Answer:
The positive value of k that the function y = sin(kt) satisfies the differential equation y'' + 144y = 0 is +12
Step-by-step explanation:
To determine the positive values of k that the function y = sin(kt) satisfy the differential equation y''+144y=0.
First, we will determine y''.
From y = sin(kt)
y' = [tex]\frac{d}{dt}(y)[/tex]
y' = [tex]\frac{d}{dt}(sin(kt))\\[/tex]
y' = kcos(kt)
Now for y''
y'' = [tex]\frac{d}{dt}(y')[/tex]
y'' = [tex]\frac{d}{dt}(kcos(kt))[/tex]
y'' = [tex]-k^{2}sin(kt)[/tex]
Hence, the equation y'' + 144y = becomes
[tex]-k^{2}sin(kt)[/tex] + [tex]144(sin(kt))[/tex] [tex]= 0[/tex]
[tex](144 - k^{2})(sin(kt)) = 0[/tex]
[tex](144 - k^{2})= 0[/tex]
∴ [tex]k^{2} = 144\\[/tex]
[tex]k =[/tex] ±[tex]\sqrt{144}\\[/tex]
[tex]k =[/tex] ± [tex]12[/tex]
∴ [tex]k = +12[/tex] or [tex]-12[/tex]
Hence, the positive value of k that the function y = sin(kt) satisfies the differential equation y'' + 144y = 0 is +12
The positive value of k that satisfies the differential equation is k = 12.
To find the value of k that satisfies the equation, we differentiate the function y = sin(kt) twice to obtain y" and we insert it into the differential equation y" + 144y = 0.
So, y' = dy/dt
= dsin(kt)/dt
= kcos(kt)
y" = dy'/dt
y" = dkcos(kt)/dt
y" = -k²sin(kt)
So, substituting y and y" into the differential equation, we have
y" + 144y = 0
-k²sin(kt) + 144sin(kt) = 0
-k²sin(kt) = -144sin(kt)
k² = 144
k = ±√144
k = ±12
Since we require a positive value, k = 12
So, the positive value of k that satisfies the differential equation is k = 12.
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Can someone help me out
3/196
Step-by-step explanation:
multiply everything
Evaluate. (1/4)^−2−(5^0⋅2)⋅1^−1 Enter your answer in the box. HELP! 100 POINTS!
Answer:
[tex]\Huge \boxed{\mathrm{14}}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Step-by-step explanation:
[tex](\frac{1}{4} )^{-2} - (5^0) (2)(1^{-1})[/tex]
Solving for exponents and multiplying:
[tex](4 )^{2} - (1) (2)(1)[/tex]
[tex]16-2[/tex]
Subtracting:
[tex]\Rightarrow \ 14[/tex]
[tex]\rule[225]{225}{2}[/tex]
Answer:
[tex]\huge\boxed{14}[/tex]
Step-by-step explanation:
[tex]\sf (\frac{1}{4} )^{-2} - (5^0 * 2 )* (1^{-1})[/tex]
Using law of exponents [tex]a^0 = 1[/tex] and [tex]1/a^m = a^{-m}[/tex]
=> [tex]4^2 - (1*2)*(1)[/tex]
=> [tex]16 - 2[/tex]
=> 14
Given the word "Nutrition", what is the probability of picking a "t" when randomly
selecting a letter? (decimal rounded to hundredth)
Answer:
0.2 repeating
Step-by-step explanation:
A number is 9 more than another number. Twice the sum of the two numbers is 10. Find the two numbers.
Answer:
7, -2
Step-by-step explanation:
we call the first number "X" and the second one "Y"
X is 9 more than Y! which means we need to add 9 to Y so it'll be equal to X. so: Y+9=X
also 2×(X+Y)=10
you can also write this down as: 2X+2Y=10
now we have:
X=Y+9
2X+2Y=10
you can now put what equals to X in the second Equation:
2(Y+9)+2Y=10 => 2Y+18+2Y=10 => 4Y=10-18 =>Y= -2
the only thing left to do is to put Y= -2 in the first equation:
X= -2+9 => X=7
An algebraic equation is an equation with unknown variables which can be represented using any number of the alphabet.
