GEOMETRY-TRIG
Rampy Ronald is fixing to make a jump with his dirt bike across an 80-foot ravine full of lava. The ramp he’s going to hit to make the jump is 15 feet long, forms a 30° with the ground and ends 5 feet from the edge of the ravine. That said, if he hits the ramp at his bike’s full speed of 60mph, he’ll reach a maximum height of 30 feet.
6. From the start of the ramp to when he reaches his maximum height, how far will Rampy Ronald have traveled horizontally?
7. Is Rampy Ronald going to make the jump, or is he fixing to land in the ravine of lava and become Roasty Ronald? Give geometric constructions backed by mathematics to support your reasoning!!!
Answers
Answer:
6. The distance Rampy Ronald would have travelled horizontally is approximately 48.428 feet for an actual maximum height of 21.486 feet
7. Rampy Ronald is going to make the jump
Please find attached the graph of the motion of Rampy Ronald, created with Microsoft Excel
Step-by-step explanation:
6. The given parameters are;
The width of the ravine = 80 ft
The inclination of the ramp with which Rampy Ronald will jump = 30°
The distance from the edge of the ravine the ramp ends = 5 feet
The speed with which Rampy Ronald will make the jump = 60 mph
The maximum height he will reach = 30 feet
Therefore, we have;
The height of the end of the ramp = 15 × sin(30°) = 7.5
The height of the end of the ramp = 7.5 feet
The height of the jump = 30 - 7.5 = 22.5
The vertical velocity = 60 × sin(30°) = 30
The vertical velocity = 30 mph
The horizontal velocity = 60 × cos(30°) = 30·√3
The horizontal velocity = 30·√3 mph
From the kinematic equation, v² = u² - 2gh, we have;
u² = 2gh
h = u²/2g = 900/(2 × 32.17405) ≈ 13.986
The maximum height reached 13.986 + 7.5 = 21.486
From v = u - gt
t = u/g = 30/32.17405 ≈ 0.932
t ≈ 0.932 s
The distance Rampy Ronald would have travelled horizontally = 30·√3 × 0.932 ≈ 48.428
The distance Rampy Ronald would have travelled horizontally ≈ 48.428 feet
7. The time before Rampy Ronald reaches ground level again, is given by the following relation;
h = 1/2·g·t²
21.846 = 1/2 × 32.17405 × t²
t = √(21.846/16.087025) ≈ 1.165
t ≈ 1.366 s
The horizontal distance traveled is therefore;
The horizontal distance traveled from maximum height is 30·√3 × 1.165 ≈ 60.535
The horizontal distance traveled from maximum height is ≈ 70.979 feet
The total horizontal distance traveled ≈ 48.428 + 60.535 = 108.963
The total horizontal distance traveled ≈ 108.963 feet
The total horizontal distance required to make it across the ravine = 5 feet + 80 feet = 85 feet
Therefore, Rampy Ronald is going to make the jump
Related Questions
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the maximum height reached by the rocket, to the nearest tenth of a foot. y=-16x^2+227x+109
Answers
Answer: y=914.1 feet max height
Step-by-step explanation:
Find the distance between (-2.8) and (11, 2). Round to the nearest hundredth 14.32 13.58 12.58 13.04 None of the other answers are correct
Answers
Answer:
14.32
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra II
Distance Formula: [tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Step-by-step explanation:
Step 1: Define
Point (-2, 8)
Point (11, 2)
Step 2: Find distance d
Simply plug in the 2 coordinates into the distance formula to find distance d
Substitute [DF]: [tex]d = \sqrt{(11+2)^2+(2-8)^2}[/tex]Add/Subtract: [tex]d = \sqrt{(13)^2+(-6)^2}[/tex]Exponents: [tex]d = \sqrt{169+36}[/tex]Add: [tex]d = \sqrt{205}[/tex]Evaluate: [tex]d = 14.3178[/tex]Round: [tex]d \approx 14.32[/tex]simplify the expression (x to the 12 power) to the 3 power
Answers
Answer:
Step-by-step explanation:
To simplify this, I can think in terms of what those exponents mean. "To the third" means "multiplying three copies" and "to the fourth" means "multiplying four copies". Using this fact, I can "expand" the two factors, and then work backwards to the simplified form. First, I expand:
(x3)(x4) = (xxx)(xxxx)
Now I can remove the parentheses and put all the factors together:
(xxx)(xxxx) = xxxxxxx
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This is seven copies of the variable. "Multiplying seven copies" means "to the seventh power", so this can be restated as:
xxxxxxx = x7
hey hello, please help
Answers
Answer:
2/10 3/10 4/10 5/10 6/10
Step-by-step explanation:
add one each time or go up every number.
plllllzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz helppppppp
Answers
Answer:
Its C
Step-by-step explanation:
All you have to do is divide 90.2 by 11
Answer:
c
Step-by-step explanation:
board sum (-4)+1=x+(-4)
Answers
x=1
i gues dont know
hav nice day✌
(Timed) Solve the system of equations work shown
Answers
Substitution Method
For x:
[tex]y = \frac{5}{4}x - 2\\y = -\frac{1}{4}x + 19\\\\\frac{5}{4}x - 2 = -\frac{1}{4}x + 19\\\\\frac{3}{2}x - 2 = 19\\\\\frac{3}{2}x = 21\\\\x = 14[/tex]
For y:
[tex]y = \frac{5}{4}(14) - 2\\\\y = 17.5 - 2\\\\y = 15.5[/tex]
Solution:
[tex](14, 15.5)[/tex]
Graphing Method
According to this graph, the solution will be [tex](14, 15.5)[/tex].
first to answer gets brainlest <33
Answers
HELP! i'll give brainliest just please help me ;(
Answers
And 14 is either SAS or none. The rest are correct
FERRIS WHEEL Suppose a Ferris wheel is 160 feet high and casts a shadow that is 64 feet long. At the same time, a ticket booth next to the Ferris wheel casts a shadow that is 2.8 feet long. What is the height of the ticket booth?
Answers
Answer:
7 feet
Step-by-step explanation:
Suppose a Ferris wheel is 160 feet high and casts a shadow that is 64 feet long. At the same time, a ticket booth next to the Ferris wheel casts a shadow that is 2.8 feet long. What is the height of the ticket booth?
We solve this question
Length of shadow/Height
Ferris wheel = Ticket booth
64 feet/160 feet = 2.8 feet/x
Cross Multiply
64x = 160 × 2.8
x = 160 × 2.8/64
x = 7 feet
The height of the ticket booth is 7 feet
What is the value of 10(4-7)/-(4-1)?
0-10
O 6
O 6
O 10
Answers
Answer:
10
Step-by-step explanation:
PLEASE HELP! BRAINLIEST to correct answer!!!
Answers
What do you need help with?
Explanation:
There is no question
In a classroom of 20 students, 70% of them have brown eyes. If a teacher picks two students at random to pass out supplies, what is the probability he chooses two students without brown eyes?
Answers
Answer:
6/20 can I get brainliest pleast
Step-by-step explanation:
[tex] \frac{70}{100} \times 20 = 14 \\ 20 - 14 = 6 \\ [/tex]
there is a chance that the teacher will pick a student without brown eyes 6/20 times
Why 27 is not a prime
Answers
Answer:
27 isn't a prime because of the fact that it can be divided by 27.
And for your information, Prime numbers are numbers that can't be divided by any number other than 1 and itself.
Hope it helps.
- Fact/Side note: A “Prime Number” is basically a number that is LARGER THAN one but it has about approximately 2 factors which it has to either be 1 or the number by itself.
Anyways, now that we broke down the definition better, we can ANSWER your question!
• Answer: The number “27” isn’t considered a prime number because it isn’t CAPABLE OF BEING to DIVIDE by 1 or itself.
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
1. Over a 4-month period, among 30 people with bipolar disorder, patients who were given
a high dose (10g/day) of omega-3 fats from fish oil improved more than those given a
placebo. (Archives of General Psychiatry 56 (1999): 407)
Answers
Answer:
Over a 4-month period, among 30 people with bipolar disorder, patients who were given a high dose (10 g/day) of omega-3 fats from fish oil improved more than those given a placebo.
