1. Write the equation that models the height of the roller coaster. Start by writing the equation of the circle. (Recall that the general form of a circle with the center at the origin is x2 + y2 = r2. (10 points) Now solve this equation for y. Remember the roller coaster is above ground, so you are only interested in the positive root. (10 points)
Answer:
a.)x² + y² = 900
b.)y = √900 - x²
Step-by-step explanation:
P.S - The exact equation is as follows :
As given,
The shape of the roller coaster is a half of a circle. Center the circle at the origin and assume the highest point on this leg of the roller coaster is 30 feet above the ground.
a.)
Equation of circle be x² + y² = r²
As given , leg of the roller coaster is 30 feet above the ground.
⇒ r = 30
⇒x² + y² = 30²
⇒x² + y² = 900
∴ we get
Equation of height of Roller coaster - x² + y² = 900
b.)
As we have, x² + y² = 900
⇒y² = 900 - x²
⇒y = √900 - x²
The equation that models the height of the roller coaster is [tex]y = \sqrt{900 -x^2[/tex]
The general equation of a circle is:
[tex]x^2 + y^2 = r^2[/tex]
From the complete question, the radius of the circle is 30 units.
This means that:
r = 30
So, we have:
[tex]x^2 + y^2 = 30^2[/tex]
Express 30^2 as 900
[tex]x^2 + y^2 = 900[/tex]
Subtract x^2 from both sides
[tex]y^2 = 900 -x^2[/tex]
Take square roots of both sides
[tex]y = \pm \sqrt{900 -x^2[/tex]
Remove the negative root
This is so because the roller coaster is above the ground, and the height will be positive.
So, we have:
[tex]y = \sqrt{900 -x^2[/tex]
Hence, the required equation is [tex]y = \sqrt{900 -x^2[/tex]
Read more about equations of circle at:
https://brainly.com/question/10244007
Antonio needs to convert 1.2 liters of milk to milliliters. How many milliliters are there in 1.2 liters of milk?
Answer: 1200 milliliters.
Step-by-step explanation: 1 liter has 100 milliliters of milk in it. So you have to multiply 1.2 by 100 to get 1200.
You purchase a new shirt that cost $15.00. Sales tax is added at the register at a rate of 8%. How much sales tax will be added to the cost of the shirt when you pay for it.
Answer:
16.2 U.S. Dollars - I hope this helps! :D
Step-by-step explanation:
need help pls!!!! Algebra
Answer:
11
Step-by-step explanation:
can someone please help me!
Answer:
60
Step-by-step explanation:
A line passes through the points (-4,3) and (0,0) what is the slope of the line?
Answer:
Slope: -3/4
Step-by-step explanation:
Use the formula:
[tex]\frac{y^{2} -y}{x^{2} -x}[/tex]Substitute the points (-4, 3) and (0,0) into the equation:
[tex]\frac{0- 3}{0-(-4)}[/tex]Solve.
[tex]\frac{-3}{4}[/tex]
Given g(x) = 3x + 14 , find x if g(x) = 20
Answer: x = 2
Step-by-step explanation: If g(x) = 3x + 14, and g(x) = 20 also, you first can set 3x+14 = 20. To find the value of x, you want to isolate the variable. You can subtract 14 from both sides to get 3x = 6. Finally, to find out the value of x, divide 3 from both sides. This leaves you with x = 2. You can check this by plugging two back into the original equation 3 times 2 = 6, and 6 plus 14 equals 20.
for the pairs below put each question in slope intercept form and whether the graphs of the line will be identical, parallel, or intersecting, Also determine how many solutions the system of equations will have
At Garland School, 3/5 of the 490 students are boys.
At Bowood School, 5/7 of the 945 students are girls.
Which school has the greater number of girls and by how many?
You must show your working.
Step-by-step explanation:
the bowood school by 455 kids
Scale on a map of Ireland is 1.2 000000 how many square centimetres are represented on the map by the province of Munster.
Question is incomplete, we will however explain how the scale works using examples
Answer and explanation:
Given the map scale 1:2000000, the fraction from this 1/2000000 is the representative fraction. The representative fraction is the ratio of distance on the map to the real distance on ground.
With the representative fraction 1/2000000, we can find how many meters on the ground is represented by a unit of measurement in centimeters on the map thus:
Given 1m= 100cm
Representative fraction broken down = 1/2×10000×100
Therefore 1cm on the map = 20000m on ground
Two different linear functions are shown below with two points given from each function. Use slope-intercept form or point-slope form to find the equation of each. Linear Function A Points: (–5, –2), (–5, 7) Linear Function B Points: (7, –5), (–2, –5) Function A has a slope of -7a slope of 0a slope of 9no slope. The equation of line A is x = -5y = -5x = -2y = 7. Function B has a slope of -7a slope of 0a slope of 9no slope. The equation of line B is x = -5y = -5x = -2y = 7.