The two numbers are 7 and -2
Let's represent the unknown numbers which are the unknown variables with the letters
Let the first number = m
The second number = n
A number is 9 more than another number. This statement is represented by the algebraic equation:
m = 9 + n .......... Equation 1
Twice the sum of the two numbers is 10. This statement is represented by the algebraic equation:
2 (m + n) = 10
2m + 2n = 10...................Equation 2
We substitute 9 + n for "m" in Equation 2
2(9 + n) + 2n = 10
18 + 2n + 2n = 10
Subtract 18 from both sides
18 - 18 + 2n + 2n = 10 - 18
4n = -8
Divide both sides by 4
4n/4 = -8/4
n = -2
We solve for m using Equation 1
m = 9 + n
m = 9 + (-2)
m = 9 - 2
m = 7
Therefore, the two numbers are 7 and -2
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For this exercise, use the following set of 16 scores (ranked) that con- sists of income levels ranging from about $50,000 to about $200,000. What is the best measure of central tendency and why? $199,999 $98,789$90,878 $87,678 $87,245 $83,675 $77,876 $77,743 $76,564 $76,465 $75,643 $66,768 $65,654 $58,768 $54,678 $51,354
Answer:
The median = Median = $77,153.5
Step-by-step explanation:
Given the data :
199999 98789 90878 87678 87245 83675 77876 77743 76564 76465 75643 66768 65654 58768 54678 51354
Measures of central tendency are used to describe the center or midpoint of a group of observation. They could include the mean, median and mode.
Mean described the average value of the distribution
Median, the middle observation.
Mode, the observation which occurs most
Using online calculator to save time ;
the mean = 83,111.06
Median = 77153.5
For the mode, all the values have a frequency of 1
Plotting the data on an histogram, it could be observed that the Data is positively skewed and hence, not symmetrical.
Since the distribution is not symmetrical, using the mean isn't the best and the mode is also not usable.
Therefore, the median seems to be the best of the 3 measures
Solve 3/5 + 3/2 (Btw it can only be shown as a mixed number)
How many tens and ones equals 4 tens. And 6 ones
Answer: 46
Step-by-step explanation:
Solve the following System of Three Equations:
x−3y+z=−15
2x+y−z=−2
x+y+2z=1
Answer:
x = -3 , y = 4 , z = 0
Step-by-step explanation:
Solve the following system:
{x - 3 y + z = -15
2 x + y - z = -2
x + y + 2 z = 1
Hint: | Choose an equation and a variable to solve for.
In the first equation, look to solve for z:
{x - 3 y + z = -15
2 x + y - z = -2
x + y + 2 z = 1
Hint: | Solve for z.
Subtract x - 3 y from both sides:
{z = 3 y + (-x - 15)
2 x + y - z = -2
x + y + 2 z = 1
Hint: | Perform a substitution.
Substitute z = -15 - x + 3 y into the second and third equations:
{z = -15 - x + 3 y
15 + 3 x - 2 y = -2
x + y + 2 (-15 - x + 3 y) = 1
Hint: | Expand the left hand side of the equation x + y + 2 (-15 - x + 3 y) = 1.
x + y + 2 (-15 - x + 3 y) = x + y + (-30 - 2 x + 6 y) = -30 - x + 7 y:
{z = -15 - x + 3 y
15 + 3 x - 2 y = -2
-30 - x + 7 y = 1
Hint: | Choose an equation and a variable to solve for.
In the second equation, look to solve for x:
{z = -15 - x + 3 y
15 + 3 x - 2 y = -2
-30 - x + 7 y = 1
Hint: | Isolate terms with x to the left hand side.
Subtract 15 - 2 y from both sides:
{z = -15 - x + 3 y
3 x = 2 y - 17
-30 - x + 7 y = 1
Hint: | Solve for x.
Divide both sides by 3:
{z = -15 - x + 3 y
x = (2 y)/3 - 17/3
-30 - x + 7 y = 1
Hint: | Perform a substitution.
Substitute x = (2 y)/3 - 17/3 into the third equation:
{z = -15 - x + 3 y
x = (2 y)/3 - 17/3
(19 y)/3 - 73/3 = 1
Hint: | Choose an equation and a variable to solve for.
