Step-by-step explanation:
Given the expression for the position of a body moving along the s-axis expressed as;
[tex]s = t^3-27t^2+200t[/tex]
The acceleration of the body function will be gotten by finding the second derivative of the displacement function as shown;
[tex]\frac{ds}{dt} = 3t^2-2(27)t+200\\ \frac{ds}{dt} = 3t^2-54t+200\\\\\\a = \frac{d^2s}{dt^2} = 2(3)t-54\\a = \frac{d^2s}{dt^2} = 6t-54\\[/tex]
First we need to get the time taken when the velocity is zero.
[tex]Given \ v(t) = \frac{ds}{dt} = 3t^2-53t+200\\at \ v(t) = 0\\0 = 3t^2-54t+200\\[/tex]
factorize;
t = 54±√54²-4(3)(200)/2(3)
t = 54±√2916-2400/2(3)
t = 54±√516/6
t = 54±22.72/6
t = 54+22.72/6 and 54-22.72/6
t = 12.79s and t = 5.21s
Get the acceleration;
at t = 12.79
a = 6t-54
a = 6(12.79)-54
a = 76.74-54
a = 22.74m/s²
at t = 5.21
a = 6t-54
a = 6(5.21)-54
a = 31.26-54
a = -22.74m/s²
Hence the body's acceleration each time the velocity is zero are 22.74m/s² and -22.74m/s²
81a + (- 18)
how do you factor the expression
Answer:
9(9a-2)
Step-by-step explanation:
81a + (-18)
= 81a - 18
= 9 (9a - 2)
Answer:
9(9a-2)
Step-by-step explanation:
Cami starts with $7 and saves $13 each week.
Maggie starts with $11 and saves $13 each week. After how many weeks will Cami and Margaret have the same amount of
money?
Answer:
No matter how many weeks pass, they will never have the same amount of money. This is because their rate of change is the same. If Cami made more money per week than Maggie, then she would eventually be able to catch up and have the same amount of money as Maggie.
Danny charges $40 for 4 hours of swimming lessons, Martin charges $85 for 5 hours of swimming lessons. Who offers a better deal?
Answer:
Danny does
Step-by-step explanation: 40 / 4 = 10
85 / 5 = 17
10 is less than 17 meaning that Danny is offering a better deal.
Hope this helps!
Answer:
Danny
Step-by-step explanation:
Danny offers $40 for four hours and Martin has a deal of $85 for five hours of swimming lessons so i know that Danny has the beater deal.
what is the nearest integer of 3^ square root 74
Answer:
74
Step-by-step explanation:
Tom's recipe requires 8 cups of sugar to make 40 sugar cookies. How many
sugar cookies will 120 cups of sugar make? *
Question 7:
Given two terms in an arithmetic sequence find the nth term.
a) 18th = 3362 and 38th= 7362
گرم
a
The answer is:
Nth term=200n-238
1/2(-4+6n)=1/3n+2/3(n+9)
The correct answer is n=4:)
Answer:
n= 4
Step-by-step explanation:
(do not round the answer)what is
A. 3.48g+8.62=29.37
Answer:
The answer is 5.9626436782
can someone help me with these questions I want to make sure I got them right
9514 1404 393
Answer:
14/9-3.65/411/2, 7/8, 5/18Step-by-step explanation:
1. n = (11/6 -2/3)(4/3) = (7/6)(4/3) = 14/9
__
2. x = (9.82 -28.18)/5.1 = -3.6
__
3. y = 3/2 -1/4 = 5/4
__
4a. t = 2(3 -1/4) = 11/2
4b. y = (1/5 +1/2)(5/4) = ((2+5)/10)(5/4) = 7/8
4c. x = (11/3 -2)/6 = (5/3)(1/6) = 5/18
Tom bought 3 boxes of books at a yard sale. If each box had 2 books how many books did he Buy ?
i will be giving brainliest.
Answer:
6
Step-by-step explanation:
2 books in each box.
There are three boxes
2 times 3 equals 6
What is the sign of 9(-0.5)
Hi
For a multiplication , law sign state : if the two terms of multiplication are of the same sign, result is positive. Otherwise, it's negative
here 9 is positive, and -0.5 negative. The two terms have contrary signs, then the result will be negative.
Suppose Jerome reads the following numbers of pages each day. Will he meet his goal of reading at least 85 pages by the end of the day Friday?
