Step-by-step explanation:
let the first consecutive integer be 'x'
let the second consecutive integer be 'x+1'
x+x+1=65
2x+1=65
2x=65-1
2x=64
x=64÷2
x=32
x+1=(32+1)
x+1=33
A physician writes a prescription for Proair HFA (albuterol sulfate) for Chronic Obstructive Pulmonary Disease (COPD). The instructions state: Inhale 1 to 2 MDI puffs (90-180mcg) q 4-6 hours.
How many puffs will the patient take daily?
The puffs that the patient will take daily include:
1 puff every 4 hours for 24hrs = 6
1 puff every 6 hours for 24hrs =4
2 puffs every 4 hours for 24hrs =12
2 puffs every 6 hours for 24 hrs =8
How to calculate the number of puffs?From the information, a physician writes a prescription for Proair HFA (albuterol sulfate) for Chronic Obstructive Pulmonary Disease (COPD). The instructions state: Inhale 1 to 2 MDI puffs (90-180mcg) q 4-6 hours.
In this case, it should be noted that puff every 4 hours for 24hrs will be 6 times. Also, 1 puff every 6 hours for 24hrs will be 4 times.
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Karen divided 560.9 by 10³ and got
a quotient of 0.5609. Julio thinks the
quotient should be 5.609. Who is correct?
Explain your answer.
Karen divided 560.9 by 10³ and got a quotient of 0.5609 ,therefore he is right.
What do you mean by division?
Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group. Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.
What do you mean by quotient ?
In mathematics, the outcome of dividing two numbers is called the quotient. In other words, the result quotient is obtained by dividing a dividend by a divisor.
How to Divide a Long Number by Decimals?
Move the decimal point all the way to the right while keeping track of how many places you've moved it if the number you're dividing by has a decimal. Then, move the decimal point the same number of places to the right in the number you are dividing.Put a decimal point immediately above the one in the number under the division bar in the quotient (answer) space.Divide until the remainder equals zero or until your answer contains enough decimal points. If the remainder repeats, you can stop as well because this shows that your answer is a repeating decimal.Hence, Karen divided 560.9 by 10³ and got a quotient of 0.5609.
It is Right answer for the this division, and steps are uploaded in mage kindly see the image also.
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Sove the inequality, I need the step by step for this please
|x +1|>-3
The solution for the inequality |x +1|>-3 is x > -4 or x < -4.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
To solve the inequality |x + 1| > -3, we need to consider two cases:
x + 1 > -3: In this case, we can subtract 1 from both sides to get x > -4.
x + 1 < -3: In this case, we can subtract 1 from both sides to get x < -4. However, we also need to reverse the inequality symbol because we are multiplying or dividing by a negative number.
So the solution for the inequality is x > -4 or x < -4.
To get the final solution, we need to consider the combined solution from both cases:
x < -4 or x > -4
This represents as follows:
[tex]\begin{bmatrix}\mathrm{Solution:}\:&\:\mathrm{True\:for\:all}\:x\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}[/tex]
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The 3-4-5 right triangle is a commonly used right triangle. Use the inverse sine function to determine the measure of the angle opposite the side of length 3.
The measure of the angle opposite the side of length 3 is approximately 53.13 degrees.
To find the measure of the angle opposite the side of length 3, we need to use the inverse sine function. The inverse sine function can be written as sin^−1(x). We can use the Pythagorean Theorem to calculate the side length of the triangle, which is 3^2 + 4^2 = 5^2. Therefore, we can use the inverse sine function to calculate the measure of the angle opposite the side of length 3. To do this, we will take the ratio of the side of length 3 to the hypotenuse, which is 3/5. We can then plug this value into the inverse sine function, which gives us sin^−1(3/5). Calculating this value gives us approximately 53.13 degrees, which is the measure of the angle opposite the side of length 3.
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How long is the line of sight? Round your answer to the nearest hundredth.
Answer:
77.78 feet-----------------------
The line of sight is the hypotenuse of the 45° right triangle.
As per the property of the 45° right triangle, the length l is:
l = b√2 orl = 55×√2 ≈ 77.78 feetAnswer:77.7f
Step-by-step explanation: pythagorean theorem
55*55=3025
3025*2=6050
square root 6050=77.7
Find an equation of the form y=f(x) for a curve with x-intercept 1 whose tangent line at any point (x, y) has slope xe^-y.
y=___
y = ln( [tex]\frac{x^2+1}{2}[/tex]) is the required equation.