In the third equation, look to solve for y:
{z = -15 - x + 3 y
x = (2 y)/3 - 17/3
(19 y)/3 - 73/3 = 1
Hint: | Isolate terms with y to the left hand side.
Add 73/3 to both sides:
{z = -15 - x + 3 y
x = (2 y)/3 - 17/3
(19 y)/3 = 76/3
Hint: | Solve for y.
Multiply both sides by 3/19:
{z = -15 - x + 3 y
x = (2 y)/3 - 17/3
y = 4
Hint: | Perform a back substitution.
Substitute y = 4 into the first and second equations:
{z = -x - 3
x = -3
y = 4
Hint: | Perform a back substitution.
Substitute x = -3 into the first equation:
{z = 0
x = -3
y = 4
Hint: | Sort results.
Collect results in alphabetical order:
Answer: {x = -3 , y = 4 , z = 0
BD bisects ∠ABC. Find m∠ABD and m∠CBD
Answer:
Since BD bisects angle ABC, the resultant angles, angles ABD and CBD will be equal in magnitude. Since we are not given either the value of ABC nor are we given the figure, the answer we can get to from the given question is
angle ABD = angle CBD
Mic
Point A is at ( – 6. 8) and point B is at (6, -7)
What is the midpoint of line
segment AB?
Answer:
(0, 0.5)
Step-by-step explanation:
Let M is the midpoint of the line
x-coordinate of the midpoint:
xM = ( xA + xB ) / 2 = (-6 + 6) / 2 = 0
y-coordinate of the midpoint:
yM = (yA + yB) / 2 = (8 - 7) / 2 = 1/2 = 0.5
Answer: M (0, 0.5)
Answer:
(0, 0.5)
Step-by-step explanation:
The Distribution of Sample Means expresses the way in which sample means taken from a population and of a given sample size are distributed around the population mean.
a. True
b. False
Answer:
This is true
Step-by-step explanation:
Because a distribution of sample means is as the set of means from all the possible random samples of a specific size, selected from a specific given population.
3=7-2(3z+2)
How to solve
Answer: z = 0 | Equation is not solvable
Step-by-step explanation:
We have 3 = 7 - 2(3z + 2)
When we distribute the 2, we get: -6z - 4 + 7 = 3
Combine like terms: -6z + 3 = 3
Subtract the left hand side 3 from the right hand side 3: -6z = 0
We can not divide by zero thus the equation is not solvable.
the sum of two numbers is 87. One of the numbers is 6 more than twice the other. what are the two numbers?
Answer:
27 and 60
Step-by-step explanation:
lets say the first number 'a' and the second number 'b'
1) The question says the sum of two number is 87 which means a + b = 87........given 1
2) we have another given which says one of the number is 6 morethan twice the other which means a = 2b + 6.......... given 2
a + b = 87
2b + 6 + b = 87 (we substitute 'a' with the given 2b + 6)
3b + 6 = 87
3b = 87 - 6
3b = 81
3b = 81
3 3
b = 27 ..... the first number
a = 2b + 6
a = 2 × 27 + 6
a = 54 + 6
a = 60..... the second number
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For any question comment me
What kind of lines are the edges of the length and the width of a piece of printer paper? A. parallel lines B. perpendicular lines C. neither
Answer:
[tex]\huge\boxed{B. \ Perpendicular \ Lines}[/tex]
Step-by-step explanation:
The edges of length and width of a piece of printer paper perpendicularly intersect each other.
=> Perpendicular Lines are those making an angle of 90 degrees with each other.
Answer:
Perpendicular lines
Step-by-step explanation:
H.
How to solve 14x + 2 = 6 (x - 0)
Answer:
Has not solution.
Step-by-step explanation:
14x÷2 = 6(x - 0)
14x÷2 = 6*x + 6*-0
14x÷2 = 6x - 0
14x = 2*6x
14x ≠ 12x
then:
This equation has not solution.
Six friends want to play enough games of chess to be sure every one plays everyone else. How many games will they have to play
Answer: 15 games
Step-by-step explanation:
Which shows a list of the first six prime numbers?
