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
The x coordinate for an ordered pair in the solution set of x+2y=11 is 3. find the y coordinate
Answer:
y=4
Step-by-step explanation:
solve for y. I have the work shown in the picture I attached.
What are the coordinates of point S”?
Answer:A
Step-by-step explanation:
Help please! The division Axiom would allow us to say which two angles are equal?
Answer:
The correct option is;
(3) ∠ADB and ∠BDC
Step-by-step explanation:
From the division axiom, we have;
(a+a)/a = 2·a/a = 2
The given parameters are;
m∠ADC = m∠ABC
[tex]\overline {BD}[/tex] bisects ∠ADC and ∠ABC
Therefore;
∠ADB ≅ ∠BDC
∠ABD ≅ ∠CBD
Therefore;
∠ADB/∠CBD = ∠BDC/∠ABD
Given that m∠ADC = m∠ABC and ∠CBD = 1/2 × m∠ABC = 1/2 × m∠ADC = ∠ABD, we are allowed to say, ∠ADB and ∠BDC are equal.
Until the scale was changed in 1995, SAT scores were based on a scale set many years ago. For Math scores, the mean under the old scale in the 1990s was 470 and the standard deviation was 110. In 2013 the mean was 515 and the standard deviation was 116. Gina took the SAT in 1994 and scored 500 on the Math test. Her cousin Colleen took the SAT in 2013 and scored 530 on the Math test. Who did better relative to their peers, and how can you tell? Group of answer choices Colleen—she scored 30 points higher than Gina. Gina—the standard deviation was bigger in 2013. Gina—her standardized score is higher than Colleen’s. Colleen—her standardized score is higher than Gina’s.
Answer:
Gina—her standardized score is higher than Colleen’s.
Step-by-step explanation:
Until the scale was changed in 1995, SAT scores were based on a scale set many years ago.
We solve this question using z score formula also know as standardized score formula which is given as:
z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.
For Gina
Gina took the SAT in 1994 and scored 500 on the Math test.
For Math scores, the mean under the old scale in the 1990s was 470 and the standard deviation was 110.
x = 500
μ = 470
σ = 110
Hence, the z score is given as:
z = 500 - 470/110
z = 0.27273
Gina's z or standardized score is 0.27273
For Colleen
Her cousin Colleen took the SAT in 2013 and scored 530 on the Math test.
In 2013 the mean was 515 and the standard deviation was 116.
x = 530
μ = 515
σ = 116
Hence, the z score is given as:
z = 530 - 515/116
z = 0.12931
Colleen's z or standardized score is 0.12931
The person who did better relative to their peers is Gina and this is because her standardized score is higher than Colleen’s.
Please quickly! Out of 5,500 people who attended the football game, fifty-six percent were rooting for the home team. How many people rooted for the home team?
Pleaser answer correctly !!!!!!!!!!!!!!!!!!! *use mathematical language* Will mark brainliest !!!!!!!!!!!!!!
Answer:
Vertical angles are always congruent, or of equal measure. ... Both pairs of vertical angles (four angles altogether) always sum to a full angle (360°). Two angles are said to be linear if they are adjacent angles formed by two intersecting lines. The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees. so therefore verticle angles DO NOT form a linear pair
Step-by-step explanation:
brainliest please ? :)
1. If mPCV = 42, then mZVCN =
Answer:
Easy lol mzvcn=48
Step-by-step explanation:
8 divided by 32.16?
I need help with this, please answer as fast as possible!!
Nothing but slope.................
Answer:
1. 1
2. 3
3. 4
Step-by-step explanation:
Simplify square root of 5 multiplied by the cube root of 5 . (10 point)
Group of answer choices
5 to the power of 7 over 6
5 to the power of 2 over 3
5 to the power of 5 over 6
5 to the power of 1 over 6
[tex] \sqrt{5} \times \sqrt[3]{5} [/tex]
[tex] {5}^{ \frac{1}{2} } \times {5}^{ \frac{1}{3} } [/tex]
[tex] {5}^{ \frac{1}{2} + \frac{1}{3} } [/tex]
[tex] {5}^{ \frac{3}{6} + \frac{2}{6} } [/tex]
[tex] {5}^{ \frac{5}{6} } [/tex]
[tex] \sqrt[6]{ {5}^{5} } [/tex]
Jen walked 1/4 of a mile in 1/2 of an hour. At this rate, how long will it take her to walk 2 miles to the park?
