Answers
Answer:
Horizontal distance = 0 m and 6 m
Step-by-step explanation:
Height of a rider in a roller coaster has been defined by the equation,
y = [tex]\frac{1}{3}x^{2}-2x+8[/tex]
Here x = rider's horizontal distance from the start of the ride
i). [tex]y=\frac{1}{3}x^{2}-2x+8[/tex]
[tex]=\frac{1}{3}(x^{2}-6x+24)[/tex]
[tex]=\frac{1}{3}[x^{2}-2(3x)+9-9+24][/tex]
[tex]=\frac{1}{3}[(x^{2}-2(3x)+9)+15][/tex]
[tex]=\frac{1}{3}[(x-3)^2+15][/tex]
[tex]=\frac{1}{3}(x-3)^2+5[/tex]
ii). Since, the parabolic graph for the given equation opens upwards,
Vertex of the parabola will be the lowest point of the rider on the roller coaster.
From the equation,
Vertex → (3, 5)
Therefore, minimum height of the rider will be the y-coordinate of the vertex.
Minimum height of the rider = 5 m
iii). If h = 8 m,
[tex]8=\frac{1}{3}(x-3)^2+5[/tex]
[tex]3=\frac{1}{3}(x-3)^2[/tex]
(x - 3)² = 9
x = 3 ± 3
x = 0, 6 m
Therefore, at 8 m height of the roller coaster, horizontal distance of the rider will be x = 0 and 6 m
Related Questions
What are the coordinates of A(8,-1) after a rotation of 180° about the origin
Answers
A window in the shape of a parallelogram has the dimensions given.
What is the area of this window?
20 ft²
24 ft²
28 ft²
40 ft²
Answers
Answer:
A. 20ft
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
i Belive the answer is c
HELP HELP HELP HELP HELP HELP!!!!!
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Answer:
..
Step-by-step explanation:
Will give brainlist if answer is correct :)
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Answer:
The answers C if you plug in the answer and re-write it 11.3.04 is correct.
Step-by-step explanation:
pi(r)^2
the diameter is 6 so the radius is 3
plug in 3 for r
pi(3)^2 = 9pi = 28.26
since the rug is a semi circle, divide 28.26 in half which is 14.13
ANSWER: B. 14.13 ft^2
Eric is going to the store to buy groceries. He has a budget of at most $20. If he wants to buy milk for $5 and all of his favorite cereals for $4
per box, how many boxes of cereal can he buy?
Answers
Answer: 4 boxes of cereal
Step-by-step explanation:
Answer:
He can only by 3 boxes
Step-by-step explanation:
20-5=15 than you divid 15 by four
Shania’s workout playlist includes songs from four types of music. ● 32 country songs ● 48 rap songs ● 12 hip-hop songs ● 8 blues songs
Answers
Answer:
Hi there
Step-by-step explanation:
What exactly is the question being asked?
The song is 4 times as likely to be country than it is to be blues.
What is Probability?Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.
The value of probability will be always in the range from 0 to 1.
Total number of songs = 32 + 48 + 12 + 8 = 100
If she randomly plays a song from this list,
Probability that the song is country = 32/100 = 8/25
Probability that the song is rap = 48/100 = 12/25
Probability that the song is hip hop = 12/100 = 3/25
Probability that the song is blues = 8/100 = 2/25
Probability of country = 8/25 = 4 (2/25) = 4 times probability of blues.
Hence the correct option is B. The song is 3 times as likely to be country than it is to be blues.
To learn more about Probability, click :
https://brainly.com/question/11234923
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The complete question is below :
Shania’s workout playlist includes songs from four types of music.
32 country songs
48 rap songs
12 hip-hop songs
8blues songs
Which is the best prediction of the type of music Shania will hear when she randomly plays a song from her playlist?
A The song is 6 times as likely to be blues than it is to be rap.
B The song is 4 times as likely to be country than it is to be blues.
C The song is 3 times as likely to be country than it is to be hip-hop.
D The song is half as likely to be rap than it is to be all other songs combined.
What is the expanded form of this number?
14.702
1. (1×10)+(4×1)+(7×1100)+(2×11,000)
2. (1×10)+(4×1)+(7×1100)+(2×1100)
3. (1×10)+(4×1)+(7×110)+(2×11,000)
4. (1×10)+(4×1)+(7×110)+(2×1100)
Answers
Answer:
Step-by-step explanation:
[tex]14.702 = (1*10) + 4*(1) +(7*\frac{1}{10}) + (2*\frac{1}{1000})[/tex]
HELP! WHY IS THIS TRIANGLE CONGRUENT! EASY PLS HELP
Answers
Answer:
D. xz=yz, angle z is shared, wz=wz
Answer:
Side-angle-side postulate
Step-by-step explanation:
First, you know that angle XZW = YZW because they are both 90 degrees.
Next, you know that side WZ = side WZ because of the reflexive property (they are the same side)
Lastly, you know that YZ = XZ because Z is the midpoint meaning it divides the entire thing perfectly in half
You have two sides and the included angle, so it is SAS.
help, I don't understand
Answers
Answer:
y=3/4x+10
Step-by-step explanation:
lts take two points
(-4,7)
(0,10)
so slope is 3/4
so 3/4*-4+b= 7
-3+b=7
b=10
y= 3/4x+10
if my answer helps please mark as brainliest.
Answer:
y = 3/4 x + 10
Step-by-step explanation:
the b is 10 because y is 10 when x is 0
to find the x, plug in any variable from the chart into the equation y=mx+b
i used (-4, 7), so the equation would be 7=m(-4)+10
solve for x
-4m=7-10=-3
m=3/4
please help:)I’m not good at math and need to get this done ASAP
Answers
Answer:
First and third options are equivalent, second and fourth options are not equivalent.
Step-by-step explanation:
Remember the relation:
[tex]a^n*a^m = a^{n + m}[/tex]
and:
[tex](a^n)^m = a^{n*m}[/tex]
We have the expression:
[tex]7^{1/5}*49^{7/5}[/tex]
We know that 49 = 7*7
Then we can write the above relation as:
[tex]7^{1/5}*49^{7/5} = 7^{1/5}*(7^2)^{7/5}[/tex]
We can use the second relationship from the above ones and write this as:
[tex]7^{1/5}*(7^2)^{7/5} = 7^{1/5}*7^{2*7/5} = 7^{1/5}*7^{14/5}[/tex]
Now we can use the first relationship to get:
[tex]7^{1/5}*7^{14/5} = 7^{1/5 + 14/5} = 7^{15/5} = 7^3 = 343[/tex]
Then:
The first option is equivalent.
The second option is not equivalent
The third option is equivalent.
The fourth option is not equivalent.
The question is. The Scale of the map is 0:5 in: 20 mi. Find the actual distance corresponding to the map distance. 2 in.
Answers
Answer:
Step-by-step explanation:
I think you mean 0.5 in:20 mi
2 in × (20 mi)/(0.5 in) = 80 mi
2 inches on the map corresponds to 80 miles.
8 miles is the real distance that corresponds to the 2 inch map measurement.
Scaling and actual distance on maps.We can utilize the map's scale to get the actual distance that corresponds to the 2 inch map distance.
The scale is presented as 0:5 in:20 mi, which implies that each 5 inches on the map corresponds to 20 miles in actual travel distance.
Let's establish a ratio to determine the actual distance:
5/2 = 20/x
If we cross-multiply, we obtain:
5x = 2(20)
5x = 40
When we multiply both sides by 5, we get:
x = 40 / 5
x = 8
Therefore, 8 miles is the real distance that corresponds to the 2 inch map measurement.
Learn more on scaling here: https://brainly.com/question/25722260
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image inserted down below
Answers
Answer:
.002
Step-by-step explanation:
take the previous numbers in the pattern and divide by 3. Do this until you get to the 8th number.
The 8th number is 0.00274348422
round to the nearest thousandth for the final answer.
Hope This Helps!!
Some one help please
Answers
Answer:
46in.
Step-by-step explanation:
2(14+9)
=28 + 18
=46in.
PLEASE HELP ME. Problem is in the photo
Answers
Answer:
13cm
Step-by-step explanation:
Hope this helps! :)
3x – 4y = 0
x - y = 1
Answers
Answer:
x=4, y=3
Step-by-step explanation:
3x-4y=0
-3x+3y=-3
-y=-3
y=3
x-3=1
x=4
Mr. Greene purchased 6 adult movie tickets for $5730. How much does one adult move ticket cost?
Answers
Answer:
$955
Step-by-step explanation:
$5730 [tex]/[/tex] 6 = $955
Solve the rational equation. x+6/x-3=4/7
Answers
Priya has a recipe for banana bread. She uses 7.5 cups of flour to make 3 loaves of banana bread. How much flour does Priya need to make 1 loaf of bread?
Answers
Answer:
It would take 2.5 cups of flour to make 1 loaf of bread.
Step-by-step explanation:
You would 7.5 divided by 3 to get how much it would take for 1 loaf of bread.
7.5/3 = 2.5
it would take 2.5 cups of flour to make 1 loaf of bread.
What's the largest 6-digit multiple of 5 that has all different digits? I'll give Brainliest to anyone who helps.