Answer:
Step-by-step explanation:
Jerome has already read 50 pages of a novel and read p pages each day from Monday to Friday.
If Jerome read at least 85 pages by the end of Friday, inequality will be,
50 + 5p ≥ 85
If Jerome reads 6 pages each day,
For p = 6,
Inequality will be,
50 + 5(6) ≥ 85
80 ≥ 85
It's not true.
Therefore, he will not meet his goal.
If p = 7,
Inequality will be,
50 + 5(7) ≥ 85
85 ≥ 85
It's true.
Therefore, he will meet his goal.
If p = 8,
Inequality will be,
50 + 5(8) ≥ 85
90 ≥ 85
It's true.
Therefore, he will meet his goal.
1. Will not
2. Will
3. Will
At a model rocket competition, Mrs. Jennings launches a rocket is launched upward
from the ground with an initial velocity of 138 feet per second.
The formula for vertical motion is
h(t) = 0.5at? + vt +s, where the gravitational constant, a, is -32 feet per second squared, v
is the initial velocity, and s is the initial height. Time t is measured in seconds, velocity
v is measured in feet per second, and heights h and s are measured in feet.
Write the function that describes the height, h in feet, of the rocket l seconds into
launch
Answer:
The function that describes the height, h in feet, of the rocket, t seconds into launch is h = -16·t² + 138·t
Step-by-step explanation:
The given parameters are;
The initial velocity of the rocket, v = 138 feet per second
The vertical motion formula = h(t) = 0.5·a·t² + v·t + s
The gravitational constant, a = -32 ft./s²
s = The initial height of the rocket
Therefore, he have;
The height of the rocket, t seconds seconds into launch is given as follows;
Height = h = h(t) - s = 0.5·a·t² + v·t
Substituting the known values gives;
h(t) - s = 0.5 × (-32) × t² + 138 × t = -16·t² + 138·t
h = -16·t² + 138·t
The function that describes the height, h in feet, of the rocket, t seconds into launch is h = -16·t² + 138·t.
Kole and his sister ordered ice cream. He spent $6.50 for his sundae. She ordered the same sundae with sprinkles, which were an extra $0.40. Kole pays for his ice cream and half of his sisters with $10. How much change will he get back?
Answer:
$0.05
Step-by-step explanation:
because he payed half of his sisters and it was $3.45 and plus his was $9.95 so he got $0.05 back
Translate the sentence six less than the product of four and a number is -2 into an equation
Answer:
4x-6=-2
Step-by-step explanation:
This is the mathematical form of the equation.
Eliza claims she can create an equation using these cards that has NO solutions. Axel says this is impossible—that every equation created with these cards will have a solution. Who is right?
Answer:
axel
Step-by-step explanation:
URGENT PLEASE HELP PLEASE
Answer: I believe the answer is A.
Explanation: hope this helps
hurryyyyyyyyyyy 5/6 - 1/4=
yes subtraction
Step-by-step explanation:
(5x4)/(6x4) - (1x6)/(4x6)
=20/24 - 6/24
= (20-6)/24
=14/24
=7/12
give me brainliest
Estimate 8 x 342 Jehhdhd
Answer:
2,736
Step-by-step explanation:
Scientists have found that the relationship between the area of an island and the number of species can be modeled approximately by S=-3.404+103.2ln(A) S=−3.404+103.2ln(A), where AA is the area in km^2km 2 and SS is the number of species.
Answer:
[tex]A=e^{(S+3.404/103.2)[/tex]
Step-by-step explanation:
Step one:
we are told that the relationship between the number of species and the island area is given as
[tex]S=-3.404+103.2ln(A)[/tex]-----------------1
based on any given value for either area or number of species, we can find the other.
say we want to find the land area for a given amount of specie
Step two:
we first make area A subject of the formula.
[tex]S=-3.404+103.2ln(A)[/tex]
let us isolate [tex]ln(A)[/tex]
[tex]S + 3.404 = 103.2ln(A)[/tex]
Divide both sides by 103.2 we have
[tex](S + 3.404)/103.2 = ln(A)[/tex]
Now, exponentiate both sides using the base e.
[tex]A=e^{(S+3.404/103.2)[/tex]----------------2
for a given value of "S" we can find the area A based on the above expression.