A. 2 hours
B. 8 hours
C. 4 hours
D. 6 hours
Answer:
The awnser is C. 4 hours
Step-by-step explanation:
It takes her 2 hours two walk 1 mile so 2*2 is 4
What is 1,035 divided by 38
Answer:
27.2368421053
Step-by-step explanation:
Write an equation in slope-intercept form that passes through the point (3,-5)
with a slope of 1.
f(0) = 3 and f(1) = 15.
Answer:
Step-by-step explanat
Given=F(0) = 3 and f(1) = 15.
So f(X)=12x+3
When X=0, f(0)=12x0+3=3
When X=1, f(1) = 12x1+3= 15
So f(X)=12x+3 is the solution o
Earth travels 30 kilometers each second as it revolves around the Sun. How many miles does Earth travel in 1 second? Round to the hundredths if necessary.
9514 1404 393
Answer:
18.64 miles
Step-by-step explanation:
There are 1.609344 km per mile, so the distance traveled in 1 second is ...
(30 km)(1 mi)/(1.609344 km) ≈ 18.64 mi
The Earth travels around the Sun at the rate of about 18.64 miles per second.
Answer:
18.64 if rounded
Step-by-step explanation:
First you need to know how many miles is 1 kilometer. That would be approximately 0.62137 miles. Multiply this by 3 and you would get 1.86411. Now multiply this by 10 to make it 30 kilometers worth of miles and not 3 kilometers. You would get 18.6411 which rounded to the hundredths place would be 18.64.
9 A book publishing company selected 30 out of 50 books submitted for publishing.
What decimal is equivalent to the fraction of books selected for publishing?
Answer:
Step-by-step explanation:
30/50= 3/5= 0.6
The ratio of boys to girls in Ms. Alper’s math classes is 5 ∶ 7. If there are 60 boys in all of her classes, how many girls are there ?
Plz help im so dumb ;-;
Answer:
I think it's 80 I'm sorry if I'm wrong
Answer:
the person above is incorrect I think it may or may not be 75
Brooklyn has 4 3/4 cups of oatmeal. She is dividing the oatmeal into 1/3-cup servings.
Answer:
14 servings
Step-by-step explanation:
4 3/4 = 19/4
19/4 ÷ 1/3
19/4 × 3
57/4
14 1/4 serving if just want one solid answer its 14
What is the Awnser to this?
28 divided 3.5
help meh plz
Answer:
8
have a good day! :)
Crew car wash is offering their unlimited “Works” package for 20% off the normal price of $720 per year . What is the annual cost of the unlimited works package with the discount?
Answer:
144
Step-by-step explanation:
It should be. I don't really know if there are answer choices or not.
PLEASE PLEASE PLEASE PLEASE HELPP!!what is The function f(x) = 4x – 8 reflected across the y-axis on a coordinate plane
2. In the linear equation y = -3x + 2, the value
(-3) represents which of the following?
a. the slope of the
line
b. the y-coordinate
of the y-intercept
c. the x-coordinate
of the y-intercept
d. the quadrant in
which the line lies
Answer:
C
Step-by-step explanation:
In the form y=mx+x, m is the x coordinate of the y intercept.
the height of an apple
Answer:
apples are usually roundish, 5–10 cm (2–4 inches) in diameter
Step-by-step explanation:
Dwarf apple trees grow about 10 feet tall, while semi-dwarf varieties can reach 15 feet. Meanwhile, standard-size apple trees often soar to heights above 20 feet and sometimes tower at 30 feet.
Apples are 5 - 10 cm in height.
