Solve y'' + 16y = 0, y(π/8) = -1, y'(π/8) = 4
y(t) = ____
Answers
The solution to the differential equation is y(t) = -1/4 cos(4t) - sin(4t).
What is the solution to the differential equation?The characteristic equation is r^2 + 16 = 0, which has solutions r = ±4i. Thus the general solution to the differential equation is
y(t) = c1 cos(4t) + c2 sin(4t).
Using the initial conditions, we have
y(π/8) = c1 cos(π/2) + c2 sin(π/2) = c2 = -1,
and
y'(t) = -4c1 sin(4t) + 4c2 cos(4t),
so
y'(π/8) = -4c1 sin(π/2) + 4c2 cos(π/2) = 4c2 = 4.
Thus, c2 = -1 and c1 = -1/4, so the solution to the differential equation is
y(t) = -1/4 cos(4t) - sin(4t).
Learn more about differential equation
brainly.com/question/14620493
#SPJ11
Related Questions
A Strong wind blows to the west at a speed of 38.7 mph relative to the ground causing a commercial plane to change course. What should be the plane's velocity in order to maintain a southward direction at a constant speed of 452 mph relative to the ground?
Answers
The speed of the plane is the rate of change of distance over time
The speed of the plane should be 453.65 mph southwest
The speed of the wind is given as:
\(\mathbf{S_w = 38.7mph}\)
The expected speed of the plane is:
\(\mathbf{S_s = 452mph}\)
So, the actual speed is calculated using the following Pythagoras theorem
\(\mathbf{S_{sw}^2 = S_w^2 + S_s^2}\)
This gives
\(\mathbf{S_{sw}^2 = 38.7^2 + 452^2}\)
\(\mathbf{S_{sw}^2 = 205801.69}\)
Take square roots of both sides
\(\mathbf{S_{sw} = 453.65}\)
Hence, the speed of the plane should be 453.65 mph southwest
Read more about speed at:
https://brainly.com/question/19261234
help a sister out please!
Answers
Answer:
it would be 8 because it is a parallelogram and they are parallel to each other
Step-by-step explanation:
CD=AB
Which is not a characteristic of the standard deviation? A. It can be calculated when the data contain negative or zero values. B. It is not applicable when data are continuous. C. It is always the square root of the variance. D. Its physical interpretation is not as easy as the MAD.
Answers
The right answer is B. It is not applicable when data are continuous, is not a characteristic of the standard deviation.
The statement "It is not applicable when data are continuous" is not a characteristic of the standard deviation.
The standard deviation is a measure of the dispersion or variability of a dataset. It quantifies how spread out the values are from the mean. Explanation for other parts are as follows:
A. It can be calculated when the data contain negative or zero values:
This is true. The standard deviation can be calculated for datasets that contain negative or zero values. It considers the deviations from the mean, regardless of their sign.
C. It is always the square root of the variance:
This is true. A quadrilateral with exactly two sets of congruent following sides is called a kite. The variance is the average of the squared deviations from the mean.
D. Its physical interpretation is not as easy as the MAD:
This is a subjective statement. The physical interpretation of the standard deviation depends on the context and the familiarity of the user with the concept. However, it is often considered a more widely used and understood measure of dispersion compared to the Mean Absolute Deviation (MAD).
The statement "It is not applicable when data are continuous" is incorrect. The standard deviation can be calculated for both discrete and continuous data. The other options provided (A, C, and D) correctly describe characteristics of the standard deviation.
To know more about Standard Deviation, visit
brainly.com/question/475676
#SPJ11
Triangle JKL is a right triangle:
J (3, 10)
K (?, ?)
L (7, 3)
What are the coordinates of point K?
Answers
Answer:
3,3 A
Step-by-step explanation:
If you put it on a graph it will make a right angle, none of the others will
Answer:
3.3 A. your welcome
Step-by-step explanation:
Two events, a and b, are independent of each other. p(a)= and p(a and b)=. what is p(b) written as a decimal? round to the nearest hundredth, if necessary.
Answers
if two occurrences A and B are unrelated to one another. Then, 3/4 or 0.75 is the likelihood of event B.