What is x-intercept?In a graph of an equation, the x-intercept is the point at which the graph of the equation crosses the x-axis. It is the point where the y-coordinate is equal to 0. The x-coordinate of the x-intercept is the solution of the equation when y = 0.
Given that the slope at point (x,y)
and we know that slope at any find is dy/dx
so dy/dx = [tex]xe^-^y[/tex]
=> dy/[tex]e^-^y[/tex] = xdx
=> [tex]e^y[/tex] dy = x dx
intergrating both side we get:
[tex]e^y[/tex] = x²/2 + c
where c is a constant
given x intercept is 1
[tex]e^0[/tex] = 1²/2 + c
=> 1 = 1/2+c
=> c= 1/2
so [tex]e^y[/tex] = x²/2 + 1/2
taking ln on both side we get:
y = ln( [tex]\frac{x^2+1}{2}[/tex]) is the required equation.
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Given: E is the midpoint of overline BD and overline AC perp overline BD .Prove : triangle BAE cong triangle DAE . Statement reason eis the midpoint of bd ac bd type of statement kote:- gd and ur cogmnents step given'
The ΔBAE is congruent to ΔDAE. ΔBAE and ΔDAE have three corresponding angles that are congruent, so they are congruent.
The Triangle Congruence Theorem states that if two triangles have three corresponding angles that are congruent, then the triangles are congruent.
This can be seen by looking at the angles BAE, BAE, and DAE. All three of these angles are equal, so they are congruent. Additionally, the side lengths of the triangles are the same, so the triangles are also congruent. The Triangle Congruence Theorem is an important tool for determining the congruence of two triangles.
It is used to compare the angles and side lengths of two triangles, and if the angles and side lengths are the same, then the triangles are congruent. When ΔBAE and ΔDAE have the same angles and side lengths, then it is clear that they are congruent.
According to question,
E is the midpoint of,
AC⊥ BD,
As given E is the midpoint of the line ,
So, BE = ED,
further, line AE = AE, because this is the common line between the two triangles.
Also, ∠BED =∠DEA =90°, as AC⊥ BD.
Therefore, the ΔBAE is congruent to ΔDAE.
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Which coordinates are solutions to the equation? Select ALL that apply.
2x−y=20
(10, 0)
(15, 10)
(5, 7)
(-4, -28)
except point (5, 7) all given coordinates are on the line.
What are coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
given, an equation 2x−y=20
to check what are the coordinate of the equation:
The easiest way to find out if a point falls on a specific line is to plug the first value of the point in for x and the second value for y.
Thus, For Coordinates(10, 0)
2x−y=20
=> 2 * 10 - 0 = 20
=> 20 = 20
Thus Coordinates are on the line.
Thus, For Coordinates(15, 10)
2x−y=20
=> 2 * 15 - 10 = 20
=> 30 -10 = 20
=> 20 = 20
Thus Coordinates are on the line.
Thus, For Coordinates(5, 7)
2x−y=20
=> 2 * 5 - 7 = 20
=> 3 = 20
Thus Coordinates are not on the line.
Thus, For Coordinates(-4, -28)
2x−y=20
=> 2 * -4 - (-28) = 20
=> -8 + 28 = 20
=> 20 = 20
Thus Coordinates are on the line.
Therefore, except point (5, 7) all given coordinates are on the line.
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The dog shelter has Labradors, Terriers, and Golden Retrievers available for adoption. If P(terriers) = 85%, interpret the likelihood of randomly selecting a terrier from the shelter.
A. Likely
B. Unlikely
C. Equally likely and unlikely
D. This value is not possible to represent probability of a chance event
The dog shelter has Labradors, Terriers, and Golden Retrievers available for adoption. P(terriers) = 85% is likely Option B
What is probability?Generally, Probability is the area of mathematics that deals with providing numerical descriptions of the likelihood that an event will take place or the likelihood that a statement will be correct.
A number between 0 and 1 may be thought of as representing the chance of an event happening, with 0 indicating that the occurrence is impossible and 1 indicating that it will definitely happen.
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she created ordered pairs, (height , weight), from the data and found they defined a function. which of the following actions would cause alex's set of ordered pairs to no longer define a function?
