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
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answer to me this question
Step-by-step explanation:
[tex]3 \frac{1}{2} - 4 \frac{3}{4} = \frac{7}{2} - \frac{19}{4} = \frac{14}{4} - \frac{19}{4} = - \frac{5}{4} [/tex]
Solve the inequality- 5/2(3x+4)<6-3x. Show your work.
Answer:
x < -8/21
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
[tex](\frac{5}{2} * 3x) + (\frac{5}{2} * 4) < -3x + 6[/tex] [tex]\frac{15}{2}x + 10 < -3x + 6[/tex]Step 2: Add 3x to both sides.
[tex]\frac{15}{2}x + 10 + 3x < -3x + 6 + 3x[/tex] [tex]\frac{21}{2}x + 10 < 6[/tex]Step 3: Subtract 10 from both sides.
[tex]\frac{21}{2}x + 10 - 10 < 6 - 10[/tex] [tex]\frac{21}{2}x < -4[/tex]Step 4: Multiply both sides by 2/21.
[tex]\frac{21}{2}x * \frac{2}{21} < -4 * \frac{2}{21}[/tex] [tex]x < -\frac{8}{21}[/tex]Therefore, the answer is x < -8/21.
What is 4 times 1 6/7. Write in the simplest form
Answer:
7 43/100
Step-by-step explanation:
4*1 6/7=4 24/7 which equals 7.43, or 7 43/100
Answer:
7 3/7
Step-by-step explanation:
4 * 1 6/7
1 = 7/7, so 1 6/7 = 7/7 + 6/7 = 13/7
4 * 13/7 = 52/7
7 can fit into 52 at most 7 times (because 7*7 is 49, and less than 52)
This leaves us with 3 left over
4 * 1 6/7 = 7 3/7
Musi measured the length and width of a soccer field and then made a drawing of the soccer field . He decided to use 1 mm on his ruler to represent 3 m on the soccer field. If his measurement of the width of the soccer field was 63m , what is the width of his drwaing?
If his measurement of the width of the soccer field was 63m , the width of Musi's drawing for a 63 m wide soccer field is 21 mm.
Musi's ruler represents 1 mm as 3 m on the soccer field. To find the width of his drawing for a 63 m wide soccer field, we can set up a proportion to relate the real width to the width on his drawing.
Let "x" represent the width of his drawing in millimeters.
The proportion can be set up as follows:
1 mm (on the drawing) / x mm (real width on the field) = 3 m (on the drawing) / 63 m (real width on the field)
Now, cross-multiply and solve for "x":
1 * 63 m = 3 * x mm
63 = 3x
Divide both sides by 3 to find the width of his drawing:
x = 63 / 3
x = 21
So, the width of Musi's drawing for a 63 m wide soccer field is 21 mm.
In summary, Musi used a scale of 1 mm to represent 3 m on the soccer field. Therefore, the width of his drawing for a 63 m wide soccer field is 21 mm.
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What is the answer to this question?
I am confused.
Answer:
y=88 x=42
Step-by-step explanation:
Since the total measurments of one triangle have to equal 180 and one angle is already 50, and the angle on the oppisite side of the y angle is 90 the only logical number for y would be 88. Hope this helped :)
For the simple linear equation below, what is the y-coordinate of the ordered pair when the x-coordinate is −5?
y=−7x
Enter your answer in the box.
(-5, ) what goes after 5
Answer:
-9
Step-by-step explanation:
6.
What is the midpoint of the line segment whose
endpoints (7,-4) and (-3, -2)?
are
Answer: (2, -3)
Step-by-step explanation:
To find the the answer, you will need to use the midpoint formula, which is as following:
(x₁+x₂/2, y₁+y₂/2)
Since we have two coordinates, let's substitute them into the equation.
(7 + (-3 )/ 2, (-4) + (-2)/2)
We should first add 7 and -3 together, as well as -4 and -2.
(4/2, -6/2)
We then divide 4 and -6 by 2. This would give us our midpoint coordinate.
(2, -3)
if 3^x = 1, find the value of x.