What is probability?The field of mathematics known as probability studies numerical descriptions of the likelihood of an event occurring or of a statement being true.. The probability of an event is a number between 0 and 1, with 0 generally signifying the event's impossibility and 1 generally signifying its certainty.
What pair of events is referred to as an independent event?These occurrences are referred to as independent events when the occurrence or non-occurrence of one event has no bearing on the occurrence or non-occurrence of any other events.
Figuratively, we have:
If we have the following, two events A and B are said to be independent.
\(\mathrm{P}(\mathrm{A} \cap \mathrm{B})=\mathrm{P}(\mathrm{A}) \mathrm{P}(\mathrm{B})\)
Events A and B happen apart from one another. P(A) = 1/6, while P(A and B) = 1/8.
The likelihood of the event B will then be.
\(\begin{aligned}&\mathrm{P}(\mathrm{A} \cap \mathrm{B})=\mathrm{P}(\mathrm{A}) \mathrm{P}(\mathrm{B}) \\&\mathrm{P}(\mathrm{B})=\frac{\mathrm{P}(\mathrm{A} \cap \mathrm{B})}{\mathrm{P}(\mathrm{A})} \\&\mathrm{P}(\mathrm{B})=\frac{1 / 8}{1 / 6} \\&\mathrm{P}(\mathrm{B})=\frac{6}{8} \\&\mathrm{P}(\mathrm{B})=\frac{3}{4}=0.75\end{aligned}\)
To know more about probability visit:
https://brainly.com/question/16032597
#SPJ4
I understand that the question you are looking for is:
Two events, A and B, are independent of each other. P(A) = 1/6 and P(A and B) = 1/8. What is P(B) written as a decimal? Round to the nearest hundredth, if necessary.
Use the drawing tool(s) to form the correct answers on the provided number line. Plot the value(s) on the number line where this function is equal to zero: f(x) = (x + 5)(x − 1).
Its on a number line :)
Answers
Answer:
Step-by-step explanation:
Hope this Helps ;)
Develop a full regression model based on all the predictor variables indicated. Choose the right model equation below
A. Assessed Value = 246.42+43.94*(Size) + 15.69*(Fireplace Coded)+8.25*(Bedrooms) B. Asking Price = 246.42+43.94*(Size) + 15.69*(Fireplace Coded)+8.25*(Bedrooms)
C. Assessed Value = 246.42+43.94*(Size) + 15.69*(Fireplace Coded)+0.9677*(Bathrooms) D. Assessed Value = 244.4325 + 43.5532*(Size)+ 8.1910*(Bedrooms)+ 0.9677*(Bathrooms)
Q2. A review of the t-test on the significance of individual independent variable suggests that, based on the p-values
A. Only one of the independent variable possibly needs to be retained B. Two of the independent variables possibly needs to be retained C. None of the independent variables could be retained D. Three of the independent variables could be retained
Q3:
Choose the right option below. Based on the full regression model involving all of the independent variables
A. VIF for Size = 2.336, VIF for Fireplace = 1.121, VIF for bedrooms = 1.979
B. VIF for Size = 5.3352, VIF for Fireplace = 10.1873, VIF for bedrooms = 2.7885
C. VIF for Fireplace = 1.1873, VIF for bedrooms = 1.9885
D. None of the above
Q4: Based on VIF values, there is concern for collinearity in this dataset
A. True B. False
Q5:
Based on the normal probability plot, the normality assumption seems to be met
A. True
B. False
Q:7: Based on conducting residual analysis the model seems
Group of answer choices
Adequate
Inadequate
Violates Independence Assumption
Not enough information to assess the LINE assumptions
Answers
Q.2: A review of the t-test on the significance of individual independent variable suggests that, based on the p-values. None of the independent variables could be retained. This is because if the p-value is high, it means the significance is low.
Q3: Choose the right option below. Based on the full regression model involving all of the independent variables. VIF for Size = 5.3352, VIF for Fireplace = 10.1873, VIF for bedrooms = 2.7885.