Option(B) is the correct answer. The answer is - Adding data from a student who is 154 cm tall and weighs 69kg.
A function is a set of ordered pairs in which no two different ordered pairs have an identical x -coordinate. An equation that makes such a set of ordered pairs defines a function.The domain of the function is the set of all inputs and the range of the function is the set of all outputs. To check to see if a set of ordered pairs or a list presented by a table is a function or not, check to make sure that each input value is paired with only one output value.Read more about function:
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Which of the following are square properties? Choose ALL that apply.
Four right angles.
Exactly one pair of parallel sides.
Diagonals are perpendicular.
Diagonals are congruent.
It’s Election Day for a club. If a president and vice president are elected, how many combinations can be made among eight people
The number of combinations that can be made among eight people is given as follows:
56 combinations.
How to obtain the number of combinations?As there are different roles, the order is important, hence the permutation formula is used to solve this question.
The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
For this problem, two people are selected from a set of 8, hence the number of combinations is given as follows:
P(8,2) = 8!/6! = 8 x 7 = 56 combinations.
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A circular dartboard is divided into regions with various central angles. The probability of a dart randomly landing in a particular region is 1/6. What is the corresponding measure, in degrees, of the central angle of this section of the dartboard?
The corresponding measure of the central angle of the section of the dartboard is 60 degrees.The probability of randomly landing in a particular region of a circular dartboard is 1/6.
The probability of randomly landing in a particular region of a circular dartboard is 1/6. This means that each region of the dartboard is equivalent in size, and thus has the same central angle. Since the dartboard is circular, the total measure of the central angles must add up to 360 degrees. Therefore, the measure of the central angle of each section of the dartboard is 360 divided by 6, which is equal to 60 degrees.
The corresponding measure of the central angle of the section of the dartboard is 60 degrees.The The corresponding measure of the central angle of the section of the dartboard is 60 degrees.The probability of randomly landing in a particular region of a circular dartboard is 1/6. of randomly landing in a particular region of a circular dartboard is 1/6.
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while grading her students' most recent quiz on equation solving, mrs. jones calculated that approximately forty percent of her students answered question number 14 with multiple choice option b, while the other sixty percent answered a or c. question #14 from Mrs. Jones's students' most recent quiz:
14) Solve the single variable equation for n.
a.n=3
b.no solution
c.infinitely many solutions
Use complete sentences to compare the similarities and differences of each of the multiple choice answer options A-C. In your answer, rationalize why a student would choose each of the options as the correct answer
If while solving an equation, a single value is obtained for the variable, then the equation has only a single solution.
The option (a) is n=3.
If while solving an equation, a single value is obtained for the variable, then the equation has only a single solution. If n=3 is obtained after solving the equation, then the student should chose option (a) as the answer.
The option (b) is "no solution".
While solving an equation, if we obtain an equation which is mathematically false, then the equation will have no solution. So, no solution is chosen when no value is obtained for n and the final equation is mathematically false.
The option (c) is "infinitely many solutions".
While solving an equation, if we obtain an equation which is mathematically correct such as 0=0, 7=7 etc., then the equation will have infinietly many solutions. So, infinitely many solutions is chosen when no value is obtained for n and the final equation is mathematically correct.
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Kory pays 1/3 of his income in tax. He then spend 4/5 of what remains after tax, and places the rest into a savings account. What fraction of his income does he put into his saving account?
Answer:
2/5 of income put into savings
Step-by-step explanation:
Let Kory's income be X
1/3 of his income goes to taxes so taxes are X/3
Remaining is (1- 2/3) of income = (2/3 ) X
He spends 4/5 of this remaining amount
So balance after expenditure = (1- 4/5) = 1/5 of the remaining income and this amount is put into savings
Fraction of income in savings = 1/5 x 2/3 X = (2/15)X
So fraction put into savings account is 1/5 of total income
If you find it confusing to work with fractions such as these, I suggest an alternate approach which may make it easier to understand
Pick an amount for total income. Since the denominators are 3 and 5, choose an amount which is divisible by both 3 and 5 or in other words divisible by 15
Let's choose 300, a convenient number
Tax Paid = 1/3 x 300 = 100
Income after tax = 300 - 100 = 200
which is same as 2/3 x 300
Spending = 4/5 x 200 = 160
Balance in savings = 200 - 160 = 40 same as 1/5 x 200
So amount in savings as a fraction of income = 40/300 = 2/15
A survey asked 1,150 people to choose their favorite laundry detergent from brands A, B, and C. Of the people surveyed, x percent chose A as their favorite brand. If x is rounded to the nearest integer, the result is 3. Which of the following could be the number of people who chose A as their favorite brand?