Step-by-step explanation:
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PLEASE ANSWER‼️‼️‼️‼️‼️‼️‼️‼️‼️‼️‼️‼️‼️‼️
Answers
Answer:
x-intercept = 9 y-intercept = 5
Step-by-step explanation:
10 POINTS NEED HELP ASAP
Answers
Answer:
I believe it is D
Step-by-step explanation:
Hope this helps!
Jonathan opened a savings account with $5500 and made no further
deposits. If the account pays3.5% simple interest, how long will it take until
the value of his account reaches $6655? *
a. 3.5 years
b. 6 years
c. 5.54 years
d. 6.5 years
Answers
Explanation: took the test
It takes 6 years to reach $6655.
What is Simple interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.
The formula written out is "Simple Interest = Principal x Interest Rate x Time."
Given:
Amount= 6655
Principal = 5500
Interest rate= 3.5%
So, Amount= P( 1 +rt)
6655 = 5500 (1 + 0.035t)
6655/5500 = 1 +0.035t
1.21 - 1= 0.035t
0.21 / 0.035 = t
t= 6 years
Hence, it takes 6 years to reach $6655.
Learn more about Simple Interest here:
https://brainly.com/question/25845758
#SPJ6
Use the order of operations to evaluate: −7.6 − 2[9 + (−6.8)] First, simplify the parentheses: [9 + (−6.8)] = 2.2. Now the expression is: −7.6 − 2(2.2). Since there are no exponents in this problem, the next step is ✔ (- 2)2.2 . Simplify the previous step and you get ✔ -7.6 – 4.4 . The final answer is
Answers
Answer:
-12.0
Step-by-step explanation:
From the above question, we are given:
−7.6 − 2[9 + (−6.8)]
We apple the PEDMAS rule
P = Parentheses, Hence:
Step 1
The first step is to simplify the parentheses
[9 + (−6.8)] = 2.2.
Step 2
We now have:
−7.6 − 2(2.2).
Step 3
We simplify Parentheses again
(- 2)2.2 = -4.4
Step 4
We simplify
-7.6 - 4.4
= -12.0
The final answer is 12.0
have a nice day, good luck
Sorry I didn't know what subject to put this in but Please help I really do need it u don't have to tho
Which fitness test measures the strength and flexibility of the lower back?
A.
Walk/Run test
B.
Curl ups
C.
Sit and Reach
D.
Trunk Lift
Answers
Answer:
Curl ups
Step-by-step explanation:
I'm not 100% sure, but it seems like the most logical answer to me.
Answer:
Trunk Lift
Step-by-step explanation:
what is the slope of the line?
Answers
Answer:
No Solution
Step-by-step explanation:
Slope is rise/run
rise = 1
run = 0
you can't divide by 0 so no solution
Answer:
The slope of the line is undefined.
Step-by-step explanation:
The slope of a line is given by [tex](y_2-y_1)/(x_2-x_1)[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points on the line. Since this is a vertical line, [tex]x_2-x_1[/tex] will, however, be equal to zero. We cannot divide by zero, so the slope of the line is not defined.
Jin's mother estimates there is a half-gallon of fruit punch remaining in the container. There are actually 72 ounces of fruit punch in the container. Find the percent error of Jin's mother's estimate. Round the percent to the nearest tenth if necessary HELP DUE IN 10 MINUTES
Answers
Answer:
89%
Step-by-step explanation:
the real answer is 64 fluid ounces
64/72*100 which is 88.89% or 89%
Hope this helps plz hit the crown :D
The percent error of Jinn's mother's estimate is 11.12%.
What is Percentage Error?The degree to which a measured or calculated value is closest to its true value is measured by its accuracy. The error percentage is calculated by multiplying the error to real value by 100. The repeatability of a set of measurements is gauged by the precision of each measurement.