Q.4: Based on VIF values, there is concern for collinearity in this dataset. True
Q5: Based on the normal probability plot, the normality assumption seems to be met. True
Q7: Based on conducting residual analysis the model seems. Adequate.
Learn more about independent variable at
https://brainly.com/question/7228371
#SPJ11
A ______ is a hypothesis that reflects the difference between groups and specifies the direction of the difference. Group of answer choices null hypothesis directional hypothesis nondirectional hypothesis accurate hypothesis
Answers
A directional hypothesis is a hypothesis that reflects the difference between groups and specifies the direction of the difference.
In contrast to a null hypothesis, which suggests there is no significant relationship between the variables being studied, a directional hypothesis makes a specific prediction about the direction of the relationship. A nondirectional hypothesis, on the other hand, predicts a relationship between the variables but does not specify the direction of that relationship.
Directional hypotheses are useful in research when there is a theoretical or empirical basis to expect a particular outcome. They can help researchers to better focus their investigation and narrow down possible outcomes, thus allowing for more robust statistical analyses. However, directional hypotheses also carry the risk of confirmation bias, as researchers might be more likely to interpret data in a way that supports their hypothesis.
In summary, a directional hypothesis predicts the difference between groups and specifies the direction of that difference, providing a more focused approach to analyzing research data compared to a null hypothesis or a nondirectional hypothesis.
know more about directional hypothesis here:
https://brainly.com/question/13187515
#SPJ11
The graph of y = x 2 is changed to y = x 2 - 3. How does this change in the equation affect the graph?
Answers
Answer:
Brings the Line down 3
To paint a house, a painting company charges a flat rate of 500 for supplies plus $50 for each hour of labor. What is the slope of the line? Use the sketch tool if it helps you with your thinking.What is the meaning of the slope in this context?
Answers
Answer:
slope = $50
Step-by-step explanation:
Given the linear equation, y = mx + b:
The slope (m) is the rate of change for every x number of labor hours. What this implies is that whenever the input (x-value) or the number of labor hours increases or decreases, the value of y (total cost) will increase by the given slope value.
Slope: The painting company charges $50 for every 1 hour of labor.
The y-intercept (b) represents the flat rate or initial value. In the given problem, it states that the company charges $500 for supplies. This means that regardless of whether the company finishes working on the painting job, they will charge their customers the flat rate.
Combined, the linear equation will be:
y = 50x + 500
Please mark my answers as the Brainliest if you find my explanations helpful :)
Drag each shape to the correct location on the tree. Drag each estimated measurement next to the correct shape. Not all shapes and measurements will be used.
A tree from a forest with a height of 30 feet is shown below. The bottom branches are about 4 feet from the ground and are 10 feet long from left to right. The tree trunk is about 2 feet wide.
What are the appropriate shapes to model the trunk of the tree and the rest of the tree? What are the approximate surface areas of each of the two shapes?
Answers
The shapes are a cone and cylinder. The surface area of the cylinder is 107 ft² and the approximate surface area of the cone is 254 ft² approximately.
How to find surface area?The appropriate shape to model the trunk of the tree is a cylinder and the appropriate shape to model the rest of the tree is a cone.
The surface area of the cylinder can be estimated as:
Surface area of cylinder = 2πr h + 2πr²
where r = radius of the cylinder (half of width of trunk) and h = height of the cylinder (height of tree minus length of branches).
Using the given measurements, estimate the surface area of the cylinder as:
Surface area of cylinder = 2π(1) (30 - 10 - 4) + 2π(1)² = 2π(16) + 2π = 34π ≈ 107 ft²
The surface area of the cone can be estimated as:
Surface area of cone = πr s + πr²
where r = radius of the base of the cone and s = slant height of the cone.
Using the given measurements, estimate the radius of the cone as:
radius = 10/2 = 5 feet
Estimate the slant height of the cone using the Pythagorean theorem:
s² = r² + h²
where h = height of the cone (length of branches) and r = radius of the base.