Answers
Answer:
987650Step-by-step explanation:
The largest 6-digit number is:
999999We need all digits different and the last one 0 or 5 because the number is the multiple of 5.
9876 are the first 4 digits and the last two 50 or 45, we'll chose 50 as 45 is smaller.
So the number is:
987650Answer:
987650 hag1 !!!
I need helppppppp TvT
Answers
Answer: A.O.C U.S.C
Wrote it: Benjamin Franklin James Madison
Ratified It: 13 colonies the federalists
Delays: the insistence of Maryland that War
all states give up their western land
claims to the central government.
Type Gov. created: loose confederate democratic republic
government
Type Cong. :Second Continental Congress the Legislative Branch
Title Exe. : President for both columns
Power to National: enumerated powers
Powers to state:these included the “police powers” of health, education, and welfare.
Round $94.10 to the nearest ten dollars
Answers
Answer:
90
Step-by-step explanation:
five or more raise the score, four or less let it rest
Answer: $90
Step-by-step explanation:
94.10 round that to the nearest ones
94 now round that to the nearest tens
90
A new phone costs $450. There is a 40% discount on the price of the phone and an 8% sales tax on the discount price. What is the final cost of the phone after the discount and the sales tax?
Answers
Answer:
it is 291.60
Step-by-step explanation:
ik this bc i had the question on my assignment
How to solve the question above?
Answers
Answer:
66 years
Step-by-step explanation:
1) Convert 1.4426 * 10^4 into a number....
= 14426
2) Divide
14426 / 218.58
= 65.9987190045
About 66 years
That's all you write cause they asked u in years, no month or other stuff :)
Answer:
Approximately 66 years
Step-by-step explanation:
1.4426×[tex]10^{4}[/tex] mm is equal to 14,426mm
14,426mm÷218.58=65.998...≅66
Terrence leaves a $3 tip at a restaurant. If that tip is equal to 15% of his total bill, what is his total bill?
Answers
Answer:
$20
Step-by-step explanation:
To find the total bill, divide the tip amount by 0.15
3/0.15
= 20
So, his total bill was $20
3 ÷ 15%
= 3 ÷ 15/100
= 3 x 100/15
= 300/15
= 20
His total bill is $20
Lena knit a total of 20 centimeters of scarfs over night. How many nights will Lena have to spend knitting in order to knit a total of 50 cm of scarfs. Assume the relationship is directly proportional.
Answers
Answer:
50cm of scarfs is equal to 2.5 nights of knitting.
Step-by-step explanation:
20cm= 1 night
10cm= 1/2 or 0.5 a night
40cm= 2 nights
50cm=2.5 nights
b) Find the value of x and y from the given figure:
Answers
x = 60
The top and bottom are identical so you have 180-60=120 then divide by 2 to get the other sides
Answer:
y = 30
x = 150
Caden exercises daily by walking on a treadmill. He sets the machine so that he will walk at a steady rate of 3.6 miles per hour.
A. If t represents time in hours and d represents distance in miles write an equation that models the relationship between these variables
B. Use your equation to calculate the distance Caden will walk in 3 of an hour .
C. Use your equation to calculate how long it will take for Caden to walk 4.32 miles
(i have to write sumn for this part)
Answers
Answer:
a) d = 3.6t
b) 10.8 miles
c) 1.2 hours
Step-by-step explanation:
For part a:
Slope of a line: y = mx + b
In this case, the equation would be: d = mt,
where m represents the speed Caden is walking at.
Note: b = 0 in this case because when Caden starts walking on the treadmill, he hasn't really covered any distance yet.
Therefore, plugging in a speed of 3.6 miles per hour, the equation is:
d = 3.6t
For part b:
This is a simple instance of plugging in 3 hours for our t value.
Therefore, d = 3.6 (3)
d = 10.8 miles
For part c:
In this case, we are given that d = 4.32 miles.
Therefore, 4.32 = 3.6t
Dividing both sides by 3.6, we get
t = 1.2 hours
Help. (Unprofessional people will be reported and so will wrong answers/people trying to be funny)
Answers
Given the ordered pairs (-3,-2) and (4,-2), what is the horizontal distance between
the points?
Answers
Answer:
7 units apart.
Step-by-step explanation:
Find the difference of the x-values from the two points.
4 - (-3) = 4 + 3 = 7
The horizontal distance from the two points is 7.
Hope this helps.
difference between algebreic expression and linear expression
Answers
In algebra, the highest power of the variable is known as the degree of the expression. Note: If the degree of an algebraic expression is 1 then it is called linear expression. If the degree of an algebraic expression is 2 then it is called quadratic expression.