1, 3, 5, 7, 9, 11
1, 2, 3, 5, 7, 9
2, 3, 5, 7, 9, 11
2, 3, 5, 7, 11, 13
Answer:
Step-by-step explanation:
the fourth option shows a list of the first 6 prime numbers
Answer: Option 4. 2, 3, 5, 7, 11, 13
Step-by-step explanation:
Remember, 1 is neither a prime number nor a composite number, it only has one factor.
So, we can exclude the first and second choice.
The third one has 9. But 9 is not a prime number.
Factor of 9: 1, 3, 9
It has 3 factors
So, this is not prime number and it should be excluded.
The fourth one is a complete list of prime numberHope this helps!! :)
Please let me know if you have any question
Use Lagrange multipliers to minimize the function f(x,y,z)=x2 +y2 +z2
subject to the following constraint: x+y+z-24=0
Assume that x, y, and z are positive
Question options :
A)64
B)192
C)128
D)384
Answer:
B)192
Step-by-step explanation:
Please find attachment
Isabella decides to sell handmade stationery. She decides to sell 2 cards for $9. Which table below show the possible values of c, the number of cards Isabella sells, and d, the number of dollars she charges?
Answer:
G.
Step-by-step explanation:
cards = 2
dollars = 9
to check that the number of cards with the correct amount d;
use the ratio and proportion.
(3 x 18)/9 = 4
(4 x 31.5)/18 = 7
(7 x 45)/31.5 = 10
therefore, option G. table G. is the correct answer
try doing the ratio and proportion on the other table and the number of cards DO NOT match with the amount. (see attached)
Which shape best describes the distribution of the following data? 1, 15, 36, 6 67,68, 68, 68, 69, 69, 69, 69, 70, 70, 70, 70, 70, 71, 71, 72 a. normal b.bimodal c.positively skewed d.negatively skewed
Answer: d.negatively skewed
Step-by-step explanation:
1
15
36
6
67
68
68
68
69
69
69
69
70
70
70
70
70
71
71
72
The distribution with the data above is negativey skewed. This was inferred from the histogram plot generated from the data.The output shows a distribution which has a long tail to the left and peaks to the right. This characteristics describes a distribution which is negatively skewed. Diagram of the obtained histogram for the distribution can be found in the attachment below.
Each statement describes a transformation of the graph of F(x) = x. Which statement correctly describes the graph of g(x) if g(x) = f(x) - 3?
Answer: B) Shift 3 units down
Recall that y = f(x) as both describe outputs of a function. The same applies for g(x) as well. Saying f(x)-3 means y-3. So we're subtracting 3 from the y coordinate of each point. A point like (1,5) moves to (1,2). Doing this to all points on f(x) will move the entire curve down 3 units.
If 3a/b -6= 21, what is the value of a/b?
Answer:
[tex]\Huge \boxed{9}[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{3a}{b} -6= 21[/tex]
Add 6 to both sides.
[tex]\displaystyle \frac{3a}{b} =27[/tex]
Dividing both sides by 3.
[tex]\displaystyle \frac{a}{b} = 9[/tex]
Use the simple interest formula to determine the missing value. p=?, r=6%, t=9 months, i=81
Answer:
P = 1800
Step-by-step explanation:
The formula to calculate simple interest (I) is
I = [tex]\frac{PRT}{100}[/tex] ( note that time is in years ), thus
9 months = [tex]\frac{9}{12}[/tex] = [tex]\frac{3}{4}[/tex] = 0.75 years
Thus
81 = [tex]\frac{P(6)(0.75)}{100}[/tex] ( multiply both sides by 100 )
8100 = 4.5P ( divide both sides by 4.5 )
P = 1800
X = 1/7y - 9
X + 9 = 1/7
7x + 63 = y
Y = 7x + 63
Answer:
9x
Step-by-step explanation:
X=1/7y-9
X+9=1/7
7x + 63 = y
Y=7x+63
Y-7x=63
Y=63/7x
Y=9x
At walmart, a bar of soap costs $3.96 plus 8% sales tax. What is the total cost of a bar soap? Round to the nearest cent.