Using the given measurements, estimate the slant height of the cone as:
s² = (5)² + (10)²
s² = 125
s ≈ 11.2 feet
Using these estimates, estimate the surface area of the cone as:
Surface area of cone = π(5)(11.2) + π(5)² = 56π + 25π = 81π ≈ 254 ft²
Therefore, the approximate surface area of the cylinder is 107 ft² and the approximate surface area of the cone is 254 ft².
Find out more on surface area here: https://brainly.com/question/26403859
#SPJ1
Answer:
Explanation: Im built different
Ted is making chocolate chip pancakes for his whole family. He wants to make 20 pancakes using a 3-cup bag of chocolate chips. How many cups of chocolate chips will be in each pancake? Write your answer as a proper fraction or mixed number.
Answers
Answer:
3/20
Step-by-step explanation:
Given: Number of cups of pancakes to be made = 20
Number of bag of chocolate chips available = 3
Therefore, cups of chocolate chips will be in each pancake= 3/20
Find the volume of the prism. Round to the nearest tenth if necessary.
Options: 308 cm^3
186cm^3
44cm^3
149cm^3
Answers
Answer:
308cm^3
Step-by-step explanation:
maths
Answer: A. 308 cm²
Step-by-step explanation: To find this, we can use the basic principle of base times height times width to find the volume, and this case, we're given all three. To get to 308, I multiplied the given dimensions (base, width and height) by each other, so: 4 times 11 times 7.
Need help asap
the garcia family has a monthly car loan payment of $400, and their average monthly credit card bill is $4,800. mr. garcia
is also paying $1,000 per month to support his elderly parents. compute the back-end ratio to the nearest percentage.
type the correct answer in the box. use numerals instead of words.
Answers
Answer:
70%
Step-by-step explanation:
write the h(z), the transfer function, for the filters described by the following difference equations: a. y[n]=x[n]-3x[n-1] 2x[n-2]-y[n-3] b. y[n]= x[n] x[n-1] x[n-3] x[n-4]-y[n-2]
Answers
The transfer function for this filter is:
H(z) = (1 - 3z^-1 + 2z^-2) / (1 + z^-3)
a. To find the transfer function H(z) for the filter described by the difference equation y[n] = x[n] - 3x[n-1] + 2x[n-2] - y[n-3], we can take the z-transform of both sides and solve for Y(z)/X(z):
Y(z) = X(z) - 3z^-1 X(z) + 2z^-2 X(z) - z^-3 Y(z)
Y(z) + z^-3 Y(z) = X(z) - 3z^-1 X(z) + 2z^-2 X(z)
Y(z) (1 + z^-3) = X(z) (1 - 3z^-1 + 2z^-2)
H(z) = Y(z) / X(z) = (1 - 3z^-1 + 2z^-2) / (1 + z^-3)
Therefore, the transfer function for this filter is:
H(z) = (1 - 3z^-1 + 2z^-2) / (1 + z^-3)
To know more about transfer function refer here:
https://brainly.com/question/13002430
#SPJ11
The figure shown is a rectangle with a semicircle on each end. What is the area of the
figure? Use 3.14 for 7 and round your answer to the nearest tenth.
76.3 in.2
8 in.
161.0 in.2
6 in
104.5 in.2
34.8 in.2
PLEASE HELP FAST
Answers
Answer:
76.3
Step-by-step explanation:
I got it correct and i did that
The figure shown is a rectangle with a semicircle on each end. The area of the figure is 76.3 in sq.
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
The figure shown is a rectangle with a semicircle on each end.
We need to find the area of the rectangle ;
The area of the rectangle = length × Width
= 8 x 6
= 48 in sq.
Now, We need to find the area of one of the semicircles.
The area of the semicircles =
\(\pi r^2/2\\\\= 3.14 \times 3^2 /2\\\\= 28.26 /2\\\\= 14.13\)
The area of 2 semicircle = 2 x 14.13
= 28.26
The area of the figure is
48 + 28.26
= 76.26 in sq.
= 76.3 in sq.
Hence, The correct answer is A.
Learn more about the area;
https://brainly.com/question/1658516
#SPJ5
During a sale a shop allows a 20% discount on all purchases. What will a customer pay for a dress which cost $3,000?
