Answers
If y = cos(kt), then its first two derivatives are
y' = -k sin(kt)
y'' = -k² cos(kt)
Substituting y and y'' into 49y'' = -16y gives
-49k² cos(kt) = -15 cos(kt)
⇒ 49k² = 15
⇒ k² = 15/49
⇒ k = ±√15/7
Note that both values of k give the same solution y = cos(√15/7 t) since cosine is even.
Related Questions
NEED HELP RELATIONSHIP IN TRIANGLES
Answers
Answer:
Step-by-step explanation:
10x-13=17x-41
DO YOUR WORK
here is a picture
five men can repair a stretch of road in 8 hrs. how many men would be needed to repair the same road in 3 1/3 hrs
also tell if its direct or inverse proportion
i just wanna check my answer, whether its correct or not
Answers
Answer: 12 men would be needed to repair the same road in 3 1/3 hrs. Inverse proportion because usually in work,food and time its inversly proportional.
8 hours --> 5 men
1 hour --> 5*8 = 40 men
3 1/3 hours --> 40/ (3 1/3) men
--> 12 men
A group of scientists is conducting an experiment on the effects of media on children. They randomly select 100 children and randomly assign
each child to one of four treatment groups. Each treatment group has a specific amount of screen time during a one-week time frame. The
first group has no screen time, the second group has two hours of screen time, the third group has four hours of screen time, and the fourth
group has six hours of screen time,
After the first week, the scientists conduct the same experiment, with the same subject groups, for three more weeks so that each group
experiences each of the four treatments.
Which statements about this study are true?
This study uses blinding.
This study uses random sampling
This study uses a control group.
ооо
This study uses blocking.
This study uses a repeated measures design.
Answers
The statements that are true about this study are:
This study uses random sampling. This study uses a control group. This study uses a repeated measures design. Random sampling occurs when each sample has an equal probability of being chosen in a study.
This is seen in the random selection of 100 children. The Control group was used with the first group that had no screen time.
The repeated measures design was also used when multiple measurements were taken during different weeks.
Learn more about experiments here:
https://brainly.com/question/17216882
A car is traveling at a speed of 70 miles per hour. What is the car's speed in miles per hour? How many miles will the car travel in 5 hours?
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Work out the missing percentages in these problems. See if you can spot the impossible problem which cannot be answered!
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Answer: please read the explanation :)
Step-by-step explanation:
Make the precent a whole number then subtract it form 100 then the answer turn it to a percent :)
1) 100 - 65 = 35 = 35% of boys in the class
2) 100 - 27 = 63 = 63% of skirts that are not red
3) 100 - 78 = 22 = 22% non swimmers
4) 100 - 43 = 57 = 57% what he got wrong
5) 100 - 45+42 = 13 = 13% the games they tied
6) 100 - 28+35 = 37 = 37% who chose football
7) 100 - 38 = 62 = 62% are dogs
8) 100 -35 = 65 = 65% scored over average
9) 100 -12 = 88 = 88% percent
10) 100 - 6 = 94 = 94% can ride the bike
Hope that helps if you need more explanation please send me :)
How do you do it i am very confused/ i just need the answer lol
Answers
Answer:
No question!
Step-by-step explanation:
Hi! Could you please insert a question so I could answer for you?
I would love to help!
Two angles are supplementary. The larger angle is 28∘ more than the smaller angle. Find the measure of the larger angle.
Answers
Supplementary means that the angles together equal 180°
So we simply do 180 - 28 = 152°
Hope this helps!
In Exercises 12-20, TA=AB=BC and TD= DE = EF
Write an Equation that relates AD and BE.
Answers
Based on the midsegment theorem of a triangle, the equation that relates AD and BE is: AD = ½(BE)
Recall:
The midsegment theorem of a triangle states that length of midsegment = ½(the third side of the triangle).Given the image attached below, where, TA=AB=BC and TD= DE = EF, considering ΔTBE:
AD = midsegment of ΔTBEBE = third side of ΔTBETherefore, based on the midsegment theorem of a triangle, the equation that relates AD and BE is: AD = ½(BE)
Learn more about the midsegment theorem of a triangle on:
https://brainly.com/question/7423948
If DEF and MNO are two triangles such that DE=MN and EF=NO, which of the following would be sufficient to prove that triangles are congruent
Answers
Answer:
D. ∠E ≅ ∠N
Step-by-step explanation:
The pair of sides meet at vertex E in ∆DEF and at vertex N in ∆MNO. Since the sides that make up angles E and N are shown congruent, it is sufficient to show ...
∠E ≅ ∠N
Then the SAS congruence postulate can be claimed.
__
Additional comment
The alternative is to show DF ≅ MO. That would allow you to claim SSS congruence. That is not an answer choice.
1. The side of a square is 5 units long. What is the area of the square?
20 units?
25 units
10 units?
15 units?
Answers
Answer: 25 units squared
Step-by-step explanation:
1) A square has 4 equal sides.