Given that Jinn's mother estimates there is a half-gallon of fruit punch remaining in the container. Therefore, the estimated amount can be written as,
Estimated amount = 0.5 gallons = 0.5 × (128 ounces) = 64 ounces
It is also given that there are actually 72 ounces of fruit punch in the container. Therefore, the percent error of Jin's mother's estimate is
Percentage Error = [ |Estimated value - Real Value| ) /Real Value] × 100%
= [( |64 ouches - 72 ounces| )/72 ounces] × 100%
= [(8 ounces)/72 ounces] × 100%
= 0.11111 × 100%
= 11.12%
Hence, the percent error of Jinn's mother's estimate is 11.12%.
Learn more about the Percentage Error here:
https://brainly.com/question/28746643
#SPJ5
Anyone want to help me with this? I will mark brainliest and thanks
Answers
Answer:
x = -8
m∠BDC = 68°
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Geometry
Definition of a Line: A line is 180°Step-by-step explanation:
Step 1: Set up Equation
m∠BDC + m∠CDA = 180°
(-7x + 12)° + (-8x + 48)° = 180°
Step 2: Solve for x
Combine like terms: -15x + 60 = 180Isolate x term: -15x = 120Isolate x: x = -8Step 3: Find m∠BDC
Define: m∠BDC = (-7x + 12)°Substitute in x: m∠BDC = (-7(-8) + 12)°Multiply: m∠BDC = (56 + 12)°Add: m∠BDC = 68°Mike and Thomas were making Lego towers. Mike stacked 249 Legos for his tower. Thomas had stacked twice as much as Mike. How many Legos did Thomas use for his tower? Write you answer in a complete sentence.
Answers
Answer:
498
Step-by-step explanation:
So,if mike stacked 249 legos and thomas did twice as much that means x2 so if you do 249 x2 you get 498.
Select the correct answer.
Janet sells custom artwork online. Her business profits for the month of August are shown in the table.
Week Profit
week 1 $56.92
week 2 -$16.54
week 3 $45.58
week 4 -$21.74
How much more profit did Janet make in week 2 than in week 4?
A.
-$38.28
B.
-$5.20
C.
$5.20
D.
$38.28
E.
$40.25
Answers
Answer:
B. -5.20.
Step-by-step explanation:
We can see that Janet made more in week 4 then in week 2, so that means the answer will have to be a negative. To find the exact answer, we take away 21.74 from 16.54. This gets us -5.2, which is equivalent to -$5.20. I hope this helps!
Graph
Y=3/4x - 1/2
Pleaseeeee help!!
Answers
Kym switched cell phone plans. She signed up for a new plan that will save her $3.50 per month compared to her old cell phone plan. The cost of the new phone plan for an entire year is $294. How much did Kym pay per month under her old phone plan?
also merry early Christmas
Answers
Answer:
Hi there,
$294 per year = $24.50 per month
Kim paid $24.50 + $3.50 = $28 per
month with her old phone plan.
Hope this helps :-)
Step-by-step explanation:
the radius of the base of a cylinder is 10 centimeters, and urs height is 20 centimeters. a cone is used to fill the cylinder with water. the radius of the cone base is 5 centimeters, and it’s height is 10 centimeters the number of times one needs to use the completely fillies cone to completely fill the cylinder with water is
Answers
Answer:
The answer is 24 times
At the beginning of the month, Arnold’s bank account balance was $217.25. During the month he made deposits of $49.58 and $105.75 and a withdrawal of $25.45. What was Arnold’s bank balance at the end of the month?
Answers
Please help me with this question.
Answers
Answer:
Monica = 48.50
Samuel = 24.25
Kara = 17.25
Step-by-step explanation:
First you write equations as you are reading the text:
m = 2s ("Monica earned twice as much as Samuel")
s = k+7 ("Samual earned 7 more than Kara")
m = 48.50
Next, you convert these equations to solve for s and k respectively.
So, if m=2s, then s=m/2:
s = m/2 = 24.25
Likewise, if s=k+7, then k=s-7
k = s-7 = 17.25
The difference between greatest and least is 48.50 - 17.25 = 31.25