The values of k that satisfy the equation 4y'' = -9y for the function y = cos kt are k = ±3/2.
Explanation:This is a question in differential equations, where we are given a cosine function y = cos kt and asked to find values of k that satisfy the given equation 4y'' = −9y.
Recall, the second derivative of cos kt is -k²cos kt which is equivalent to -k²y.
Substituting that into the differential equation, we get 4(-k²y) = -9y. If we simplify this, we get k² = 9/4. Therefore, the values of k which satisfy the given equation are k = ±3/2.
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The values of k that satisfy the differential equation 4y'' = −9y are k = ±3/2.
We can find the values of k that satisfy the differential equation 4y'' = −9y by solving for k.
First, we can rewrite the differential equation in its general form:
ay'' + by' + cy = 0
where a = 4, b = 0, and c = -9.
Next, we can find the characteristic equation:
ar^2 + br + c = 0
Plugging in the values of a, b, and c, we get:
4r^2 + 0r - 9 = 0
Solving for r, we get:
r = ±3/2
Therefore, the general solution to the differential equation is:
y = Acos(3t/2) + Bsin(3t/2)
where A and B are arbitrary constants.
Finally, we can substitute y = cos kt into the original differential equation and solve for k:
4k^2cos kt + 9cos kt = 0
Dividing both sides by cos kt, we get:
4k^2 + 9 = 0
Solving for k, we get:
k = ±3/2
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Rectangle A measures 12 cm by 3 cm. Rectangle B is a scaled copy of Rectangle A. Select all of the measurement pairs that could be the dimensions of Rectangle B.
A. 6 cm by 1.5 cm
B.10 cm by 2 cm
C. 13 cm by 4 cm
D.18 cm by 4.5 cm
E.80 cm by 20 cm
Answer:
A
Step-by-step explanation:
The scale copy of a shape is the resulting shape when the original shape is dilated. Possible scaled rectangles of rectangle A are:
A. 6cm by 1.5cm because
D. 18cm by 4.5cm because
E. 80cm by 20cm because
Given that
[tex]Length = 12cm[/tex]
[tex]Width = 3cm[/tex]
Divide the length and the width of the rectangle
[tex]k = Length \div Width[/tex]
[tex]k = 12cm \div 3cm[/tex]
[tex]k = 4[/tex]
This means that a scaled copy of rectangle A must have a value of 4 when the dimensions are divided.
Possible rectangles are:
A. 6cm by 1.5cm because [tex]6cm \div 1.5cm = 4[/tex]
D. 18cm by 4.5cm because [tex]18cm \div 4.5cm = 4[/tex]
E. 80cm by 20cm because [tex]80cm \div 20cm = 4[/tex]
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6 shirts 4 different pairs of pants, how many different combinations could she wear?
The vertices of ΔABC are (-2,0), (-2, 3), and (-5, 1). T(x,y) = (x + 1, 3y) represents the transformation of the triangle. What are the coordinates of the vertices for ΔA'B'C'? Are the pre-image and image congruent? Justify your answer.
using the equation for the transformation:
(x+1, 3y)
add 1 to very X and multiply y by 3
so (-2,0) becomes (-1,0)
(-2,3) becomes (-1,9)
(-5,1) becomes (-4,3)
new coordinates are (-1,0) (-1,9) (-4,3)
you don't have an image attached, so to see if they are congruent, the sides need to stay the same lengths and the angles need to stay the same, from the coordinates of the new triangle, I would say they are not congruent
which container holds more a half gallon milk jug or a 2 L juice bottle
Which postulate or theorem proves that these two triangles are congruent?
ASA Congruence Postulate
SAS Congruence Postulate
HL Congruence Theorem
AAS Congruence Theorem
Answer:
AAS Congruence Theorem
Step-by-step explanation:
i dont know bro
Answer: AAS Congruence Theorem
Step-by-step explanation:
In the given picture , we have given two triangles ΔFGJ and ΔHJG with one common edge i.e. GJ
Now, in the given triangles ΔFGJ and ΔHJG we have
∠F=∠H [given]
and ∠FGJ=∠HJG [given]
Also, GJ=GJ [Reflexive property]
Therefore, by AAS Congruence Theorem,
ΔFGJ ≅ ΔHJG
AAS Congruence Theorem says that if any two angles and a side one triangle are congruent to any two angles and a side of another triangle, then these two triangles are congruent.limit as x approaches 0 of csc3x/cotx
The limit of csc(3x)/cot(x) as x approaches 0 is 1, after applying trigonometric identities and the properties of limits.
Explanation:The student is asking for the limit of the function csc(3x)/cot(x) as x approaches 0. This is a limit problem in calculus, which is a part of mathematical analysis that deals with the behavior of functions near certain points. To find the limit as x approaches 0 for the function csc(3x)/cot(x), we need to apply trigonometric identities and the properties of limits. The function csc(3x) can be rewritten as 1/sin(3x) and cot(x) as cos(x)/sin(x). So the original limit becomes:
lim(x → 0) [csc(3x)/cot(x)] = lim(x → 0) [(1/sin(3x)) × (sin(x)/cos(x))].
Using the trigonometric limit lim(x → 0) (sin(x)/x) = 1 and lim(x → 0) (cos(x)) = 1, we can simplify the expression by substituting 3x for x in the limit sin(x)/x. We get:
lim(x → 0) [(1/sin(3x)) × (sin(x)/cos(x))] = lim(x → 0) [(sin(x)/cos(x)) × (1/(3sin(3x)))] × (3x/x).
As x approaches 0, cos(x) approaches 1 and 3x/x approaches 3, hence:
lim(x → 0) [(sin(x)/cos(x)) × (1/(3sin(3x)))] × (3x/x) = lim(x → 0) (sin(x)/x) × lim(x → 0) 1/cos(x) × lim(x → 0) (3x/3sin(3x)) = 1 × 1 × (3/3) = 1.
The final limit of csc(3x)/cot(x) as x approaches 0 is 1.
Mrs. Williams is knitting a blanket for her newborn granddaughter. The blanket is 2.25 meters long and 1.8 meters wide. What is the area of the blanket? Write the anwser in centimeters.
Solve the inequality -×/7+4>3×.
Determine whether the origin is included in the shaded region and whether the shaded region is above or below the line for the graph of the following inequality: y < 3/2x + 2
The origin is not included in the shaded region and the shaded area is above the line.
The origin is not included in the shaded region and the shaded area is below the line.
The origin is included in the shaded region and the shaded area is above the line.
The origin is included in the shaded region and the shaded area is below the line.
Answer
third option
Step-by-step explanation:
In May, there were 157 people living in Kristin's neighborhood. By August, the population had increased 21%. How many people were in Kristin's neighborhood by August?
A.330
B.190
C.33
D.1900
Some of the cds produced by a manufacturer are defective. from the production line, 5 cds are selected and inspected. how many sample points exist in this experiment?
Final answer:
There are 32 sample points in this experiment.
Explanation:
In this experiment, the manufacturer selects 5 CDs from the production line to inspect. To determine the number of sample points in this experiment, we need to consider the possible outcomes for each CD. For each CD, it can either be defective or non-defective, meaning there are 2 possible outcomes. Since there are 5 CDs being inspected, we multiply the number of outcomes for each CD by itself 5 times to find the total number of sample points. Therefore, there are 32 sample points in this experiment.
Therefore, the total number of sample points in this experiment is 32, calculated by multiplying the number of outcomes for each CD (2) by itself 5 times . This accounts for all possible combinations of defective and non-defective CDs in the sample of 5.
If n people are seated in a random manner in a row containing 2n seats, what is the probability that no two people will occupy adjacent seats? 10. a box contains 24 light bulbs, o
To find the probability that no two people will occupy adjacent seats, consider that n people are seated in a random manner in a row containing 2n seats. Using counting rule for combinations the total number of ways to select n seats of 2n seats is N=(2n/n).
Now consider an event M that all two people occupy adjacent seats. This can be done by occupying all odd seats so that the even seats are left empty. This arrangement leaves the last 2nth seat empty. Even if one occupies that seat the condition of the event will not break. So, we have (n + 1) seats available for the n people to seat so that no two people occupy adjacent seats. N(M) = (n+1). Thus, the probability that no two people will occupy adjacent seats in a row of 2n seats can be computed as shown :
The probability that no two people will occupy adjacent seats is [(2n-1)!!]/[(2n)!].
Explanation:To find the probability that no two people will occupy adjacent seats, we need to count the total number of possible arrangements where no two people are seated next to each other, and divide it by the total number of possible arrangements.
Let's consider a scenario where we have 2 people and 4 seats. In this case, the possible arrangements where no two people are seated next to each other are:
_ A _ A _A _ A __ A _ ASo, there are 3 possible arrangements where no two people are seated next to each other out of the total 6 possible arrangements.
Generalizing this, for n people seated in a row containing 2n seats, there are (2n-1)!! possible arrangements where no two people are seated next to each other. The double exclamation mark denotes the double factorial.
Hence, the probability is [(2n-1)!!]/[(2n)!].
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A market sells bananas for $0.69 per pound. Which expression represents the cost, in dollars, of p pounds of bananas? 1 p/69 2 0.69p 3 p/0.69 4 69p
Answer:
Option 2. 0.69p
Step-by-step explanation:
A market sells bananas for = $0.69 per pound
The cost, in dollars of p pounds of bananas = 0.69 × p
So the expression represents the cost, in dollars of p pounds of bananas
= 0.69p
Option 2. 0.69p is the right answer.
A clydesdale drinks about 120 gallons of water every 4 days.At this rate,about how many gallons of water does a clydesdale drink in 28 days
Segments and angles practice with special angles find the measures of the lettered angles
find the value of x
Line segment AB is the perpendicular bisector of line segment XZ. Which statement is true? A) XZ = AB B) XB = XZ C) ∠ABZ = ∠ABX D) ∠BAZ = ∠ABX
A perpendicular bisector is a special type of bisector because it intersects a segment at a 90 degree angle, and it passes through the segments midpoint.
Therefore based from this, we can create two true statements:
XB = BZ
and
∠ABZ = ∠ABX
Therefore the answer is:
C
Answer:
The answer is C. <ABZ = <BAX hop this hope this help
The organizers of a drama club wanted to sell 350 tickets to their show.The actual sales were no more than 35 tickets from his goal.Write an d solve an absolute value inequality to find the range of the number of tickets that could have been sold
y=x^2+8x+6 16x-2y=-44
The function shown is reflected across the y-axis to create a new function.
Which is true about the domain and range of each function?
A.Both the domain and range change.
B.Both the range and domain stay the same.
C.The domain stays the same, but the range changes.
D.The range stays the same, but the domain changes
Reflecting a function across the y-axis will not change its domain or range; for an even function, such as one described by y(x) = -y(-x), the function is inherently symmetric about the y-axis, and thus both the domain and range remain unchanged.
Explanation:When a function is reflected across the y-axis, its domain and range may be impacted. Reflecting a function across the y-axis replaces each point (x, y) with (-x, y). If the original function is y(x) = -y(-x), then we are dealing with an even function, which is symmetric about the y-axis. In the case of even functions, reflecting them across the y-axis does not change the graph because they are already symmetric. Hence, the domain and the range of the function remain the same after the reflection.
The domain of a function is the set of all possible x-values, and the range is the set of all possible y-values. For a function reflected across the y-axis, the x-values are negated, but since the domain typically includes both positive and negative values for x, the overall set of possible x-values (the domain) does not change. Moreover, the y-values stay the same since they are not affected by the reflection across the y-axis, and thus the range remains the same as well.
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Reflecting a function across the y-axis will not change its domain or range; for an even function, such as one described by y(x) = -y(-x), the function is inherently symmetric about the y-axis, and thus both the domain and range remain unchanged.
The correct option is A. Both the domain and range change.
When a function is reflected across the y-axis, its domain and range may be impacted. Reflecting a function across the y-axis replaces each point (x, y) with (-x, y). If the original function is y(x) = -y(-x), then we are dealing with an even function, which is symmetric about the y-axis. In the case of even functions, reflecting them across the y-axis does not change the graph because they are already symmetric. Hence, the domain and the range of the function remain the same after the reflection.
The domain of a function is the set of all possible x-values, and the range is the set of all possible y-values. For a function reflected across the y-axis, the x-values are negated, but since the domain typically includes both positive and negative values for x, the overall set of possible x-values (the domain) does not change. Moreover, the y-values stay the same since they are not affected by the reflection across the y-axis, and thus the range remains the same as well.
The correct option is A. Both the domain and range change.
the slope of the line below is 2/5 and the y-intercept is (0,4) what is the slope intercept equation of the line?
Describe how to graph the solution of y ≤ −x² + 2x.
Multiply 5 4/7 × -2 2/5
A) -10 8/35
B) 10 8/35
C) -13 13/35
D) 13 13/35
A recipe calls for 40 ounces of meat. How many pounds of meat does the recipe require?
The recipe requires 2.5 pounds of meat.
we have,
To convert ounces to pounds, we use the conversion factor that 16 ounces is equal to 1 pound.
This means that every pound is made up of 16 ounces.
Given that the recipe calls for 40 ounces of meat, we can divide this quantity by the conversion factor of 16 ounces per pound to find the equivalent in pounds.
Dividing 40 by 16 gives us 2.5. So, the recipe requires 2.5 pounds of meat.
This conversion is based on the relationship between ounces and pounds, where each pound consists of 16 ounces.
So,
When converting from ounces to pounds, we divide the number of ounces by 16 to find the equivalent number of pounds.
Therefore,
The recipe requires 2.5 pounds of meat.
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what is 2 1/3 divided by 2/5
Select the function that represents the transformation of the parent function three units to the left and up two.
f(x) = |x - 3| - 2
f(x) = -|x - 3| + 2
f(x) = |x + 3| + 2
f(x) = -|x + 3| + 2
Answer:
The correct option is C. f(x) = |x + 3| + 2
Step-by-step explanation:
The parent function in this case is : mod x = |x|
Let the parent function be f(x) = |x|
Now, The parent function is transformed 3 units to the left
⇒ f (x) = f(x + 3)
⇒ f(x) = |x + 3|
Also, The parent function is transformed up by 2 units
⇒ f(x) = f(x) + 2
⇒ f(x) = |x + 3| + 2
Therefore, The correct option is C. f(x) = |x + 3| + 2
N a triangle, the measure of the first angle is twicetwice the measure of the second angle. the measure of the third angle is 68 degrees68° more than the measure of the second angle. use the fact that the sum of the measures of the three angles of a triangle is 180degrees° to find the measure of each angle.
A minivan can hold up to 7 people how many minivans are needed to take 45 people to a baseball game
The quotient of the number of students and 3
Answer:
This can be written as x/3, in which x is the number of students.
Step-by-step explanation:
The term quotient means to find what happens when you divide the first by the second. Then we need to pick a variable for the unknown number of students.
Reduce fractions expressing probability to lowest terms. in 3,000 repetitions of an experiment, a random event occurred in 500 cases. the expected probability of this event is? 1/6 5/5 1/3 2/3