Checking by differentiation,
y′ = -6sin(3t) + 12cos(3t)
y′′ = -18cos(3t) - 36sin(3t)
9y = y′ = -6sin(3t) + 12cos(3t)
y ′′ + 9y = 0
To verify that y=2cos3t+4sin3t is a solution to y ′′ +9y=0, we need to differentiate y twice and substitute the result into the differential equation.
First, we find the first derivative of y with respect to t:
y′ = -6sin(3t) + 12cos(3t)
Then, we take the second derivative of y with respect to t:
y′′ = -18cos(3t) - 36sin(3t)
Next, we substitute y′′ and y into the differential equation:
y′′ + 9y = (-18cos(3t) - 36sin(3t)) + 9(2cos(3t) + 4sin(3t))
Simplifying this expression, we get:
y′′ + 9y = -18cos(3t) - 36sin(3t) + 18cos(3t) + 36sin(3t)
y′′ + 9y = 0
Therefore, we have shown that y=2cos3t+4sin3t is a solution to y ′′ +9y=0, as the sum of the two terms reduces to 0 when substituted into the differential equation. This verifies that the function y satisfies the differential equation.
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A group of people hoping to win tickets
to a concert includes 15 people over age 30,
14 people between 20 and 30 years old,
and 10 people under 20. If a 14-year-old
enters the pool of applicants, what will be the
probability of someone over age 30
winning the tickets?
Probability of someone over age 30 winning the tickets is; 38.46%
How to find the probability of winning?We are given;
Number of People over 30 years of age = 15
Number of people between 20 and 30 years old = 14
Number of People under 20 years old = 10
Total number of people in the group = 15 + 14 + 10 = 39
Thus;
Probability of someone over age 30 winning the tickets = 15/39 = 38.46%
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Expand.
Your answer should be a polynomial in standard form.
(p²+p-6) (p²-6)
A spiral tile has a width of 1/4 foot how many tiles will fit end to end on a 4 foot wall
16 tiles will fit end to end on a 4 foot wall.
In unitary method we will learn how to find the value of a unit from the value of a multiple and the value of a multiple from the value of a unit.
When we go to the market to buy any article, we ask the shopkeeper to tell the price of the article. This is called unit price. We calculate the price of number of articles, we want to buy, with the help of this unit price. Sometimes, we calculate unit price when the price of a multiple is given.
1 tile in 1/4 foot
So in 4 foot wall the number of tiles = 4/(1/4) = 16 tiles.
Thus 16 tiles will fit end to end on a 4 foot wall.
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find the inverse of
f(x) = -6xˆ2 + 24x - 100
Answer:
See below
Step-by-step explanation:
y = -6x^2 + 24x-100
solve for 'x'
y + 100 = -6x^2 + 24x = -6(x^2-4x) complete the square for x
(y+100) /(-6 ) = (x-2)^2 -4 add 4 to both sides
(y+100)/(-6) +4 = (x-2)^2 sqrt both sides
sqrt [ ( y+100)/(-6) + 4 ] + 2 = x change x and y
y = ± sqrt [ (x+100)/(-6) + 4 ] + 2 simplify (if needed)
y = ± sqrt( -x/6 -12.666) + 2
Brittany and four of her friends want to join a softball league. The league requires teams to have at least nine players, but teams cannot have more than eighteen players. In interval notation, how many more people can join Brittany's team?
The additional number of people is [4, 13]
How to determine the number of people?Brittany and four of her friends are five people.
So, we have:
n = 5
The conditions are given as
At least = 9At most = 18Let the additional number of people be x
So, we have the following inequalities
x + 5 ≥ 9 and x + 5 ≤ 18
Subtract 5 from both sides
x ≥ 4 and x ≤ 13
Express as interval notation
[4, 13]
Hence, the additional number of people is [4, 13]
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Faith is tracking the number of burpees she does at a constant rate. Last
week, she completed 60 burpees in 5 minutes. This week, she completed
78 burpees in 6 minutes. How many burpees did Faith do per minute last
week and this week?
Please help me I will mark u the brainliest
Ruthie is trying to choose what reading material she wants to take on a vacation. She wants to read 1 fiction book, 1 nonfiction book, and 3 magazines. If Ruthie has 8 fiction books, 7 nonfiction books, and 3 magazines to choose from, how many possible combinations of books and magazines could she take with her.
E. 3 F.8 G.56 H.112
The number of possible combinations would be 56.
What is permutation?Permutation is the changing of the order in which things have been arranged or the arranging of things in a certain order.