2) The area of a square is length x width.
3) Therefore, 5x5 = 25 units squared (area is always reported in units squared).
Which of the segments below is a secant?
С
F
О.
В
Д.
А
u
А. ОВ
B. AB
ООО О
C. DE
D. AD
Answers
Answer:
it is d i believe
The secant of a circle is line segment AD. Therefore, option C is the correct answer.
What is secant of a circle?A line that crosses a circle at two different locations is said to be a secant of the circle. The Roman verb secare, which meaning to cut, is the source of the word secant. It can also be thought of as the chord of a circle extended outside of the circle.
Given that, circle with center O.
In the given figure, FC is chord, OB is radius, AB is tangent, AD is secant and DE is tangent.
Therefore, option C is the correct answer.
Learn more about the secant of a circle here:
https://brainly.com/question/23026602.
#SPJ7
help me pls no links
Answers
Answer:
this is a tough one but i know that sometimes it may seem hard but, with the right amount of practice, the hardest equations become the easiest to overcome. (Hint: Use PEMDAS)
Step-by-step explanation:
hope this helps you!
Answer:
I cant answer it i just need to talk to you its mya......
Step-by-step explanation:
Ali had 5/7 of a spool of yarn. He used 5/6 of his yarn for a project. What fraction of the spool was used for the project? Write your answer in simplest form.
- Due 11:59 today
- Will mark brainliest
Answers
Answer:
Step-by-step explanation:
We have no idea what time zone you are in so hope this gets there soon enough.
Do you mean "What fraction of a FULL spool of yarn did he use?" because he used 5/6 of the spool he had.
IF SO
Then
(5/7)(5/6) = 25/42
That's just under 60% of a full spool would be used to complete the same project again.
Which value of y makes the equation y+4.2=21 true?
I NEED THE ANSWER ASAP I ONLY HAVE 20 MINS TO COMPLETE
A. y = 16.8
B.y=17.2
C.y=17.8
D=25.2
Answers
Answer:
A: 16.8
Step-by-step explanation:
4.2 and 16.8 both have decimal place values. If you line up the decimals when you add them, then you get 21.
round the following number to the nearest ten 7377.38?
Answers
Answer:
7377.4
Step-by-step explanation:
8. Which of the following are equivalent expressions?
a) x2, -X2, -(x2)
b) 3x - 7, (3x) - 7, 3(x - 7)
c) -2x + 8, -(2x + 8), -(2x - 8)
+
Answers
Answer:
a) -x2 , -(x2)
b)3x-7 , (3x) - 7
c) -2x+8 , -(2x-8)
Answer this!
18 divides x
Answers
this makes no sense so maybe try something better
Two angle measures of this triangle are 60°. Which type of triangle is it? O A. obtuse O B. scalene O C. equilateral O D. right
plz need help now :(
Answers
Answer:
equilateral
Step-by-step explanation:
all the sides are equal
Brent checks the sales records for a random sample of 16 days and finds the mean number of gallons sold is 150 gallons per day; the sample standard deviation is 12 gallons. With 95% confidence, estimate the what is mean number of gallons that Brent should stock daily.
Answers
Answer:
[143.61, 156.39]
Step-by-step explanation:
Because the population standard deviation is not available AND the sample size is less than 31, we can use a t procedure here.
Plug these values into your calculator:
Sample mean = 150
Sample size = 16
Standard deviation = 12
Confidence level = 95% = 0.95
and get [143.61, 156.39] as your confidence interval
how do I do this problem?
Answers
Answer:
Yes
Step-by-step explanation:
4 is greater then or equal to -6+5
4 is greater then -1 so the equation is true
Consider the following function.
f(x) = 1 + 5/x - 4/x2
(a) Find the vertical asymptote(s).
(b) Find the interval where the function is increasing.
Find the interval where the function is decreasing.
(c) Find the local maximum and minimum values.
(d) Find the interval where the function is concave up.
Find the interval where the function is concave down.
Find the inflection point.
(e) Use the information from parts (a)-(d) to sketch the graph of f.
Answers
Answer:
See below
Step-by-step explanation:
I assume the function is [tex]f(x)=1+\frac{5}{x}-\frac{4}{x^2}[/tex]
A) The vertical asymptotes are located where the denominator is equal to 0. Therefore, [tex]x=0[/tex] is the only vertical asymptote.
B) Set the first derivative equal to 0 and solve:
[tex]f(x)=1+\frac{5}{x}-\frac{4}{x^2}[/tex]
[tex]f'(x)=-\frac{5}{x^2}+\frac{8}{x^3}[/tex]
[tex]0=-\frac{5}{x^2}+\frac{8}{x^3}[/tex]
[tex]0=-5x+8[/tex]
[tex]5x=8[/tex]
[tex]x=\frac{8}{5}[/tex]
Now we test where the function is increasing and decreasing on each side. I will use 2 and 1 to test this:
[tex]f'(2)=-\frac{5}{2^2}+\frac{8}{2^3}=-\frac{5}{4}+\frac{8}{8}=-\frac{5}{4}+1=-\frac{1}{4}[/tex]
[tex]f'(1)=-\frac{5}{1^2}+\frac{8}{1^3}=-\frac{5}{1}+\frac{8}{1}=-5+8=3[/tex]
Therefore, the function increases on the interval [tex](0,\frac{8}{5})[/tex] and decreases on the interval [tex](-\infty,0),(\frac{8}{5},\infty)[/tex].
C) Since we determined that the slope is 0 when [tex]x=\frac{8}{5}[/tex] from the first derivative, plugging it into the original function tells us where the extrema are. Therefore, [tex]f(\frac{8}{5})=1+\frac{5}{\frac{8}{5}}-\frac{4}{\frac{8}{5}^2 }=\frac{41}{16}[/tex], meaning there's an extreme at the point [tex](\frac{8}{5},\frac{41}{16})[/tex], but is it a maximum or minimum? To answer that, we will plug in [tex]x=\frac{8}{5}[/tex] into the second derivative which is [tex]f''(x)=\frac{10}{x^3}-\frac{24}{x^4}[/tex]. If [tex]f''(x)>0[/tex], then it's a minimum. If [tex]f''(x)<0[/tex], then it's a maximum. If [tex]f''(x)=0[/tex], the test fails. So, [tex]f''(\frac{8}{5})=\frac{10}{\frac{8}{5}^3}-\frac{24}{\frac{8}{5}^4}=-\frac{625}{512}<0[/tex], which means [tex](\frac{8}{5},\frac{41}{16})[/tex] is a local maximum.
D) Now set the second derivative equal to 0 and solve:
[tex]f''(x)=\frac{10}{x^3}-\frac{24}{x^4}[/tex]
[tex]0=\frac{10}{x^3}-\frac{24}{x^4}[/tex]
[tex]0=10x-24[/tex]
[tex]-10x=-24[/tex]
[tex]x=\frac{24}{10}[/tex]
[tex]x=\frac{12}{5}[/tex]
We then test where [tex]f''(x)[/tex] is negative or positive by plugging in test values. I will use -1 and 3 to test this:
[tex]f''(-1)=\frac{10}{(-1)^3}-\frac{24}{(-1)^4}=-34<0[/tex], so the function is concave down on the interval [tex](-\infty,0)\cup(0,\frac{12}{5})[/tex]
[tex]f''(3)=\frac{10}{3^3}-\frac{24}{3^4}=\frac{2}{27}>0[/tex], so the function is concave up on the interval [tex](\frac{12}{5},\infty)[/tex]
The inflection point is where concavity changes, which can be determined by plugging in [tex]x=\frac{12}{5}[/tex] into the original function, which would be [tex]f(\frac{12}{5})=1+\frac{5}{\frac{12}{5}}+\frac{4}{\frac{12}{5}^2 }=\frac{43}{18}[/tex], or [tex](\frac{12}{5},\frac{43}{18})[/tex].
E) See attached graph
what is 5÷ 3 1/3 on khan academy
Answers
Answer:
1.5
Step-by-step explanation:
Hope this helped!
whats b + 29 + 12b + 5b² if b = -3
Answers
Answer:
215
Step-by-step explanation:
-3+29+12(-3)+5(-3)[tex]^{2}[/tex]
-2 2/3 divided by 1 5/6 + 2
NO MIXED NUMBERS
Answers
Answer:
14/15
Step-by-step explanation:
Answer:
6/11
Step-by-step explanation:
-2 2/3 divided by 1 5/6 = -16/11 and when you add two to that you get 6/11.
Does (–1, 2) make the equation y = x + 9 true?
Answers
Answer:
(-1, 2) does not make the equation y=x+9 true.
Step-by-step explanation:
y=x+9
(-1, 2)=(x, y)
2=(-1)+9,
-1+9=8,
2 does not equal to 8.
Answer: No.
PLEASE HELP IM REALLY NEED HELP
Answers
Answer:
x=7
Step-by-step explanation:
3.5/3= 1.1666666666
6*1.16666666= 7
x=7
Which of the following equations represents the graph shown?
Answers
Answer:
F(x)=-x+2
Step-by-step explanation:
equation
mx+b
m= slope
x
b = y-intercept
40 percent of students survey said that they are night owls . If 300 students said that they are night owls how many students were surveyed ?
Answers
Based on the calculations that 300 is 40%, 375 is considered 50% or halfway.. in this case, we must multiply 375 by 2 and we will discover how many students were surveyed:
375 x 2 = 750
13. What is the equation of the line through the two points (5,2) and (5.-3)
Answers
Answer:
yes i love this app , this app so good
i need help with this question
Answers
Answer:
so its 4 just bc
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
5x + 40 + 2(2x + 20) + x = 360
10x + 80 = 360
10x = 280
x = 28
5x + 40 =? 180
140 + 40 =? 180
180 = 180
