Question 8: The equation of motion of a particle is
s = t^3 4t^2 + 2t + 8
Where s is in meters
and t is in seconds
Find the acceleration after t=5 seconds.
Answers
Answer:
D) [tex]22\:\text{m/s}^2[/tex]
Step-by-step explanation:
Acceleration is the derivative of velocity, which is the derivative of position, so we must differentiate the function twice:
Position of Particle: [tex]s(t)=t^3-4t^2+2t+8[/tex]
Velocity of Particle: [tex]v(t)=3t^2-8t+2[/tex]
Acceleration of Particle: [tex]a(t)=6t-8[/tex]
After [tex]t=5[/tex] seconds, the acceleration of the particle is [tex]a(5)=6(5)-8=30-8=22\:\text{m/s}^2[/tex]
The acceleration of the particle after 5 seconds is 38 m/s².
What is acceleration?Acceleration is the rate of change of velocity or the slope of velocity.
We know that the first derivative of motion or speed is velocity and the second derivative of motion or speed is acceleration.
∴ We have to take the derivative of s = t³ + 4t² + 2t + 8 twice to obtain the equation of acceleration and replace t with 5 to get the acceleration value after 5 seconds.
Now, s = t³ + 4t² + 2t + 8 meters.
ds/dt = 3t² + 8t + 2 m/s.
d²s/dt² = 6t + 8m/s²
Now, at t = 5 seconds d²s/dt² = 6t + 8 is,
d²s/dt² = 6(5) + 8 m/s².
d²s/dt² = 38 m/s².
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Related Questions
Question 7(Multiple Choice Worth 1 points)
(01.03 MC)
What is the simplified expression for
4^4•4³
3
4^5
Answers
4² is simplified expression for [tex]\frac{4^{4} 4^{3} }{4^{5} }[/tex].
What is Indices?Index (indices) in Maths is the power or exponent which is raised to a number or a variable.
Here, Given expression = [tex]\frac{4^{4} 4^{3} }{4^{5} }[/tex]
[tex]\frac{4^{4} 4^{3} }{4^{5} }[/tex] = [tex]\frac{4^{4+3} }{4^{5} }[/tex]
= 4⁷/4⁵
= 4⁷⁻⁵
= 4²
Thus, 4² is simplified expression for [tex]\frac{4^{4} 4^{3} }{4^{5} }[/tex].
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A community organization wants to determine area support for the construction of a new skate park in the center of town. The organization decides to survey 500 people to see whether they are willing to have their taxes increased for one year to fund the construction of the skate park.
What is the best way to randomly choose these 500 people?
Answers
The method that can be used to randomly choose these 500 people is the use of systematic random sampling.
What is random sampling?Random sampling is defined as the method of sampling in which the whole sampling frame is being considered.
In order the survey a community of people to see whether they are willing to have their taxes increased for one year to fund the construction of the skate park, both the male and female should be considered.
The systematic random sampling will give the both male and female equal opportunity to the chosen.
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if 3\2 =x\12 what is the value
Answers
[tex]\frac{3}{2} =\frac{x}{12}[/tex]
---Cross multiply
2x = 36
---Divide both sides by 2
x = 18
Hope this helps!
Which single transformation will have the same effect on the figure?
A. reflection over the x-axis
B. rotation of 270° about the point (0, 0)
C. translation described by (x, y) → (x-6, y)
D. translation described by (x, y) → (x, y-6)
Answers
Answer:
D. translation described by (x, y) → (x, y-6)
Step-by-step explanation:
The triangle stays in the same orientation just in a diffrent spot on the graph, that spot being 6 units down from where it starts.
Find the value of x.
25
X
20
X = [?]
Enter the number that belongs in
the green box.
Answers
Answer:
Step-by-step explanation:
x^2 + 20^2 = 25^2
x^2 + 400 = 625
625-400=225
sqrt(225) = 15
x = 15
To receive monthly payments of $1500 for 20 years, how much would a person have to invest now in an annuity with an annual interest rate of 3.1% to achieve this goal? Round the answer to the nearest dollar.
Answers
Given the possibility of an investment with an annual interest rate of 3.1 %, the person must deposit $ 580645.16 to receive monthly payments of $ 1500 for 20 years.
How to determine the require investment to receive a desired monthly payment
According to this question, the person have decided to invest money to receive a monthly payment, meaning no savings and the adequacy of using the simple interest formula:
g = C · (r/100) (1)
Where:
C - Invested money, in monetary units.r - Monthly interest rate, in percentage.g - Monthly payment, in monetary units.If we know that g = 1500 and r = 3.1/12, then the invested money must be:
C = 100 · g/r
C = 100 · [1500/(3.1/12)]
C = 580645.16
Given the possibility of an investment with an annual interest rate of 3.1 %, the person must deposit $ 580645.16 to receive monthly payments of $ 1500 for 20 years.
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Given f(x)=3x2+5 and g(x)=x−2.
What is (fg)(x)?
Answers
PURRRRRR:
yeat or cartiiii
ANSWER:
The product of the functions is 3x³ - 6x² + 5x - 10
Composite functions
Given the following functions expressed as
f(x) = 3x² + 5
g(x) = x - 2
In order to determine the value of (fg)x, we will take the product of the functions as shown
f(x)g(x) = 3x²+5)(x-2)
Expand to have;
f(x)g(x) = 3x³ - 6x² + 5x - 10
Hence the product of the functions is 3x³ - 6x² + 5x - 10
Question 6 (5 points)
Find the amplitude of the function y = 3/2 cos(3x) + 1.
A) 1
B) 3
C) 3/2
D) ¹/3
Answers
The amplitude of the function is 3/2 after comparing with the general equation option (C) is correct.
What is cos function?It is defined as the function which is in the form of cosine waves in nature, and it has a domain of all real numbers and lies between the [a, a] where is a amplitude of the function.
We have a cos function:
y = 3/2 cos(3x) + 1
We know,
f(x) = acos(bx - c) + d
The above function represents the cos function where:
a = amplitude
b = is the period of the function
c = phase shift
d = vertical shift
On comparing we get:
a = 3/2
Thus, the amplitude of the function is 3/2 after comparing with the general equation option (C) is correct.
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Please help I will give the most points
Answers
Answer:
7
Step-by-step explanation:
The format for a coordinate pair is (x-coordinate, y-coordinate). This means the y-coordinate comes second, and since the 7 comes second here we can say that 7 is the y-coordinate.
That is the answer
- Kan Academy Advance
Write down the letter of the shape that is congruent to the shaded shaPe
Answers
Answer:
E looks like it is most congruent
Step-by-step explanation:
What is the solution to the trigonometric inequality sin^2(x) > cos(x) over the interval 0<= x <= 2pi radians?
Answers
The solutions to the trigonometric inequality in the interval is given by:
[tex]\frac{\pi}{6} \leq x \leq \frac{5\pi}{6}[/tex], or [tex]\frac{7\pi}{6} \leq x \leq \frac{11\pi}{6}[/tex]
What is the trigonometric inequality?It is given by:
[tex]\sin^{2}{x} > \cos{x}[/tex]
We have the following identity:
[tex]\sin^2{x} = 2\sin{x}\cos{x}[/tex]
Hence:
[tex]2\sin{x}\cos{x} > \cos{x}[/tex]
[tex]2\sin{x} > 1[/tex]
[tex]\sin{x} > \frac{1}{2}[/tex]
Between the first and second quadrant, the solution is:
[tex]\frac{\pi}{6} \leq x \leq \frac{5\pi}{6}[/tex]
Between the third and fourth quadrants, the solution is:
[tex]\frac{7\pi}{6} \leq x \leq \frac{11\pi}{6}[/tex]
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Write the place value of the 1 in 742.513
Answers
Tenths
Hundredths
Thousandths
Ten Thousandths
And so forth.
In this one, the 1 falls into the hundredths place, since it is the second digit after the decimal point.
Hope this helps!
Hi Student!
Looking at the problem statement, we are asked to find the place value of the 1 in the number 742.513. Let's go from right to left and name each of the place values. 7 is in the hundreds place, 4 is in the tens place, 2 is in the ones place, 5 is in the tenths place, 1 is in the hundredths place, 3 is in the thousandths place.
Therefore, our final answer for which place value the number 1 in 742.513 is, we come to the conclusion of the hundredths place.
For x/3 - 8 = 15, if x = 69
Answers
Answer:
x/3 - 8 =15
x/3 =15+8
69/3 =23
69 =23*3
69. =69
Mr Stephen saved 350 rupees per month how much money will he save in 3 years
Answers
Answer:
the answer to that question is 12,600 rupees
Which of the following phrases are inequalities?Choose 2 answers: A. (8 + f)(8 - f) > 36
B.
C.
D.
E.
