I assume "first phase" refers to the first 6.00 seconds of the dash.
Since the sprinter starts from rest and accelerates uniformly, he covers a distance x after time t of
x = 1/2 at²
where a is his acceleration.
The sprinter's velocity v after time t is
v = at
so that if he attains a speed of 14.7 m/s after 6.00 s, he does so with acceleration a such that
14.7 m/s = a (6.00 s) ⇒ a = 2.45 m/s²
Then in the first 6.00 seconds, the sprinter travels
x = 1/2 (2.45 m/s²) (6.00 s)² = 44.1 m
(3x-1)•(5x-3)
find area and perimeter in feet
Answer:
21 is the answers to your question
Given cos 0 = 1/6 and angle 0 is in Quadrant IV, what is the exact value of sin 0 in
simplest form? Simplify all radicals if needed.
cos 0 = 1/6
1 - cos²0 = sin²0
sin²0 = 35/36
in quadrant IV (4) the cos is positive sin is negative.
sin0 = - √35/6
17. Alexis has a painting presently valued at $2000. An art dealer told her the painting would
appreciate at a rate of 8% each year. In how many years will the painting be worth $5000?
Round your answer to the nearest tenth.
Show work please
Answer:
18.8 years
Step-by-step explanation:
8% of $2000 = $160
To be worth $5000, the painting need to rise by $3000
And every year it rise by $160, so it will need 3000 : 160 = 18.75 (round to 18.8) years.
HELP?!?!
The shaded octagon is transformed to the unshaded octagon in the coordinate plane below.
Which statement about the transformation is true?
The unshaded octagon is a reflection because it is a flip over a diagonal line.
The unshaded octagon is a dilation because it is smaller than the shaded octagon.
The unshaded octagon is a horizontal translation because it is directly to the left of the shaded octagon.
The unshaded octagon is a vertical translation because it is directly under the shaded octagon.
Answer:
(A) The unshaded octagon is a reflection because it is a flip over a diagonal line.
Step-by-step explanation: Trust, rust, and pixie dust
Answer:
A is correct
The unshaded octagon is a reflection because it is a flip over a diagonal line.
i took the test
Solve the equation: 30 = 5 + 0.5d
Answer:
d = 50
Step-by-step explanation:
30 = 5 + 0.5d ( subtract 5 from both sides )
25 = 0.5d ( divide both sides by 0. 5 )
50 = d
What is the equation of a horizontal line passing through the point (1, 14)?
y=1
y= 14
x=1
x=14
Answer:
y = 14
Step-by-step explanation:
If the line is horizontal, it will always have the ssame value of y for all values of x. Therefore, y = 14.
Jimmy's height is 156 cm, Kessie's height is 168 cm, while Lya's height is 132 cm. Define:
Answer:
132<156<168 or 12×1, 12×2 ...
Step-by-step explanation:
Jimmy's 24cm taller than Lya, and Kessie's 12cm taller than Jimmy
The first term of geometric series is -3, the common ratio is 6, and the sum of the series is -4,665. using a table of values, how many terms are in this geometric series
[tex]\qquad \qquad \textit{sum of a finite geometric sequence} \\\\ \displaystyle S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=\textit{last term's}\\ \qquad position\\ a_1=\stackrel{\textit{first term}}{-3}\\ r=\stackrel{\textit{common ratio}}{6} \end{cases}[/tex]
[tex]\stackrel{S_n}{-4665}~~ = ~~-3\left( \cfrac{1-6^n}{1-6} \right)\implies -4665=-3\left( \cfrac{1-6^n}{-5} \right) \\\\\\ -4665=\cfrac{3}{5}(1-6^n)\implies -4665\cdot \cfrac{5}{3}=1-6^n\implies -7775=1-6^n \\\\\\ -7776=-6^n\implies 7776=6^n\implies 6^5=6^n\implies \boxed{5=n}[/tex]
Answer:
5 terms
Step-by-step explanation:
The attached table shows that the sum of 5 terms is -4665.
__
Additional comment
A table for a problem like this is easily made using a spreadsheet. Each value is 6 times the previous, and each sum is the new value added to the previous sum. The first value and the first sum are -3.
In the attached, we have simply summed the terms, each term being computed using the explicit formula for this geometric sequence.
Ryan and Carlos are getting in shape for football season. Ryan starts at 140 pounds and gains two pounds per week. Carlos starts at 195 pounds but
loses three pounds per week. In how many weeks will they both weigh the same amount, and what will that weight be? (Hint: these are y = equations)
Answer:
In 11 weeks they will both be 162lbs each
Step-by-step explanation:
Simplify (3x2 − 2) (2x2 − 6x 3). 5x2 − 6x 1 5x2 − 6x − 1 x2 − 6x 1 5x2 − 8x 3.
Answer:
-566
Alternative form:
-5.66 x [tex]10^{2}[/tex]
A box is 20 inches long and 21 inches high. What is the diagonal length of the box?
Answer:
29 inches
Step-by-step explanation:
Answer:
Use Pythagoras' Theorem:
c²=a²+b²
c²=20²+21²
c²=841
c=√841
c=29 inches
Step-by-step explanation:
15x+3y=27 into slope-intercept form, simplifying all fractions.
Answer:
y = -5x + 9
Step-by-step explanation:
Slope-intercept form is the form
y = mx + b
So you need to rearrange the terms to get the y all by itself on the left. On the right, the x term goes first and last the constant (a plain number) see image.
2) Riddington and Greenwick are two small villages.
The population of Riddington has increased from 80 people to 120 people.