Answers
Answer:
2,400
Step-by-step explanation:
if you buy an item at $3000 with 20% discount, you will pay 3000 - 600 = 2400 dollars.
i hope it helps :)
$3000-600=$2,400
You get .20 by taking 20% and moving the decimal 2 places to the left. Then you multiply the amount of money by the decimal percentage. Then subtract that amount from $3000 because it is a discount. Then you get the answer of $2,400.
Show the sequence {an} given by an = converges and has limit an → using the 1+ 4n precise definition of limits (e-N definition). Problem 2. Suppose we have sequences {an}_₁ and {bn}₁ such that they converges with an →3 and bn →-4 as n→[infinity]. 1. Consider the sequence {n}1 given by cn = 2an+ for all n . Is the sequence {n} convergent or divergent? If converges, what is the lim cn ? 1 bn n+00 2. Consider the sequence {d}1 given by dn = anbn +4a² for all n . Is the sequence {dn} convergent or divergent? If converges, what is the limit lim d₂ ? n+00
Answers
The sequence {cn} is convergent with limit 2 and the sequence {dn} is convergent with limit 20.
The first sequence {an} is defined as, an = 1 + 4/n. Using the e-N definition, we will show that this sequence converges to 1.Suppose ε > 0.
We need to find a natural number N such that |an – 1| < ε for all n > N.To do this, we can write |an – 1| = |1 + 4/n – 1| = |4/n| = 4/n, since 4/n > 0.
We want to find N such that 4/n < ε. Solving for n, we have n > 4/ε. This means we can take N to be any natural number greater than 4/ε.
Then for all n > N, we have |an – 1| < ε. Therefore, by the e-N definition of limits, we have an → 1 as n → ∞.
The second sequence {cn} is defined as cn = 2an + bn. Since {an} and {bn} are convergent with limits 3 and -4, respectively, we have cn → 2(3) + (-4) = 2 as n → ∞.
Therefore, {cn} converges to 2.The third sequence {dn} is defined as dn = anbn + 4a².
Since {an} and {bn} are convergent with limits 3 and -4, respectively, we have dn → 3(-4) + 4(3)² = 20 as n → ∞. Therefore, {dn} converges to 20.
Therefore, the sequence {cn} is convergent with limit 2 and the sequence {dn} is convergent with limit 20.
To know more about converges visit:
brainly.com/question/31064900
#SPJ11
Greg has 5 baseball bats that have lengths of: 3/4 yards, 2/3 yards, 1/2 yards, 7/8 yards, 1 1/8 yards. What is the difference in length between his longest and shortest bats?
Answers
Answer:
1 1/8-4/8= 3/8
Step-by-step explanation:
Make sure they all have the same common denominator (24). Then pick out the smallest number and largest number,, and subtract.
how to set up 54.88x7.3
Answers
Answer:
400.624
Step-by-step explanation:
54.88
x 7.3
_____
16464
+ 38416
________
400.624
have a nice day.
Find the sum of whole numbers from 1 to 830
Answers
344865
Explanation
Use the following formula:
\(\sum ^n_{i=1}i=\frac{n(n+1)}{2}\)
In this case, n=830, thus you get your answer by entering 830 in the formula like this:
\(\begin{gathered} \sum ^n_{i=1}i=\frac{n(n+1)}{2} \\ \sum ^{830}_{i=1}i=\frac{830(830+1)}{2} \\ \sum ^{830}_{i=1}i=\frac{830(831)}{2} \\ \sum ^{830}_{i=1}i=\frac{689730}{2} \\ \sum ^{830}_{i=1}i=344865 \end{gathered}\)so, the answer is
344865
HELP THIS IS WORTH 100 POINTS WILL MARK BRAINLIEST
Answers
Answer:
I cant see it
Step-by-step explanation:
a weights m kg,b weight is 20 kg less than three times that of a. If their total weight is 100 kg. Find the weight of a
Answers
Answer:
30kg
Step-by-step explanation:
what we know is that 3a - 20kg is b. and if a + 3a -20kg = 100kg, it becomes algebra .