Answers
how to solve for axis of symmetry for y=(x+2)(x-4)
Answers
Answer:
x = 1
Step-by-step explanation:
you can first find the two zeroes
that would be
x + 2 = 0
x - 4 = 0
x = {-2, 4}
then you average them
-2 + 4 = 2
2 / 2 = 1
the aos is 1
Answer:
x=1
Step-by-step explanation:
[tex]y=x^{2} -4x+2x-8[/tex]
[tex]y=x^{2} -2x-8[/tex] [tex](a=1, b=-2)[/tex]
[tex]x=-\frac{b}{2a} =\frac{-2}{2*1}[/tex]
[tex]x=1[/tex]
[tex]y=(x+2)(x-4), x=1[/tex]
[tex]y=(1+2)(1-4)[/tex]
[tex]y=-9[/tex]
Given line PQ bisects line RS, LR=LS
Prove: Triangle PQR= Triangle PQS
Answers
Answer:
See Below
Step-by-step explanation:
Since PQ is perpendicular to RS, the angles PQR and PQS would be right angles, and right anglers are congruent, so <PQR ≅ <PQS. We are given that <R and <S are the same length, so they are congruent(<R ≅ <S). Since PQ is included in both triangles and it is the same length as itself(PQ ≅ PQ).
We have three congruent parts, two angles and one side. Therefore, using AAS, ΔPQR ≅ ΔPQS
Answer:
See below ~
Step-by-step explanation:
Given :
⇒ PQ ⊥ RS
⇒ ∠R = ∠S
===============================================================
Solving :
⇒ PQ = PQ (common side)
⇒ ∠R = ∠S (given)
⇒ ∠PQS = ∠PQR = 90° (⊥ bisector forms equal right angles)
⇒ ΔPQR ≅ ΔPQS (by ASA congruence)
30 POINTS ANSWER ASAP PLS
Complete the square to justify that Julia’s graph is correct.
6x2 + 12x + 6y2 – 48 ≤ 0
Answers
Answer:
1) x + 1
2) y - 0
3) 9
Step-by-step explanation:
Answer:
the first answer is (x+1) the second box (y-0) and the last box is 9
Step-by-step explanation:
Select the correct answer from each drop-down menu. Segment AB has seven equally spaced points on it. Starting at A and moving left to right, the points are C, D, E, F, G, H, and I. In the diagram, is divided into equal parts. The coordinates of point A are (-3, 9), and the coordinates of point B are (9, 5). The coordinates of point C are . The coordinates of point E are . The coordinates of point H are .
Answers
The coordinates of points C, E and G are respectively; C(-0.75, 8.5), E(3.75, 7.5) and H(7.5, 6)
How to find the Coordinates of a Line Segment?
We are told that the line AB is divided into 7 equally spaced points labelled as C, D, E, F, G, H and I.
Now, coordinates of A and B are; A(-3, 9) and B(9, 5)
Since they are equally spaced, then it means that point F is the midpoint of the line. If (x, y) is the coordinate of F, then;
x, y = (-3 + 9)/2, (9 + 5)/2
x, y = (6, 7)
H is the midpoint of FB. Thus;
H(x, y) = (6 + 9)/2, (5 + 7)/2
H(x, y) = (7.5, 6)
D is midpoint of A and F. Thus;
D(x, y) = (-3 + 6)/2, (9 + 7)/2
D(x, y) = (1.5, 8)
E is midpoint of F and D. Thus;
E(x, y) = (1.5 + 6)/2, (8 + 7)/2
E(x, y) = (3.75, 7.5)
C is midpoint of D and A. Thus;
C(x, y) = (-3 + 1.5)/2, (9 + 8)/2
C(x, y) = (-0.75, 8.5)
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Answer:
Select the correct answer from each drop-down menu.
Segment AB has seven equally spaced points on it. Starting at A and moving left to right, the points are C, D, E, F, G, H, and I.
In the diagram, is divided into equal parts. The coordinates of point A are (-3, 9), and the coordinates of point B are (9, 5).
The coordinates of point C are
.
The coordinates of point E are
.
The coordinates of point H are
.
cordinates for c are -1.5, 8.5 E is 1.5, 7.5 H is 6,6
Step-by-step explanation:
what's the answer
1. The function below shows the weekly earnings of Alice from her job last summer.
Answers
a) We kindly invite to check the image attached below to see a detailed graph of the piecewise function.
b) The piecewise function is continuous.
How to understand a piecewise functionA piecewise function is a conditional combination of two or more functions, whose expression depends on which value of the domain is the function evaluated at.
a) The piecewise function described in the question is plotted on a graphing tool (i.e. Desmos), whose result is presented in the image attached below.
b) A function is continuous if and only if there is one value from range for every value of domain. The piecewise function is continuous as linear functions are continuous and the two functions of the conditional combination have the same value for x = 30.