A 68-year old retiree has a pension savings of $43,000, a 401k of $75,000, and an IRA account of $62,000. Before 2008, he had 2% more cash in the pension, 12% more in the IRA, and −1% in the 401k. He wants to take out 2% from each account before he turns 72, which will cost him a penalty of an extra 3% from the current total amount in his pension, 4% from the 401k, and 6% from the IRA. What is the highest amount that will be taken from a single account, including the penalty, if the retiree takes the money out now from each?
Answer:
The answer is the IRA
Step-by-step explanation:
If he takes out 2% from each account, the highest penalty will be for the IRA account which is, 6% of 62,000 is $3,720. He will also take 2% of that 62,000 which will be $1,240. The total will be $4,960.
For the 401k account the withdrawal is $1,500 and the penalty is $3,000. That is $460 less than the IRA account.
I hope this answer helps.
Answer:
54280
Step-by-step explanation:
2+6=8
.08 * 59000=4720
59000-4720=54280
Kale is hiking 2,345 ft above sea level. The peak of the mountain he is climbing is 3,283 feet above sea level . What is the vertical distance between kale and the mountain peak ?
938 ft
942 ft
1,142 ft
5,628
Answer:
a
Step-by-step explanation:
Answer:
so A. is the correct answer
Step-by-step explanation:
If Kale is at 2345 feet and needs to reach 3283, he will need to travel another 938 feet.
Help rn please!! Urgent
Answer:
x² + 2x - 15 = 0
Step-by-step explanation:
- 5 and 3 are zeros of quadratic function.
(x + 5)(x - 3) = 0
x² + 2x - 15 = 0
Use synthetic division to solve (2x^3+4x^2-35x+15)/(x-3). What is the quotient?
Answer:
the quotient is 2x^2+10x-5
A figure has an area of 64 unit square which describes the area of the figure after a dilation with a scale factor of 3/2
Answer:
It's 144 units^2
Step-by-step explanation:
You have to take your 3/2 and square it, turning it to 9/4 and multiply that by 64, which gives you 144.
cordenadas cartesianas
I need to know 9 and 10
Answer:
x=36°
y=144°
Step-by-step explanation:
y is the corresponding angle of angle 144° and since corresponding angles are always congruent y=144°
x is the same side interior angle of angle 144° and since same side interior angles are also supplementary angles that add up to 180° x=36°
180°-144°=36°
hopefully this helps :)
Jennifer walks 3/4 mile in 1/4 hour, and Gavin walks 1/8 mile in 1/12 hour. Part A. What is Jennifer's walking rate, in miles per hour? Part B. What is Gavin's walking rate, in miles per hour? Part C. Jennifer and Gavin both plan on walking 4.5 miles, and they want to finish at the same time. If Gavin starts walking at 1:00 pm, at what time should Jennifer start walking? Use words, numbers, and/or pictures to show your work. Write your answer(s) on the paper provided.
Answer:
Step-by-step explanation:
Part A: 3/4 divided by 1/4= 3/4 * 4/1 = 3, Jennifer walks 3 miles per hour.
Part B: 1/8 divided by 1/12= 1/8 * 12/1 = 1.5 or 1 and 1/2 miles per hour
For Part C I dont know, Sorry guys
Consider a parabola P that is congruent to y=x^2, opens upward, and has vertex (0,0). Find the equation of a new parabola that results if P is reflected in the x-axis, and translated 1 unit to the left and 3 units up.
9514 1404 393
Answer:
y = -(x+1)^2 +3
Step-by-step explanation:
Translating f(x) left by 1 unit replaces x with x+1.
Translating f(x) up by 3 units replaces f(x) with f(x)+3.
Reflecting f(x) over the x-axis replaces f(x) with -f(x).
__
When y = x^2 is reflected over the x-axis, it becomes ...
y = -x^2
When y = -x^2 is translated 1 unit left, it becomes ...
y = -(x +1)^2
When y = -(x+1)^2 is translated 3 units up, it becomes ...
y = -(x +1)^2 +3
what is the smallest even number you can make with the numbers 5,7,4,9
Answer:
-4
Step-by-step explanation:
5 - 9 = -4.
Only 4 - 9 = -5 is smaller, but it is an odd number.
Answer:
-1
Step-by-step explanation:
5-7= -2, 7-9= -2
4-9= -5, 4-5= -1