So, we move it over to the sides:
4a = 120kg
(here i moved -20kg to the 100kg and did the reverse. I also added the a's)
which means a = 120kg divided by 4
a = 30kg
HELP ASAP WILL GIVE BRAINLIEST!! Write the equation in point-slope form for the line that contains the points
(-2,-3).(4.3)
Answers
Slope-intercept form:
y=x-1
Point-slope form:
Y+3=1(x+2)
jazz sold 1/2 sack of vegetable pear and 5/2 sack of squash. how many sacks of vegetables did he sell altogether?
Answers
Answer:
Jazz sold 3(6/2)sacks of vegetables.
Step-by-step explanation:
5/2 + 1/2 = 6/2. If you convert 6/2 into a mixed number you get 3.
Find the perimeter of a square that has a side length of 4.3x + 2 inches.
Answers
The calculated perimeter of the square from the side length is 17.2x + 8
Finding the perimeter of a square from the side lengthFrom the question, we have the following parameters that can be used in our computation:
A square that has a side length of 4.3x + 2 inches.
Using the above as a guide, we have the following:
Perimeter = 4 * side length
Substitute the known values in the above equation, so, we have the following representation
Perimeter = 4 * (4.3x + 2)
When teh brackets are opened, we have
Perimeter = 17.2x + 8
Hence, the perimeter is 17.2x + 8
Read more about perimeter at
https://brainly.com/question/19819849
#SPJ1
Im an older lady not the best at this type of math please help
Answers
We need to first find the intersection between Q and R, which is the common elements between both groups. We have:
\(Q\cap R=\mleft\lbrace r,e,x\mright\rbrace\)Now we need to determine the union between them:
\(P\cup(Q\cap R)=\mleft\lbrace e,x,a,c,t,r,e,x\mright\rbrace\)which cannot be probabilities:
square root of 2, 0, -53, .08, 5/3, 3/5, 1.31
Answers
The numbers that cannot be probabilities are: square root of 2, -53, 5/3, and 1.31.
Probability is a measure of the likelihood of a particular event occurring in a random experiment. It is a value between 0 and 1, with 0 indicating that an event is impossible, and 1 indicating that an event is certain to occur.
In statistics, probability is used to make predictions or draw inferences about a population based on a sample of data. For example, if we were to flip a coin, the probability of getting heads is 0.5, or 50%. In general probability can be defined as the ratio of the number of favorable outcomes to the total number of possible outcomes, which is the mathematical framework behind the random experiments.
From the set of numbers, 0, 0.08, and 3/5 are all possible values of probability.
Therefore, square root of 2, -53, 5/3, and 1.31 cannot be probabilities.
Learn more about probability here: https://brainly.com/question/24756209
#SPJ4
In the triangle below, suppose that m ZA= (x+7)°, mZB=(7x−3)°, and m≤ C= (3x)°.
Find the degree measure of each angle in the triangle.
(7x - 3)º
A4
(x + 7)⁰
B
(3x)
Someone anyone help me on this:,)
Answers
Answer:
m(A) = 23°
m(B) = 109°
m(C) = 48°
Step-by-step explanation:
. The coordinates of a triangular piece of a mobile are (0, 4) , (3, 8) , and (6, 0) . The piece will hang from a chain so that it is balanced. At what coordinates should the chain be attached
Answers
The chain should be attached at (3, 4) to balance the triangular piece of the mobile.
To find the coordinates where the chain should be attached to balance the triangular piece of the mobile, we can determine the centroid of the triangle. The centroid is the point of intersection of the medians, which are line segments connecting each vertex of the triangle to the midpoint of the opposite side.
Using the given coordinates: (0, 4), (3, 8), and (6, 0), we find the midpoints of the sides: (1.5, 6), (4.5, 4), and (3, 2). The centroid is the average of these midpoints: (3, 4).
Therefore, the chain should be attached at the coordinates (3, 4) to achieve balance. This point represents the center of mass of the triangular piece, ensuring equal distribution of weight and stability when hung from a chain.
To learn more about “centroid” refer to the https://brainly.com/question/7644338
#SPJ11