Analysis:
Total number of fiction books available = 8
number of fiction books Ruthie wants = 1
Number of combination for Ruthie = 8C1 = 8 ways
Total number of non fiction books available = 7
number of non fiction books needed by Ruthie = 1
possible combination = 7C1 = 7 ways
Total number of magazines available = 3 ways.
Total possible combinations for all the Reading materials = 8 x 7 x 1 = 56 ways.
number of magazines Ruthie wants = 3C3 = 1 way
In conclusion, the number of possible combinations of The reading materials is 56.
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Quick algebra 1 assignment for 50 points!
Only answer if you know the answer, tysm!
1. Create 5 questions referencing “Relations and Functions” Below is an example of this.
——————————————————————
Example :
Is the set of ordered pairs below a function? Yes or no, explain your reasoning.
{(4,6),(10,-2),(13,7),(15,8),(10,11)}
——————————————————————
2. Answer each question and show a brief step by step process on how you got the answer to each of your questions.
As per definition
In. a function every domain has an unique range of it
f(x)=yHere
f(4)=6f(10)=-2f(13)=7d(15)=8f(10)=11f(10) has two corresponding values hence it's not a function
What is the first step in the construction of a line perpendicular to and passing through an external point m? assume that the construction uses only a compass and a straightedge. a. place the compass needle on m and, keeping the compass width the same, draw two arcs that intersect . b. place the compass needle at any point on , and set the compass width to m. c. draw a line from point m passing through , and mark the point of intersection. d. place the compass needle at any two points on , and draw two arcs through m.
The first step in the construction of a line perpendicular to line AB and passing through an external point m is:
a. place the compass needle on m and keeping the compass width the same, draw two arcs that intersect the line AB
What are the steps to construct a perpendicular line from an external point?To construct a perpendicular line, a compass and a scale are used.
Consider a line AB and an external point M.
Step 1:
Place the compass needle on M and keeping the compass width the same, draw two arcs that intersect the line AB.
Step 2:
Name the two intersecting points on line AB as X and Y.
Draw the arcs from these two points to the opposite side of point M with the same compass width.
Step 3:
Name the intersecting point of two arcs as N.
Draw a line connecting the two points M and N using scale.
Step 4:
Using a protractor, measure the angle of the line MN with the line AB.
The angle must show 90°.
Thus, the line MN perpendicular to line AB and passing through an external point M is constructed.
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Answer:
a. place the compass needle on m and keeping the compass width the same, draw two arcs that intersect the line AB
Step-by-step explanation:
Which is the graph of a quadratic equation that has a positive discriminant?
Answer:
CORRECT graph is Graph C.
________________________________
HOPE IT HELPS
Which statement is correct when a scatterplot is constructed?
The correct statement about when a scatterplot is constructed is the independent variable is the input variable and should be represented by the x-axis. Option A
Steps in constructing a scatterplotChoose independent and dependent variableDraw a known x-axis for the independent variableAdd y-axis for the dependent variableMake all the points in the scatterplotLabel graph and axesFrom the given steps, we can see that when a scatter plot is constructed, the independent variable is the input variable and should be represented by the x-axis.
Hence, the correct statement about when a scatterplot is constructed is the independent variable is the input variable and should be represented by the x-axis. Option A
The complete question is;
Which statement is correct when a scatterplot is constructed? The independent variable is the input variable and should be represented by the x-axis.
The independent variable is the input variable and should be represented by the y-axis.
The dependent variable is the input variable and should be represented by the x-axis.
The dependent variable is the input variable and should be represented by the y-axis.
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Answer: A; The independent variable is the input variable and should be represented by the x-axis.
Step-by-step explanation:
I just know
Write the equation of the line which passes through (5, −2) and (3, 4) in standard form.
The equation of the line is 3x + y = 1
How to determine the equation of the line?The points are given as:
(5, −2) and (3, 4)
Start by calculating the slope (m)
m =(y2 - y1)/(x2 - x1)
This gives
m = (4 + 2)/(3 - 5)
Evaluate
m = -3
The equation is then calculated as:
y = m(x - x1) + y1
This gives
y = -3(x + 2) +5
So, we have:
y = -3x - 6 + 5
Evaluate the like terms
y = -3x - 1
Rewrite as:
3x + y = 1
Hence, the equation of the line is 3x + y = 1
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HELP HELP HELP
HELP HELP HELP
HELP HELP HELP
Using proportions, the lengths of the unknown sides are given as follows:
2x = 10.x - 3 = 2.What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, the triangles are similar, hence the lengths of it's sides follow the proportion given next:
[tex]\frac{2x}{4} = \frac{5}{x - 3}[/tex]
Applying cross multiplication:
2x(x - 3) = 20
2x² - 6x - 20 = 0
x² - 3x - 10 = 0
(x - 5)(x + 2) = 0.
Then the positive solution is:
x - 5 = 0 -> x = 5.
And the lenghts are:
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a grandfather age is the same as his granddaughters age in months. Together they are 91. What is the age of the grandfather
The age of the grandfather in years according to the task content is; 84.
What is the age of the grandfather?It follows that the age of the grandfather and granddaughter are; x and y respectively.
Hence, the two equations which follow are;
x = 12y
x + y= 91
Hence, the age of the grandfather, x can be evaluated as follows;
x = 12(91-x)
13x = 1092
x = 1092/13
x = 84 years.
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Rosa goes to the home of Mr. and Mrs. Johnson twice a week to work with their 4-year-old on his letters and numbers. Rosa is providing
Rosa is providing home-based tutoring.
What is Home-based tutoring?
At-home tutoring is a type of tutoring that takes place in the student's house. Tutoring is frequently related to an academic subject or test preparation. This is in contrast to tutoring centers or after-school programs that give tutoring.A home tutor is an instructor who conducts classes in the convenience of your own home. Because they give personalized attention, these classes are frequently more expensive than those offered at tuition centers. In-home tutoring typically has fewer pupils, and the lessons are even more exclusive.Tutoring's goal is to help students help themselves, or to aid or guide them to the point where they are independent learners and no longer require a tutor.Therefore, Rosa is providing home-based tutoring.
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The binomial x + 11 is a factor of x^2 – 121. What is the other factor?
Answer:
x - 11
Step-by-step explanation:
someone please help with this please
Answer:
b = 21
Step-by-step explanation:
In general for these trig problems look for the angle whose measure you are given or need to find and for the sides you are given lengths or whose sides you need to find.
Given:
side AB = 10 cm
m<C = 25°
Find:
side AC
The angle of interest here is <C whose measure is 25°.
Now look at the given side and the side you are looking for with respect to angle C, the given angle.
For angle C, AC is the adjacent leg.
For angle C, AB is the opposite leg.
Which trig function relates the opposite leg to the adjacent leg?
It is the tangent, since, in general, tan X = opp/adj.
tan C = opp/adj
tan 25° = AB/AB
tan 25° = 10 cm/b
Solve for b.
b × tan 25° = 10 cm
b = 10 cm / tan 25°
Using your calculator, divide 10 by the tangent of 25°.
b = 21.44506...
Answer: b = 21
Answer:
[tex]b = \bf 21 \space\ cm[/tex]
Step-by-step explanation:
• To solve for a side using SOH CAH TOA, first check the angle whose measure is given.
In this case, we know ∠ C is 25°.
• Next we have to figure out the relationships between the given angle and two sides: one side whose length we know, and the other whose length we have to find.
In this case, the side opposite to ∠ C is known to be 10 cm, and the side adjacent to ∠ C is AC, whose length, b, we have to find.
• The trigonometric ratio that relates the adjacent and opposite sides of an angle is tan, where:
[tex]\boxed{tan \theta = \frac{opposite}{adjacent} }[/tex] .
We can use this relationship to calculate the value of b:
⇒ [tex]tan (25 \textdegree) = \frac{10}{b}[/tex]
Solving for b:
⇒ [tex]b \cdot tan (25 \textdegree) = 10[/tex]
⇒ [tex]b = \frac{10}{tan (25 \textdegree)}[/tex]
⇒ [tex]b = 21.45[/tex]
⇒ [tex]b \approx \bf 21 \space\ cm[/tex] (rounded to the nearest whole number)
Brad has $12 more than John. Together they have $84
Hello,
John : n
Brad : n + 12
n + n + 12 = 84
2n + 12 = 84
2n = 84 - 12
2n = 72
n = 72/2
n = 36
John $36 and Brad $36 + $12 = $48
Answer:
jhon =36 brad=48
Step-by-step explanation:
B=J+12
J+B=84
12+J+J=84
2J=72
J=36
B=J+12=36+12=48
To which place would you estimate the given numbers so as to get answers quickly to the following sums?
(a) 3529 × 3689 (b) 33 × 99 (c) 777 × 523 (d) 495420 × 123512
For easy estimation, option A = nearest hundred,B = nearest ten, C = nearest hundred and D= nearest thousand.