3x-1=?
maybe 3x-1=5
3x=5+1
3x=6
X=6/3
X=2
700, 3128, 5024,9000,10018 cuáles son divisibles entre 8
Answer:
3128, 5024, 9000
Step-by-step explanation:
3128÷8=391; 5024÷8=628; 9000÷8=1125
What is the slope of the line that passes through the points (-4,-2) and (-4,22)
Answer:
0
Step-by-step explanation:
( x1, y1 ) = ( - 4, - 2 )
Here,
x1 = - 4
y1 = - 2
( x2, y2 ) = ( - 4, 22 )
Here,
x2 = - 4
y2 = 22
Formula : -
Slope = ( y2 - y1 ) / ( x2 - x1 )
Slope
= ( 22 - ( - 2 ) ) / ( - 4 - ( - 4 ) )
= ( 22 + 2 ) / ( - 4 + 4 )
= 24 / 0
= 0
Arrange the following in descending order: 1/5,3/7,7/10
Answer:
7/10 - 3/7 - 1/5
Step-by-step explanation:
3/7-7/10-1/5
Step-by-step explanation:
-5x + 13 = -17 two step equation
Answer:
X = 6 see below
Step-by-step explanation:
-5x + 13 = - 17
Step One:
subtract 13 from each side
-5x = - 30
Step two:
divide each side by - 5
x = 6
5x= 20 word problem
[tex]{{ \large{ \blue{ \rm{{↬}}}}}} \large \rm \: \: 5x \: = \: 20[/tex]
[tex]{{ \large{ \blue{ \rm{{↬}}}}}} \large \rm \: \: x \: = \: \cancel\frac{20}{5} \\ [/tex]
[tex]{{ \large{ \blue{ \rm{{↬}}}}}} \large \rm \: \: x \: = \: 4[/tex]
[tex] \mapsto \rm \: 5x = 20[/tex]
[tex] \mapsto \rm \: x = \cancel\frac{20}{5} \\ [/tex]
[tex] \red \mapsto \ \boxed{ \rm \red { = 4}}[/tex]
Ty’Reese is 12 years old and collects trading cards. He has 972 cards. He wants to put them into albums. Each album holds 36 cards. How many trading card albums will he need?
In the wοrd prοblem, He need 27 albums fοr tοtal trading cards.
What is wοrd prοblem?Wοrd prοblems are οften described verbally as instances where a prοblem exists and οne οr mοre questiοns are pοsed, the sοlutiοns tο which can be fοund by applying mathematical οperatiοns tο the numerical infοrmatiοn prοvided in the prοblem statement. Determining whether twο prοvided statements are equal with respect tο a cοllectiοn οf rewritings is knοwn as a wοrd prοblem in cοmputatiοnal mathematics.
Here the given Tοtal number οf cards = 972
Number οf cards each album hοld = 36
Nοw ,Tοtal number οf album
=> Tοtal number οf card / Number οf cards each album hοld
=> 972/36
=> 27.
Hence He need 27 albums fοr tοtal trading cards.
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Bill baked n cookies. His friends ate 12 of them. Using n, write an expression for the number of cookies that remained.
Answer:
n-12= number of cookies left
Answer:
y=n-12
Step-by-step explanation:
y= how many cookies are left
n = number of cookies
-12 = how many his friends ate
Simplify each equation. Tell whether the equation has one, no, or infinite solutions.
3x - 7 = 3(x-3)+2
A) infinite solutions
B) One
C) no solutions
Answer:
-7 = -7
a. infinite solution
hjjhhhhhhjjjjjjjjhjjhhhhh hhhhhj h
Answer:
YASSSSSSSS
Step-by-step explanation:
Answer:
dnbdjdndh hdhdhbdjf
xnxnxnnxnxnfnf
ndndndndjf
Solve for x. 8x-6+11+12x=180
Answer:
x=35/4
Step-by-step explanation:
20x +5=180
20x=180-5
20x=175
x=175/20=35/4
Answer:
[tex]x=8.75[/tex]
Step-by-step explanation:
[tex]8x-6+11+12x=180~(Given)\\\\20x+5=180~(Simplify)\\\\20x+5-5=180-5~(Subtract~5~on~both~sides)\\\\20x=175~(Simplify)\\\\\frac{20x}{20}=\frac{175}{20}~(Divide~20~on~both~sides)\\\\x=8.75[/tex]
Dont get this, please help
Answer:
1. Enlarge, Shrink
2. Smaller
3. Bigger
Step-by-step explanation:
Dilation is something expanding or shrinking, like how your eyes dilate.
Simply think of the scale factor as what you are multiplying the entire figure by. If you are multiplying it by let's say 2, it would double in size, thus getting larger. If you were to multiply it by 1/2, then it would decrease, or shrink, to half its original size.