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√17 is a number between
Answers
evaluate that equation 3√1÷125
Answers
Answer:
0.2683281573
Step-by-step explanation:
The sum of the digits of a three-digit number is 12. The tens digit, t, is 2 more than the hundreds digit, h. The units digit, u, is equal to the sum of the tens and hundreds digits. What is the number?
Answers
Answer:
246
Step-by-step explanation:
h = 2
t = 4
u = 6
t - h = 4 - 2 = 2
u = h + t = 2 + 4 = 6
Find the constant of proportionality for the table of values.
The constant of proportionality is k = ___
Answers
Answer:
K=3.5
Step-by-step explanation:
1. y/x=k
2. 7/2 or
[tex]7 \div 2 =[/tex]
( 3.5 )
3. 10.5/3 or divided by 3 is 3.5
4. Continue divided y/x and if you get same answer than your constant of proportionality is 3.5 only for this question.
What is the midpoint of the segment shown below?
O A. (-9, 3)
O B. (-9, 3)
O c. (-9, ;)
D. (-9, 3)
Answers
Answer:
where the segment ??????!??!??!?
Step-by-step explanation:
give me the segment I may be able to answer
HELP PLSSSSSSSSS WIL GIVE BRAINLEST Nathan needs 10 ounces of lemonade.
He needs to know how much liters that is.
A 16
B 5
C 943
D 0.295735
Answers
The volume of 10 ounces of lemonade in litres is 0.295735 litres.
How to convert from ounces to litres?
He needs 10 ounces of lemonade.
To know the volume in litres, we have to convert from ounces to litres.
Therefore,
1 ounces = 0.0295735 litres
10 ounces = ?
cross multiply
volume in litres = 0.0295735 × 10
volume in litres = 0.295735
Therefore, the volume of the lemonade in litres is 0.295735 litres.
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Solve for x.
3x-3/4x+3
-
When angles form a linear pair, their sum is 180°.
8x 3 + 4x + 3 = 180
[?]+[] = 180
Hint: First we must combine like terms. Calculate the sum
of 8x and 4x and enter the value of the coefficient.
Enter
can anyone help me ? and show solving steps if possible
Answers
Answer:
Step-by-step explanation:
Remark
They are asking you to combine like terms. The total should be 180.
Givens
2 angles
8x - 3 4x + 3Total 180
Solution
8x - 3 + 4x + 3 = 180 The threes cancel. So add what's left. They are of opposite signs, so they cancel.
12x = 180 Divide both sides by 12
12x/12 = 180 /12
x = 15
In this question we are provided with the two angles that is 8x - 3 and 4x + 3 respectively. It is also given that the sum of this two angles is 180°.
To solve this question we will combine the like terms and there sum must be 180°.
[tex] \small\sf{ 8x - 3 + 4x + 3 = 180°} [/tex]
[tex] \bull \: \small\sf{ We \: will \: cancel \: 3 \: because \: they \: are \: of \: opposite \: signs }[/tex]
[tex] \small\rm 8x + 4x = 180 \degree[/tex]
[tex] \bull \: \small\sf{Addition} [/tex]
[tex] \small\rm{ 12x = 180 \degree}[/tex]
[tex] \bull \: \small\sf{ Divide\: both \: side \: by \: 12}[/tex]
[tex] \small\rm{ \dfrac{12x}{12} = \dfrac{180}{12} \: = 15 \degree}[/tex]
[tex] \small \underline{ \boxed{\sf{x = 15} }}[/tex]
[tex] \rule{71mm}{4pt}[/tex]
Belle walks
7
10
mile each morning and
1
4
10
miles each evening.
How many miles does she walk in 5 days?
I'll mark brainliest
Answers
Answer:
I'm not really sure what you mean by the numbers because that's alot.
Step-by-step explanation:
But all you have to do is:
Plus the morning and evening amount and then times it by 5
Like this: y + z x 5
I hope this helped!
Sorry if it didnt...
But have a nice day
Joe bought a $40 video game for only $28, what was the percent discount on
the item?
Answers
Answer:
30 % off
Step-by-step explanation:
12 dollars off of 40
40 (x) = 12
x = 12/40 = .3 or 30 %
Find the area with the radius of 27
Answers
Answer: The answer is 2289.06
Step-by-step explanation: I assume it’s a circle as it has a radius so simply multiply 3.14 by the radius 27^2