What is height?Height, altitude, elevation mean vertical distance either between the top and bottom of something or between a base and something above it
Given is an apple.
When harvested, apples are usually roundish, 5–10 cm (2–4 inches) in diameter.
Therefore, apples are 5 - 10 cm in height.
To solve more questions on distances, visit the link below -
brainly.com/question/30215119
#SPJ6
15 - 3k = 10(k-5)
Can someone please answer this
Answer:
k = 5
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASEquality PropertiesStep-by-step explanation:
Step 1: Define equation
15 - 3k = 10(k - 5)
Step 2: Solve for k
Distribute 10: 15 - 3k = 10k - 50Add 3k to both sides: 15 = 13k - 50Add 50 to both sides: 65 = 13kDivide 13 on both sides: 5 = kRewrite: k = 5Step 3: Check
Plug in k into the original equation to verify it's a solution.
Substitute in k: 15 - 3(5) = 10(5 - 5)Subtract: 15 - 3(5) = 10(0)Multiply: 15 - 15 = 0Subtract: 0 = 0Here we see that 0 does indeed equal 0.
∴ k = 5 is a solution of the equation.
Answer:
k=5
Step-by-step explanation:
1. Apply distributive property: 15-3k=10k-50
2. Bring all variables to one side: 15-3k=10k-50
+3k +3k
15=13k-50
3. Isolate K by bring the term in it's way to the other side: 15=13k-50
+50. +50
65=13k
4. Isole your variable by divide by 13: 65=13k
65/13 13/13
5=k
13-715x=130x
show work plzz
Answer:
Solving equation [tex]13-715x=130x[/tex] we get [tex]x= \frac{1}{65}[/tex]
Step-by-step explanation:
We need to solve the equation [tex]13-715x=130x[/tex]
Combining like terms and solving
[tex]13-715x=130x\\Adding \ 715x \ on \ both \ sides:\\13-715x+715x=130x+715x\\13=845x\\Divide \ both \ sides \ by \ 845\\\frac{13}{845}=\frac{845x}{845}\\=>x= \frac{1}{65}[/tex]
So, solving equation [tex]13-715x=130x[/tex] we get [tex]x= \frac{1}{65}[/tex]
At an office supply store, 8 boxes of pens and 3 folders cost $6.50. At the same store, 8 boxes of pens and 1 folder cost $5.90. How much does one box of pens cost? How much does 1 folder cost? Please explain.
Answer:
$0.30
Step-by-step explanation:
the difference of the folders is 2.
The difference of money is $0.60
60/2 = 30
$0.30
please help me this question
Answer:
[tex]C) 1210m^2[/tex]
Step-by-step explanation:
Initial Length of the rope (r) = 12 m
Final length of the rope (R) = 23 m
[tex]Additional\ area\ acquired\ = Final Area- Initial Area\\=\pi R^2- \pi r^2\\=\pi (R^2-r^2)\\=\pi (23^2-12^2)\\=\pi (529-144)\\=\pi (385)\\=385\pi \\\\As\ \pi = \frac{22}{7} \\\\Hence,\\385\pi \\=385 * \frac{22}{7} \\=55*22\\=1210 m^2[/tex]
Evaluate 9/12 × 6/9 Give your answer in its simplest form.
Answer:
1/2
Step-by-step explanation:
reduce 12 with 6 and 9 with 9 and your equation is now 1/2 x 1/1
you now multiply ur franction, which gives you 1/2
hope this helped :)
Kim decides to give her old toys to her younger cousins. She gives her cousin Sarah 2/3. Then, she gives her cousin Ryan 2/5 of the remaining toys. She has 6 toys left. How many toys did Kim have to begin
Answer:
30
Step-by-step explanation:
Work backwards:
6 is 3/5 of a number, and that number is 1010 is 1/3 of a number, and that number is 30Check your work:
2/3 of 30=20 toy to Sarah30-20=10 toys left2/5 of 10=4 toys to Ryan10-4=6 toys left