I. 30
II. 35
III. 45
A. I only
B. II only
C. III only
D. I and II only
E. I, II and III
The answer is D. I and II only. The number of people who chose A as their favorite brand could be 30 or 35 since x is rounded to the nearest integer, which is 3. However, it cannot be 45 since 3 is the nearest integer.
1. x is rounded to the nearest integer, which is 3
2. If x is equal to 30, then the number of people who chose A as their favorite brand would be 30
3. If x is equal to 35, then the number of people who chose A as their favorite brand would be 35
4. If x is equal to 45, then the number of people who chose A as their favorite brand would be 45
5. Since 3 is the nearest integer, the number of people who chose A as their favorite brand cannot be 45
6. Therefore, the answer is D. I and II only.
1,150 respondents were asked to select their preferred brand among brands A, B, and C of laundry detergent. x% of those polled indicated that A was their preferred brand. The outcome is 3 if x is rounded to the nearest integer. This means that x could be 30, 35, or 45. However, since 3 is the nearest integer, the number of people who chose A as their favorite brand cannot be 45. Therefore, the answer is D. I and II only, meaning that the number of people who chose A as their favorite brand could be 30 or 35. This is because if x is equal to 30, then the number of people who chose A as their favorite brand would be 30 and if x is equal to 35, then the number of people who chose A as their favorite brand would be 35.
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A mother is 66 inches tall, and her daughter is 33 inches tall. Which of the following equations describes the relationship between m, the height of the mother, and g, the height of the daughter?
A. g=2/m
B. g = 2m
C. g=m/2
D. g=m-2
Answer: your answer is c
Step-by-step explanation:
Please help me!! It is 5 questions
You prοbably know our football and basketball teams, but we have 21 Divisiοn I varsity programs that all raise the bar whenever they compete.
How many attended the Nοrth Carolina State or the Butler game?There were 465 people whο were surveyed in all.
The attendance at the FSU-Marist game was (M), n(M)=240.
The attendance at the FSU-Butler game was (B), n(B)=200.
The tοtal number οf spectators for the FSU-NC State game was n(NCS)=240.
The cοmbined attendance at the NC State game and the Marist game was n(MNCS)=90.
The cοmbined attendance at the Butler vs. NC State game was n(NCSB)=80.
The cοmbined attendance at the Butler and Marist games was n(BM)=100.
n(MBNCS)=30 peοple attended all three of the games.
When NC State's first football game was οrganised by students in 1892, the school's long histοry of intercollegiate athletics officially started.
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a) You see a general expression written as ax? + bx4 + cx3 + dx2, determine the possible number of zeroes that could exist. (2 marks) b) Factor 2x3 - 9x2 + 7x + 6 and list all roots for the expression. (7 marks) c) Given that x = -1 and x = 2 are roots for ax4 + 3x3 – 12x2 + bx + 6, determine the values of a and b. (7 marks)
The maximum number of zeroes in a generic equation with the form axe? + bx4 + cx3 + dx2 is 5.
What is meant by expression?A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. Any one of the following mathematical operations can be used.A statement using numbers, variables, and operations is known as an expression. An equation has an equals sign, whereas an expression lacks one. This is the main distinction between the two types of sentences. Terms and operations are used to create mathematical expressions.a) [tex]$ax^{5}[/tex]
b) Factor 2x3 - 9x2 + 7x + 6 is
(x - 3) (x -2) (2x + 1)
c) x = -b / 2a
Replace x by -2, from the vertex:
-2 = -b / 2a
Solve for b:
-b = -4a
Or
b = 4a
By evaluating the equation with the vertex's x-value, we can determine the y-value from the vertex:
y = ax2 + 4ax - 6
Simplify, 6 for y, and -2 for x:
6 = a(-2)2 + 4a(-2) - 6
6 = 4a - 8a - 6
solve for a:
a = -3
Simplifying the above equation,
b = 4a, b = -12
The value for a is -3.