Answer:
1: enlarge, shrink
2: smaller
3: bigger
Hope this helps! SO sorry if incorrect!!!!!!
how to use intersection in the real world.
Which of the following is correctly written in Standard Form?
A.) -6x + 3y = 8
B.) y = 6/5x + 4
C.) 6x - 2y = 4
D.) 6/5x + 3y = 8
HELP NEEDED PLZ
19. Graph the function 3x + 2y = 8 with the given
domain: (-2,0, 2, 4}
TEK 3C
Justify/Show your work:
Answer:
Step-by-step explanation:
u may not understand this but what is 10 g/cm³ a measure of
. is it Volume Mass or density
which expressions represent 94 increased by twice a number
Answer:
2x+94
Step-by-step explanation:
because 2x means 2×x +94
x= unknown number
+=increase
Solve for x:
10 = x+25
Answer:
[tex]\boxed{\sf x=-15}[/tex]
Step-by-step explanation:
[tex]\sf 10=x+25[/tex]
[tex]\sf x+25=10[/tex]
[tex]\boxed{\mathrm{Subtract\:}25\mathrm{\:from\:both\:sides}}[/tex]
[tex]\sf x+25-25=10-25[/tex][tex]\sf x=-15[/tex]Answer:
x = -15
Step-by-step explanation:
Your cousin’s birthday is this weekend. You want to buy a CD that costs $12.99 and a birthday card that costs $2.50. You have saved $25. Write an inequality to find the most money you have for other spending.
Answer:
None
Step-by-step explanation:
It would be easier to ask your teacher instead of getting wrong answers from random people. Ever think of that :0
Find x and y please!! I’m desperate!!!
Answer:
x = 4
y = 2
Step-by-step explanation:
the third angle of the triangle
180 - (148 + 18) = 14º
Therefor
3x + y = 14
5x - y = 18
Add the equations
8x = 32
Divide both sides by 8
x = 4
Plug in x = 4
3(4) + y = 14
12 + y = 14
y = 2
9514 1404 393
Answer:
(x, y) = (4, 2)
Step-by-step explanation:
The triangles are similar by AA similarity, so the corresponding angles are congruent.
5x -y = 18 . . . . . . unmarked angles are congruent
18 +(3x+y) +148 = 180 . . . . . sum of angles in a triangle is 180°
__
After subtracting 166 from both sides, the second equation simplifies to ...
3x +y = 14
Adding this to the first equation gives ...
8x = 32
x = 4 . . . . . . divide by 8
Then substituting for x in the first equation gives ...
5(4) -y = 18
20 -18 = y = 2
The values of the variables are x = 4, y = 2.
_____
The angle marked with a double mark is 14°, given by the simplified second equation.
Factor Completely. (and please show work)
4x^2 - 8x +3
Step-by-step explanation:
=>4x²-8x+3
=> 4x²-2x-6x+3
=> 2x(2x-1)-3(2x-1)
=>(2x-1)(2x-3).
hope this helps you.
Hello. . .
I need help please. . .
answers/w explanation. ✅
Nonsense answers, or answers that's not the question I ask for will be reported.
Answer:
x = 1 , y = 4
Step-by-step explanation:
I am assuming you're looking for what x and y are? If so, then we know that
DC and AB equal each other, so
4x + y = 8
CB and AD equal each other, so
2x + y = 6
We have two equations that cannot be solved on their own, so we must solve them as a system of equations. One process to solve is elimination.
4x + y = 8
2x + y = 6
we can multiply the second equation all by -1 to make the y's cancel out and give us x. so,
4x + y = 8
-1(2x + y) = 6
4x + y = 8
-2x -y = -6
now solve them vertically. we get:
2x = 2
and so x = 1.
Now that we found x, we must find y. Using any of the two equations froom above, we can substitue our x value of 1 into it to find y. I will use the first one.
4x + y = 8
4(1) + y = 8
4 + y = 8
y = 8 - 4
y = 4
so our x is 1 and y is 4.
hope this helps! (:
Write the equation of a line in slope-intercept form that has a slope of -1/4x and a y-intercept of 5
Answer:
Step-by-step explanation:
Slope = m = -1/4
y-intercept = b = 5
Slope intercept form = y = mx +b
[tex]y =\dfrac{-1}{4}x+5[/tex]