The population of Greenwick has decreased from 200 people to 120 people.
Show that Riddington has had the greater percentage change in its population.
You must show all your working.
Answer:
See belowStep-by-step explanation:
Find the amount of change in both cases and convert the change into percentage, then compare final results.
1. Riddington
Change:
120 - 80 = 40Percent change:
40/80*100% = 50% increase2. Greenwick
Change:
200 - 120 = 80Percent change:
80/200*100% = 40% decreaseAs we see 50% > 40% so this proves the statement.
The area of a circle is 22.68cm2.
Find the length of the radius rounded to 2 DP.
Answer: r=2.69. Calculate the radius of circle:Round the number: r=2.69Answer: r=2.69
Is (6,3) a solution to the equation "a"? Yes or No.
Yes
No
Answer:
Yes
Step-by-step explanation:
Write an equation for the line parallel to the given line that contains C.
c(3,8); y= 5/8x + 8
Answer:
x= - 64/5
Step-by-step explanation:
1- Substitute y = 0
2- Multiply both sides
3- Move the variable to the left
4- Divide both sides
What fraction of an hour is four minutes
Answer
1hr/15 mins=60 mins/15 mins=4 minutes.
Step-by-step explanation:
Please help mee
A punch recipe requires 2 cups of cranberry juice to make 3 gallons of punch. Using the same recipe, what is the amount of cranberry juice needed for 1 gallon of punch?
Answer:
0.66 cups of cranberry juice is needed to make 1 gallon of punch
Step-by-step explanation:
2 / 3 = 0.66
i hope this helped! have a wonderful rest of your day :)
Which polynomials are prime? Check all of the boxes that apply.
x2 + 9
x2 – 9
x2 + 3x + 9
–2x2 + 8
Answer:
Answer:
The prime polynomials are
x² + 9
x² + 3x + 9
Step-by-step explanation:
How do I solve this?
the model is using "t" as years after 2003, if we want to know the population in that country using that model at year 2003, then "t" must be 0, when t = 0, that's the initial population for that model.
[tex]A=920.2e^{0.005t}\implies A=920.2e^{0.005(0)}\implies A=920.2(1)\implies A=920.2[/tex]
Find a polynomial that represents the surface area of a sphere with a radius of (3x – 5) cm.
The surface area of a sphere is 4π^2. Leave your answer in terms of it.
Answer:
π(36x^2 - 120x + 100)
Step-by-step explanation:
4π(3x - 5)^2 = 4π[(3x)^2 - 2*3x*5 + 5^2] = 4π(9x^2 - 30x + 25)
= π(36x^2 - 120x + 100)
Help if you understand Thanks
Answer:
b
Step-by-step explanation:
Repeating domain (x-values) does not represent a function.
Option b does not have any repeating domains.
Hope this helps!
Answer:
The answer is the third one.
Step-by-step explanation:
Hopefully this is helpful :)
Evaluate and must show work
But i don’t think there is anything left to be done is there?
Please help
Answer:
ln(x)/2 -3.810930
Step-by-step explanation:
The relevant rules of logarithms are ...
ln(ab) = ln(a) +ln(b)
ln(a^b) = b·ln(a)
ln(a/b) = ln(a) -ln(b)
ln(e) = 1
__
Your expression expands to ...
[tex]\ln\left(\dfrac{4\sqrt{x}}{9e^3}\right) = \ln(4\sqrt{x})-\ln(9e^3)=\ln(4)+\dfrac{1}{2}\ln(x)-(\ln(9)+3\ln(e))\\\\=\dfrac{1}{2}\ln(x)+\ln(4)-\ln(9)-3\\\\\approx\dfrac{\ln(x)}{2}-3.810930[/tex]
NEED HELP!! Urgently!
Please Help! ASAP. Will give Brainliest
Answer:
3 Not too sure though
Step-by-step explanation:
don't input my answer, i'm not too sure!
1/2 + 2/9 + 27/53 as a fraction
Answer:
1175/954 there your answer
PLEASE HELP!!! If the height of the lighthouse is 53 meters and the angle of elevation is 47°, which of the following may be used to find the distance, z, between the boat and the base of the lighthouse?
Answer:
tan(47)=53/z
Step-by-step explanation:
Using trig ratio tan(x)=O/A
there x is the angle of elevation, O is the side opposite the angle (the lighthouse) and A is the side adjacent the angle (distance between boat and bottom of lighthouse)
Therefore, tan(47)=53/z
[tex]\\ \tt\hookrightarrow tan47=\dfrac{H}{B}[/tex]
[tex]\\ \tt\hookrightarrow tan47=\dfrac{53}{B}[/tex]
[tex]\\ \tt\hookrightarrow B=\dfrac{53}{tan47}[/tex]
( SHOW UR WORK) Find the value of 8.41 + 42.320
Answer:
See below.
Step-by-step explanation:
42.32
+8.41
50.73
-hope it helps
Answer:
50.73
Step-by-step explanation:
8.41
42.32
+_________
50.73
Hope this helps! Have a great day!!
What is the ratio in decimal form of 75 people in a 10ft X 10ft square?
Answer:
(100 ft^2) / (75 people) is a ratio: 1.3333... ft^2/person
Step-by-step explanation:
There are 75 people in a 100 square foot area. The amount of space (floor space) is (100 ft^2) / (75 people) = 1 1/3 square feet.
(100 ft^2) / (75 people) is a ratio: 1.3333... ft^2/person
Can someone help me with this please!
Answer:
Step-by-step explanation: