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:
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this week sage spent $30 for hot dogs and supplies. he earned $18. Did he make money or lose money this
Answer:
He lost $12.
Step-by-step explanation:
Money Earned=$18
Money Spent=$30
Here, Money Spent is larger than Money Earned, which means that he lost money.
$30-$18
$12
He lost $12.
Answer:
he made money and lose money this week
Step-by-step explanation:
HOpe this helps
Expand each expression and simplify your answers as far as possible
1. 8x - 2(3 - 2x)
2. 4x + 5-3(2x - 4)
Answer:
1. 12x - 6
2. -2x + 17
Step-by-step explanation:
1.
8x - 2(3 - 2x)8x - (-2)(3) + (-2)(-2x) 8x + (-6) + 4x(8x + 4x) + (-6)12x - 62.
4x + 5 + (-3)(2x) + (-3)(-4) 4x + 5 - 6x + 12(4x - 6x) + (5 + 12)-2x + 17Answer:
[tex]\boxed{\sf 12x-6}[/tex]
[tex]\boxed{\sf -2x+17}[/tex]
Step-by-step explanation:
[tex]\sf 1)\: 8x - 2(3 - 2x)[/tex]
Apply Distributive Property to multiply -2 by (3-2x):
→ [tex]\sf 8x-6+4x[/tex]
Combine like terms:
→ [tex]\sf (8x+4x)[/tex]
[tex]\sf 12x[/tex][tex]\boxed{\sf 12x-6}[/tex]
______________________________
[tex]\sf 2)\: 4x + 5-3(2x - 4)[/tex]
Apply Distributive property:
Multiply -3 by (2x-4):
[tex]\sf 4x+5-6x+12[/tex]
Combine like terms:
→[tex]\sf (4x+(-6x))[/tex]
[tex]\sf -2x[/tex]→ [tex]\sf (5+12)[/tex]
[tex]\sf 17[/tex][tex]\boxed{\sf -2x+17}[/tex]
_____________________________
the length and breadth of a piece of land are 20meters and 15 meters respectively. What is the perimeter of this land?
Answer:
20x15=300
When you need to calculate the Length and Width of a piece of land or anything else, all you need to do is multiply the two numbers.
Step-by-step explanation:
When you have 20 units of land in as the length and 15 units of land as width, then you should multiply.
2x4=?
When you do 2x4, you have to do 2+2+2+2=
but, here, you have a piece of land to calculate, so basically, you have to multiply still. In that way, you will be able to get what 20 and 15's product is.
I'm sorry, sometimes I just can't explain that well, but just remember, in these types of problems, just multiply, that is your answer.
Thank You! I hope I made your day just a little better!
Have a great time studying!
the heights in cm of some pupils are 138 119 182 174 142 117 152 152
mean; 147
median; 147
mode; 152
What is -(x + 4) - 3x = x in Distributive property?
Answer:
x = -4/5
Step-by-step explanation:
Original equation: -(x+4)-3x=x
Remember distributive property allows us to get rid of the parenthesis by bringing a multiplication from outside to inside a parenthesis.
-(x+4) = -x-4
= -x-4-3x=x
Now we combine like terms in this case we have (-x) and (-3x)
= -4x-4=x
Subtract x from both sides
= -4x-4=x
-x -x
----------------
-5x-4=0
Add 4 to both sides
-5x-4=0
+4 +4
---------------
-5x=4
Our final step is to divide both sides by -5
-5x=4
---- ----
-5 -5
x = -4/5
Hope this helps!!!
HELP PLEASE SHOW ME HOW TO DO THIS
Answer:
Step-by-step explanation:
Salary increase in 2 years = Salary in fifth year - salary in 3rd year
= 87,023 - 43,250
= $ 43,773
Salary increase per year= 43773/2 = $ 21,886.50
A dump truck can hold 2¼ tons of gravel. The pay loader loading the truck puts 750 pounds of gravel in the truck at one time. How many loads does the pay loader need to dump in the truck before it is full?
Answer:
6 loads would be required to fill the truck with 2¼ tons
Step-by-step explanation:
1 ton= 2000 pounds
2¼ tons= 4500 pounds
4500/750=6
Please allow me to know this helped by clicking thank you, rating or brainly.
Thank you,
Miss Hawaii
Answer:
6 loads
Step-by-step explanation:
Graph the inequality. x < 2
Step-by-step explanation:
there u have it, since y is 0, we make a straight line that passes through 2 and shade the numbers that are <2
help please !! geometry
A school gym is set up for an
assembly. There are 17 rows with 28
chairs in each row. Parents are sitting
in half the chairs, but the other half
are empty. How many chairs are empty?
Answer:
238 chairs are empty
Step-by-step explanation:
Firstly,
you'll have to times 17 by 28 to get the total chairs in the school gym
17 × 28
= 476
Next,
divide it by 2 because half of the gym???
476/2
= 238
So, the amount of the empty chairs in the school gym are 238 in total ｡◕‿◕｡
In the algebraic expression 5x + 8y – 12z, the values 5, 8, and –12 are _____
Answer:
Coefficients!!!
Step-by-step explanation:
They're numbers that are multiplied by a variable.
Answer:
Step-by-step explanation:
I believe the answer would be coefficients. Coefficients are the number that is being multiplied by the variable.
PLSSS HLEPP ME OUTT ITS URGENTTTT
Answer:
Step-by-step explanation:
(1860-11)=1849
√(1849) = 43
(A quick trial)
PLEASE HELP ILL MARK BRAILIEST!!!!!
Answer:
(-6,2)
Step-by-step explanation:
Answer:
y=4/5x-17/5
Step-by-step explanation:
Hope this helps!
The second picture is the same as the picture you have thus the equation is correct
Find the least common multiple for the pair of numbers. 18,7
Answer:
the lcm is 126
What do I put in the blank box? Could you also add step by step explanation? If you cant its fine :)
Answer:
its 34/5
Step-by-step explanation:
change that mixed fraction by simply multiplying 6×5 then add 4 you'll get 34 then place it over the denominator 5 =34/5........ hope it helps
equation of line M is Y=5/8x+1 . Line N is perpendicular to M. What is the slope of line N?
Step-by-step explanation:
the slope of a line is always the factor of x in the equation. in our case here : 5/8.
the slope is the y/x ratio indicating how many units y changes, when x changes by a certain amount of units (e.g. when going from one point on the line to another).
the perpendicular slope (crosses the original line in a right angle = 90 degrees) turns x and y upside-down and flips the sign.
so, in our case, it is -8/5.
Please solve no.a) from here for me
Answer:
x < 1 and x > -2
Step-by-step explanation:
5x - 1 < 4 and 3x + 5 > x + 1
Step 1.) Transfer the -1 over by the 4 by adding it because you use the opposite symple when its transfered.
5x < 5 and 3x + 5 > x + 1
Step 2.) Divide 5 by 5 to get the variable alone
x < 1 and 3x + 5 > x + 1
Step 3.) Subtract x from 3x which gives 2x and subtract 5 from 1 which gives -4
x < 1 and 2x > -4
Srep 5.) Divide -4 by 2 to get the variable alone and you get -2
x < 1 and x > -2
Help! What can we do to kill off the zombies?? The scientists realize that salt kills the zombies, if enough is poured on them (one full can). The reaction between the salt and zombie blood causes the zombie to disintegrate. Morton's salt has a plant in Tooele county just west of Grantsville, and can distribute cans of salt to people residing in Utah. If Morton's salt can distribute 300,000 cans of salt each day, write an equation to model the number of cans of salt distributed after n days.
Question 4 options:
f(n)=300,000n
f(n)=300,000+n
f(n)=300,000n
f(n)=300,000n/n
Answer:
I think its f(n)=300,000n
Step-by-step explanation:
Answer:
f(n)=300,000n
Step-by-step explanation:
Can someone answer this for me
a
Convert 0.58 into
percentage
Answer:
58%
Step-by-step explanation:
PLEASE help!! I’ll give brainliest!!
The graph shows the number of gallons in a pool being drained and
represents a linear function.
Which statement about this function is correct?
A. The y-intercept is (0, 8500), and the 8500 represents the number
of gallons before draining the pool.
B. The y-intercept is (0, 8500), and the 8500 represents the number of
gallons drained per hour.
C. The y-intercept is (8500, 0) and represents the number of hours it
takes to drain the pool.
D. The y-intercept is (8500,0) and represents the number of gallons
drained per hour.
Answer:A. The y-intercept is (0, 8500), and the 8500 represents the number
of gallons before draining the pool.
Step-by-step explanation:
The y-intercept is (8500,0) and -540 represents the number of gallons drained per hour. Then the correct option is D.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The graph shows the number of gallons in a pool being drained and represents a linear function.
Let 'x' be the number of hours and 'y' be the volume. And the points are (4, 6340) and (6, 5260). Then the equation of the line is given as,
(y - 6340) = [(6340 - 5260) / (4 - 6)] (x - 4)
y - 6340 = - 540x + 2160
y = - 540x + 8500
The y-intercept is (8500,0) and -540 represents the number of gallons drained per hour. Then the correct option is D.
More about the linear equation link is given below.
https://brainly.com/question/11897796
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During the summer, Hector does yard work, and Geri babysits.To show their earnings, Hector makes a graph, and Geri makes a table. Which statement is true?
Answer:
Step-by-step explanation:
$6.59
Answer:
Hector earns $6.50 more per hour than Geri.
Helppp I will give u 100 if you give me a good answer
Answer: it allows you to see both sets of data more clearly and compare them rather than having them on two different charts.
Step-by-step explanation:
somebody please just answer.......................
Answer:180 is what it need to be
Step-by-step explanation:
write the equation
it passes through (-5,-7) and (-5,7)
Answer:
x = -5
Step-by-step explanation:
Find the gradient:
m = change in y ÷ change in xm = (7 - -7) ÷ (-5 - -5)m = 14 ÷ 0m = 0 - There is no gradient, and it is a vertical lineThe equation is x = -5, because in both co-ordinate pairs, the x is -5 - only the y changes
Hope this helps!
10.
Find the measure of angle 1.
8x - 4
16x + 8
Answer:
53°
Step-by-step explanation:
As we can see that ∠3 and ∠7 are corresponding angles. Therefore,
∠3 = ∠76x+8 = 8x-76x-8x = -7-8-2x = -15x = -15/-2x = 15/2Now calculate the angles of ∠3 and ∠7.
∠36x+86×15/2+845+853°∠78x-78×15/2-760-753°Now we can see that ∠3 and ∠1 are alternate angles and ∠7 and ∠1 are alternate exterior angles. Thus, we can say that
∠3 = ∠7 = ∠1 = 53°Hence the measure of ∠1 is 53°.
♦♦♦♦♦Hope it helps♦♦♦♦♦
The difference of half
of a number and three
is equivalent to
negative
five.
3/2=3-5
Step-by-step explanation:
jdjdnsnsnsmanzna
find f'(x)of f(x)=x^2-6x
Answer:
[tex]f(x) = {x}^{2} - 6x \\ {f}^{'} (x) = 2x - 6 \\{f}^{'} (x) = 2(x - 3)[/tex]
In the inequality 4>-4, which number appears farther right on a number
line and why?
O A. -4 appears farther right because -4 is smaller than 4.
O B. -4 appears farther right because - 4 is larger than 4.
C. 4 appears farther right because 4 is larger than -4.
D. 4 appears farther right because 4 is smaller than -4.
PLEASE HELP ASAP!! THIS IS ONE OF MY FINAL TEST… AKA- ITS MOST OF MY GRADE
Answer:
"C" 4 appears farther right because 4 is larger than -4.
Dont leave any links please
Answer:
m^2/n
Step-by-step explanation:
The following laws of exponent are useful to this problem:
[tex] \displaystyle \large{ {(mn)}^{b} = {m}^{b} {n}^{b} } \\ \displaystyle \large{ {n}^{ - b} = \frac{1}{ {n}^{b} } }[/tex]
We are given the expression:
[tex] \displaystyle \large{( {m}^{8} {n}^{ - 4} )^{ \frac{1}{4} } }[/tex]
Use the first law of exponent above.
[tex] \displaystyle \large{( {m}^{8} {n}^{ - 4} )^{ \frac{1}{4} } = {m}^{(8)( \frac{1}{4}) } {n}^{ ( - 4)( \frac{1}{4}) } } \\ \displaystyle \large{( {m}^{8} {n}^{ - 4} )^{ \frac{1}{4} } = {m}^{2 } {n}^{ - 1} }[/tex]
Make sure to recall the important necesscary fundamental math such as operation with negative numbers/integers, basic division, fraction, etc.
From the expression, apply the second law of exponent to n^-1.
[tex] \displaystyle \large{( {m}^{8} {n}^{ - 4} )^{ \frac{1}{4} } = {m}^{2 } ( \frac{1}{ {n}^{1} } )} \\ \displaystyle \large{( {m}^{8} {n}^{ - 4} )^{ \frac{1}{4} } = {m}^{2 } ( \frac{1}{ {n} } )} \\ [/tex]
Multiply m in.
[tex] \displaystyle \large{( {m}^{8} {n}^{ - 4} )^{ \frac{1}{4} } = \frac{ {m}^{2} }{ {n} } }[/tex]
Thus the answer is m^2/n.