Answer:
5
Step-by-step explanation:
Pls help pls thank you
Answer:
2 1/2 pounds
Step-by-step explanation:
help pls :) it’s due in a few mins
what is the difference between associative property,communitive property,and distributive property? (will mark brainliest)
Answer:
Commutative switches the numbers, while associative keeps the numbers positions but changes the parentheses. I hope that helped
HERES JOHNYYYY!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
What division problem can be represented using the number line?
The sum of twice a number and 4 times another number is 4. The difference of the numbers is 5. Find the numbers(help a sis out)
Answer:
1st number = 4
2nd number = -1
Step-by-step explanation:
Let n = 1st number
Let m = 2nd number
2n + 4m = 4
n - m = 5
Substitu method, let n = 5 + m
2(5+m) + 4m = 4
10 + 2m + 4m = 4
6m = -6
m = -1
find n:
n - (-1) = 5
n + 1 = 5
n = 4
4x – y = 7 3y – 12x = –21
Answer:
y= 4x − 7 or 0=0
Step-by-step explanation:
4x−y+−4x=7+−4x
2/3 + 3/5 = ? (Simplfy it)
Answer:
1 AND 4/19
Step-by-step explanation:
2/3=3/5
lcm=15
10/15+9/15=19/15= 1 AND 4/19
option D: 8 square root 3 cm
pls help
thanks
Answer:
is b
Step-by-step explanation:
An online video streaming service offers two plans for unlimited streaming.
Plan A has a one-time $25 membership fee and is $8 per month.
Plan B has a $12 membership fee and is $5 per month.
Write the system of equations!
Answer:
b
Step-by-step explanation:
Find the value of x. 4 х 25 10 X = = [?]
Answer:
X=10
Step-by-step explanation:
question 8 is in the pic
Answer:
A. The median score of Class A is greater than the median score of Class B.
Step-by-step explanation:
This is the only true statement.
Hope it helps!
Answer:
A the media score of the class A is greater than the media score of class B
The radius of a circle is 5 cm. What is the radius of another circle whose area is 25 times that of the first one?
Answer:
Step-by-step explanation:
a₁ = πr₁⁵ = 25π cm²
a₂ = 25(25π) = 625π cm²
r₂ = 25 cm
Mr. Spence asks his math students to identify TWO shapes based on the
following clues: 1- each shape must have ALL sides equal length, 2- each shape
must have 4 sides, 3- each shape must have 2 pairs of parallel sides. Which two
shapes are being described?
A. Rhombus, rectangle B.square, rhombus C. Square,parallelogram D. Rectangle, trapezoid
Answer:
Step-by-step explanation:
d
Pleasee helppp answer correctly !!!!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!!!
Answer:
Now how did I get the translation rule (x + 1, y + 3). Well basically, I did this :-
-4 - (-5) = 1
12 - 9 = 3
Now let us plug it in the translation rule to see if I get (-4, 12).
(x + 1, y + 3)
(-5 + 1, 9 + 3)
(-4, 12)
I get the same answer given in the problem. Hope this helps, thank you !!
TOPIC: You and two friends have $20 to spend on snacks after school.
Explain how you would divide the money between the three of you.
Explain where you would go and what you would buy with your money.
A professional gambler reported that at the end of the first race at the track he had doubled his money. He bet $33 on the second race and tripled the money he came with. He bet $60 on the third race and quadrupled his original bankroll. He bet $68 on the fourth race and lost it, but still had $64 left. With how much money did he start?
Answer:
$33
Step-by-step explanation:
A professional gambler reported that at the end of the first race at the track he had doubled his money. He bet $33 on the second race and tripled the money he came with. He bet $60 on the third race and quadrupled his original bankroll. He bet $68 on the fourth race and lost it, but still had $64 left. With how much money did he start?
Let us represent, the amount of money he had at the start= x
Money after the first race=2x
Money he had after betting=2x-33
Money after the second race=3x
Money he had after betting on the third race=3x-60
Money after the race=4x
Money he had after betting on the fourth race=4x-68
Money after the race=$64
4x-68=64
4x=68+ 64
4x = 132
x=132/4
x = 33
Therefore, he had $33 at the start
The original price of a car is $25000. Each year, its value depreciates (loses value) by 13%. Three years after its purchase, what is the value of the car?
Answer:
$16,462.58
Step-by-step explanation:
25000(1-.13)^(n)
where n is the years
25000(.87)^3
put this into a calculator and get
16462.57
will give brainliest Pleaseeee HELP asap no guessing please
Answer:
S, T & R
Step-by-step explanation:
T is 1/2 of S and R is 1/2 of T
good luck, i hope this helps :)