The value for b is -12
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whats 2 2 56799065 times 569050890562 plus 69 x 420 plus 9 10 9 10 21 69 420 21 - 9 x3 y3 z3
The answer for 2 2 56799065 times 569050890562 plus 69 x 420 plus 9 10 9 10 21 69 420 21 - 9 x3 y3 z3 is 32185024125880310
Let x = 2, y = 56799065, z = 569050890562, a = 69, b = 420 and c = 9.
The equation is: 2x + y × z + a × b + (9 + 10 + 9 + 10) × (21 + 69 + 420 + 21) - 9 × 3 × y × 3 × z × 3
We can calculate this equation as follows:
2 × 2 + 56799065 × 569050890562 + 69 × 420 + (9 + 10 + 9 + 10) × (21 + 69 + 420 + 21) - 9 × 3 × 56799065 × 3 × 569050890562 × 3
= 4 + 32185023742042530 + 28380 + 145800 - 1365466177461590
= 32185024125880310
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Joanie is organizing her closet. She has 3 times as many black shirts as gray shirts, plus 3 new black shirts she just bought. She has 5 times as many white shirts as gray shirts, minus the one white shirt she donated. Joanie has 2 times more gray short than brown shirts. If she has the same number of black and white shirts, how many gray shorts does Joanie have?
If Joanie is organizing her closet. She has 3 times as many black shirts as gray shirts, plus 3 new black shirts she just bought. The number of gray shirts that Joanie have is: 2.
How to find the number of shirts?Let x represent the number of gray shirts
Let Joanie black shirts = 3x + 3
Let Joanie white shirts = 5x - 1
Let Joanie brown shirts = 2x
So,
3x + 3 = 5x - 1
Substract 3 from both side
3x + 3-3 = 5x - 1 -3
3x = 5x -4
Substract 5x from both side
3x-5x = 5x -4 -5x
-2x = -4
Divide both side by
x = -4/-2
x =2
Therefore, Joanie has 2 gray shirts.
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Luisa has four boxes of chocolate bars there are 10 chocolate bars in each pack in each chocolate bar has eight pieces find two equivalent expressions that could be used to find the total number of chocolate pieces Luisa has
The two equivalent expressions that could be used to find the total number of chocolate pieces that Luisa has are given as follows:
(4 x 10) x 8.4 x (10 x 8).How to obtain the number of chocolate pieces that Luisa has?To obtain the number of pieces that Luisa has, we must consider that:
She has four boxes.Each box is composed by 10 bars.Each bar is composed by 8 pieces.Hence the multiplication operation giving the number of pieces is given as follows:
4 x 10 x 8.
The associative property of multiplication states that the order in which 3 or more terms are multiplied does not change the product, hence the equivalent expressions are given as follows:
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Two lines are parallel when their slopes are the same
Two lines are perpendicular when the product of their slopes is -1
Two lines are intersect when their slopes are different
Let's define our slopes as m1 and m2, != means not equal
Solution:
1) m1 = m2 Parallel
2) m1*m2=-1 Perpendicular
3) m1*m2=-1 Perpendicular
4) m1=m2 Parallel
5) m1=m2 (-4 = -4) Parallel
6) m1 != m2 Neither
7) m1 != m2 Neither
8) m1*m2=-1 Perpendicular
use method of reduction of order to find a second solution of the given equation; t^(2)y''+2ty'-2y=0, t>0
if y_1(t)=t , (given hint): set y_2= v(t)t
The second solution of the given differential equation t^2y''+2ty'-2y=0, t>0 is y_2(t) = c/t where c is an arbitrary constant.
The second solution of the given differential equation t^2y''+2ty'-2y=0, t>0 is y_2(t) = c/t where c is an arbitrary constant.
y_2(t) = t^2v'(t) + 2t v(t) - y_1(t)
Substituting y_1(t) and y_2(t) in the given equation, we get
t^2v''(t) + 2tv'(t) - 2v(t) = 0
This is a first order linear differential equation and can be solved as
v'(t) = -2v(t)/t
Integrating both sides, we get
v(t) = c/t^2
Therefore, the second solution of the given equation is
y_2(t) = c/t
The second solution of the given differential equation t^2y''+2ty'-2y=0, t>0 is y_2(t) = c/t where c is an arbitrary constant.
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