Calculation of numbers using east estimations3529 and 3689
3529 to the nearest hundred = 3500 and,
3689 to the nearest hundred = 3700
∴ Required sum = (3500+3700) = 7200
33 and 99
33 to the nearest ten = 30 and,
99 to the nearest ten = 90
∴ Required sum = (30+90) = 120
120777 × 523
777 to the nearest hundred = 800 and,
523 to the nearest hundred = 500
∴ Required sum = (800+500) = 1300
1300495420 and 123512
495420 to the nearest thousand = 495000 and,
123512 to the nearest thousand = 124000
∴ Required sum = (495000 + 124000 ) = 619000
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Here's a Question for you! Solve for Reasoning
Step-by-step explanation:
3) Triangle QTR is similar to triangle STP (AA)
4) RT/PT = QR/PS (corresponding sides of similar triangles are proportional)
Which statement below correctly depicts the expected value of a fair game?
E(X) = 0
E(X) = 1
E(X) > 0
E(X) >1
Answer:
e(x)=0 will be your answer
Step-by-step explanation:
First of all it is important to know about the fair game. A game is said to be fair if it has equal chances of winning for both the parties.
In Statistical terms, this can be said as expected value =0
If E(X) = 1 where X is from the player, then organizer of the game would have more chances of losing.
Similarly if E(X)>0where X is from the player, then organizer of the game would have more chances of losing.
Also if E(X)>1, where X is from the player, then organizer of the game would have more chances of losing.
Hence a fair game is one where
Answer: A. E(X) = 0
Step-by-step explanation:
i need help with this page
Answer:
See picture below.
Step-by-step explanation:
this table shows how many students fro two high schools attended a football game. A student is randomly selected. what is the probability that a student attended the game, given that the student if fro North Beach? Round your answer to two decimal places.
Using it's concept, the probability that a student attended the game, given that the student if fro North Beach is:
B. 0.65.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, we have that 170 people attended the game, out of which 110 are from North Beach, hence the probability is:
p = 110/170 = 0.65.
Hence option B is correct.
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Answer:0.55 is the correct answer
Step-by-step explanation:
Please help!
Choose the notation that represents the shaded region.
A - B
B - A’
C - A’∪B
D - A’∩B
Answer:
D
Step-by-step explanation:
A' represents everything outside of the circle A
B represents the space within circle B
A' intersection B is everything not in A that is in B.
determine the slope of the line
Answer:
2
Step-by-step explanation:
We can find the slope of the line by using the slope formula
m = ( y2-y1)/(x2-x1) where ( x1,y1) and (x2,y1) are points on the line
Using the points (0,-4) and (2,0)
m = ( 0 - -4)/ ( 2 - 0)
= ( 0+4)/( 2-0)
= 4/2
= 2
You are dealt one card from a 52-card deck. Find the probability that you are not dealt a 7. Express the probability as a simplified fraction. Group of answer choices
Answer:
12/13
Step-by-step explanation:
there are 4 7's in a 52 card deck, that means the other 48 cards are not 7's. 48/52 = 12/13
Can someone help me with this having trouble !
Answer:
B. The coefficient of the second term is -5.
and
D. The coefficient of the fourth term is -10.
Step-by-step explanation:
The coefficient is the number being multiplied by a variable.
Hope this helps!
Answer:
Tick:
- the coefficient of the second term is -5
- the coefficient of the fourth term is -10
Explanation:
The coefficient of an expression is simply the number placed before and multiplying the variable (e.g. 10x ; the coefficient is 10, the variable is x)
Hope this makes sense. Feel free to inquire further if need be!
- profparis
In a zoo, the ratio of female to male tiger is 2:3.
There are 30 male tigers.
How many tigers are female?
I need help! ASAP
As shown in the figure below, a || b and c is the transversal, m∠1= 40°, m∠2= 70°.
Question: m∠3= ?
Answer:
Step-by-step explanation:
your answer will be 110degrees
Please explain if you can
Using it's concept, the probabilities are given as follows:
19. A. 1/3.
20. F. 1/6.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, there are 1 + 1 + 3 + 4 + 3 = 12 papers. 4 have a score of 6, hence, in item 19, the probability is:
p = 4/12 = 1/3.
Which means that option A is correct.
2 papers have a score greater than 12, hence the probability in item 20 is given by:
p = 2/12 = 1/6.
Which means that option F is correct.
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