$4.27
(3.96) 1.08
4.27
What is the greatest common factor of 25 and 80?
Answer:
GCF of 25 and 80 = 5
Answer:
GCF of 25 and 80 is 5
Step-by-step explanation:
Given an isosceles right triangle with side 6 m, what is the length of the hypotenuse?
Show work please
Answer: 6√2m or 8.49.
Step-by-step explanation:
Drawing the right angled triangle and label the sides, AC, which is the hypotenuse and the longest, AB , one if the sides, and BC the third sides. Since it is an isosceles right angle triangle with the right angle at B, based on my own diagram here, two of the sides are equal.
AB = BC = 6m
Now to find the hypotenuse, we apply the Pythagoras theorem which states that the square of the sum of the two sides equal the square of the hypotenuse side.That is
AC² = AB² + BC²
AC² = 6² + 6²
= 36. + 36
= 72
AC² = 72, Therefore, AC which is the hypotenuse
AC = √72
= √36 × √2
= 6√2m. or 8.49m
PLEASEEEEE HELPPP MEEE WITHH THIS QUESTIONN PLEASEEE
Answer: A
Step-by-step explanation:
To find the average rate of change, you use the formula [tex]\frac{f(b)-f(a)}{b-a}[/tex]. The best way to get the correct answer is to plug in each interval to make sure it equals 0.
-1 ≤ x ≤ 2: Correct
[tex]\frac{f(2)-f(-1)}{2-(-1)}[/tex] [solve for f(2) and f(1)]
[tex]\frac{1-1}{3}=\frac{0}{3} =0[/tex]
------------------------------------------------------------------------------------------------------
-3 ≤ x ≤ -2: Incorrect
[tex]\frac{f(-2)-f(-3)}{-2-(-3)}[/tex] [solve for f(-2) and f(-3)]
[tex]\frac{5-11}{1} =\frac{-6}{1}=-6[/tex]
------------------------------------------------------------------------------------------------------
-5 ≤ x ≤ 5: Incorrect
[tex]\frac{f(5)-f(-5)}{5-(-5)}[/tex] [solve for f(5) and f(-5)]
[tex]\frac{19-29}{10} =\frac{-10}{10} =-1[/tex]
------------------------------------------------------------------------------------------------------
2 ≤ x ≤ 3: Incorrect
[tex]\frac{f(3)-f(2)}{3-2}[/tex] [solve for f(3) and f(2)]
[tex]\frac{5-1}{1} =\frac{4}{1} =4[/tex]
------------------------------------------------------------------------------------------------------
After going through all the intervals, we found that A was the only one that has an average rate of change of 0.
Abigail is putting juice into cone-shaped containers to make frozen treats. She has approximately one quarter of a gallon, or 58 cubic inches, of juice to make the treats with. Each
container has a height of 3 inches.
Use the information to complete the table indicating the maximum number of treats that Abigail could make with 58 cubic inches of juice.
Answer/Step-by-step explanation:
Maximum number of treats = amount of juice (58 in³) ÷ volume of cone-shaped container to be used
We are given different containers with the same height of 3 in, but different radius. Volume of a cone is given as ⅓*πr²h
Complete the table as follows:
Maximum no. of treats to be made with container of radius (r) 0.5 in, height 3 in:
Take π as 3.14
Volume = ⅓*3.14*0.5²*3 = 0.79 in³
Max no. of treats = 58 ÷ 0.79 = 73.4
73 containers can be filled completely. Therefore, maximum number of treats she could make is 73
Maximum no. of treats to be made with container of radius (r) 1 in, height 3 in:
Take π as 3.14
Volume = ⅓*3.14*1²*3 = 3.14 in³
Max no. of treats = 58 ÷ 3.14 = 18.5
18 containers can be filled completely, therefore, maximum number of treats to be made with this cone is 18 treats.
Maximum no. of treats to be made with container of radius (r) 1.5 in, height 3 in:
Take π as 3.14
Volume = ⅓*3.14*1.5²*3 = 7.07 in³
Max no. of treats = 58 ÷ 7.07 = 8.2
Max no of treats to be made is 8.
Divide. 19,432 and 56 pls help me
Answer:
347
Step-by-step explanation: