A mass suspended from a spring is raised a distance of 5 cm above its resting position. The mass is released at time t=0 and allowed to oscillate. After one third of a second, it is observed that the mass returns to its highest position, which was 4.5 cm above its resting position. What is the rate of change of the position of the mass at t = 2.1 seconds?
Rates of change are the change of a quantity over another.
The rate of change of the mass position at 2.1 seconds is -89.6 cm/ s
The given parameters are:
[tex]\mathbf{A = |5|}[/tex] -- the amplitude
[tex]\mathbf{T = \frac 13}[/tex] --- the period
The position of the mass is modeled by:
[tex]\mathbf{y= Acos(wt)}[/tex]
Where:
[tex]\mathbf{w = \frac{2\pi }{T}}[/tex]
So, we have:
[tex]\mathbf{w = \frac{2\pi}{1/3}}[/tex]
[tex]\mathbf{w = 6\pi }[/tex]
[tex]\mathbf{y= Acos(wt)}[/tex] becomes
[tex]\mathbf{y = |5|cos(6\pi t)}[/tex]
[tex]\mathbf{y = 5cos(6\pi t)}[/tex]
Differentiate
[tex]\mathbf{y' = 5 \times -sin(6\pi t) \times (6\pi)}[/tex]
[tex]\mathbf{y' = -30\pi sin(6\pi t) }[/tex]
When t = 2.1, we have:
[tex]\mathbf{y' = -30\pi sin(6\pi \times 2.1) }[/tex]
[tex]\mathbf{y' = -30\pi sin(12.6\pi) }[/tex]
[tex]\mathbf{y' = -30\pi \times 0.9510}[/tex]
[tex]\mathbf{y' = -89.6296}[/tex]
Approximate
[tex]\mathbf{y' = -89.6}[/tex]
Hence, the rate of change of the mass position at 2.1 seconds is -89.6 cm/ s
Read more about rates at:
https://brainly.com/question/15579510
What type of angles are these?
Vertical angles
Complementary angles
Adjacent angles
Supplementary angles
Linear pair
Answer:
adjacent angle
Step-by-step explanation:
a linear pair =180 so not it
supplementary and complementary can't be it either due to neither being right angles
not a vertical angle
right next to each other with a common line to connect them so adjacent angle
Using the slope formula, find the slope of the line through the given points.
(1,6) and (3,4)
which is greater -5/8 or 6/10 and why
Answer:
The answer is -5/8, smaller fractions are always closer to a whole number which make them more, another way to look at it is 5 is 3 numbers away from 8, and 6 is 4 numbers away from 10, which makes -5/8 greater.
Hope this helps!
if M is a multiple of 3 and 7 then it is a multiple of 21
Answer:
It will be true , it is a multiple of 21
If f(x)= 3x-2 find x if f(x)= 19
Answer:
x=6
Step-by-step explanation:
3(6)+1=18+1=19.
Hello if you answer this question i will post another question giving 100 points
Answer:
ok?
Step-by-step explanation:
Brainliest?Answer:
what's your question even-
40 Points! I'm counting on you TT
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
Let's find the slope of the line using the points (0 , 4) and (-8 , 0) from the given graph :
Slope (m) :
[tex] \dfrac{y2 - y1}{x2 - x1} [/tex][tex] \dfrac{4 - 0}{0 - ( - 8)} [/tex][tex] \dfrac{4}{8} [/tex][tex] \dfrac{1}{2} [/tex]hence, the correct choice is C
Please help me on these :(
Step-by-step explanation:
8) 125=x+90° (exterior angle= sum of two opposite interior angle)
x= 35°
9) y=80° ( vertically opposite angle)
x= 180-50-80= 50°.
hope this helps you.
can anyone plz tell me how to lucid dream tonight without an alarm im 13 and i never had one ill give brainliet
get a journal and pencil and when you go to sleep, don't put on any alarms. then write down in the morning what you dreamt about. every detail you can thing of. if you have the dream again, write down more details. this will help you begin to lucid dream.
Gabriella swims 2 laps per minute. What is the rate unit?
laps per minute
laps
1
2
Answer:
2
Step-by-step explanation:
Answer:
Laps per minuet
Example:
You are traveling at a rate of 45 miles per hour (or mph). Determine the unit rate and the rate unit.
Solution:
45 is the numerical part of the rate, or the unit rate.
Miles per hour is the unit part of the rate, or the rate unit.
A local school is conducting a fundraiser. The relationship between the number of raffle tickets sold, X, and the total amount of money raised in dollars, Y, is shown in this table.
X Y
5 $25
15 $75
25 $125
100 ?
How much money is raised when 100 tickets are sold?
$175
$175
$225
$225
$400
$400
$500
[tex]( - 2 \\ \times \frac{1}{5} )[/tex]
[tex] \times [/tex]
[tex] ( - 5 \frac{3}{4} )[/tex]
put the answer as a mixed number please
Answer:
Step-by-step explanation:
[tex](-2)*\dfrac{1}{5}*(-5\dfrac{3}{4})=(-2)*\dfrac{1}{5}*\dfrac{-23}{4}\\\\ = \dfrac{23}{5*2}\\\\=\dfrac{23}{10}\\\\=2\dfrac{3}{10}[/tex]
Sally left the city for vacation. Sara left 5 hours later going 58 mph faster to catch up.
After 4 hours Sara caught up. What was Sally's average speed.
O 72.5 mph
O 54.6 mph
0 46.4 mph
0 64.5 mph
Answer:46.2
Step-by-step explanation:
hope this helps
Giving right answer branleist
Work out 1.6 X 10⁴ + 0.8 X 10⁴.
math work
Answer:
2.4× 10^4
Step-by-step explanation:
you just sum 1.6 with 0.8
[tex]2.4 \times {10}^{4} [/tex]
I need help Please!!!!!!!!!!!!!!!!!!!!!!! I will give brain to who ever gets it right
Answer: i think its all of them are 5
Step-by-step explanation: sorry if im wrong
Complete the following tables by filling in the missing values and determine the rule for each table:
I need help with this can you show me how to work it out pls
Answer:
Answer is in the pic
Step-by-step explanation:
A translation is just a movement of the figure so in this case you just add 3 to the x part of the coordinate.
so originally k (-2,5) m (-3,1) l (1,1)
add 3 to x so
k (1,5) m (0,1) l (4,1)
Which of the following is an example of a set of like terms? *
17y, 17, y
15x, -x, 33x
18, 21g, 24
-5x, -5xy, -5y
There are 75 students enrolled in a camp. The day before the camp begins, 8% of the students cancel. How many students actually attend the camp?
Answer:
Answer=69
Step-by-step explanation:
8% of 75=6
75-6=69
What equation is equivalent to 4x+3x=7-6
Answer: A: 3x + 6 = 4x + 7 1: 9x = 4x + 7
B: 3(x+6) = 4x + 7 2: 3x + 18 = 4x + 7
C: 4x + 3x = 7 - 6 3: 3x = 4x + 7
4: 3x - 1 = 4x
5: 7x = 1
Step-by-step explanation:
Solve 3x^2+ 5 = 2 using square roots
Answer:
[tex]x=\pm i[/tex]
Step-by-step explanation:
[tex]3x^2+5=2[/tex]
[tex]3x^2=-3[/tex]
[tex]x^2=-1[/tex]
[tex]x=\pm i[/tex]
PLEASE HELP WILL MARK BRAINLIEST!
Answer:
2 x 4 − x 3 + x 2 − 9
Step-by-step explanation:
Here is a list of numbers:
8.4, 8.6, 7, 7.6, 2.4, 9.7, 5.8, 5.2, 3.3
State the median.
Answer:
7
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
arrange the numbers in the other of magnitude
:
2.4,3.3,5.2,5.8,7,7.6,8.4,8.6,9.7
then check for the middle number(s)
median = 7
The length of a rectangle is 2x + 6. Its width is 52. Find the value of ac if the perimeter is 138m².
Answer:
ac = 18.5
Step-by-step explanation:
perimeter of a rectangle = [tex]2(l+b)[/tex]
= 138m^2= 2(2x + 6 ) + 52
= 4x + 12 + 52 = 138
= 4x + 64 = 138
= 4x = 138 - 64
= 4x = 74
= x = 74/4
= x = 18.5
A line passes through point A(12,18). A second point on the line has an x-value that is 125% of the x-value of point A and a y-value that is 75% of the y-value of point A. Use point A to write an equation of the line in point-slope form.
Answer:
the answer is Y = -1.5x + 36
Find the y intercept for the equation of the line that passes through point (-1 , 5)if the slope is 5
Answer:
the y-intercept is 10
Step-by-step explanation:
PLEASE HELP ME!!!
I need this ASAP please
8 and 6
20:8 and x:6
ask urself: what is the scale factor?
[tex]20:8 = \frac{20}{8} = 2.5\\so, multiply 6 by 2.5, which is 15\\therefore, x = 15[/tex]
Express the ratio of 300 miles to 25 gallons of gasoline as a untie rate
Answers:
12 miles per gallon
1.2 miles per gallon
50 miles per gallon
32 miles per gallon
Answer:
12 miles per gallon (answer A)
Step-by-step explanation:
300:25
Divide each side by 25:
12:1
12 is your answer
Hope that helps