Write the equation that models the height of the roller coaster

Answers

Answer 1

Considering the circle described, the height of the roller coaster is modeled by the following equation:

[tex]y = \sqrt{900 - x^2}[/tex]

What is the equation of a circle?

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

In this problem, the roller coaster is represented by a circle centered at the origin, with radius 30, hence:

[tex]x^2 + y^2 = 30^2[/tex]

[tex]x^2 + y^2 = 900[/tex]

The height is the value of y, hence, considering it is a positive value:

[tex]y^2 = 900 - x^2[/tex]

[tex]y = \sqrt{900 - x^2}[/tex]

More can be learned about the equation of a circle at https://brainly.com/question/24307696

#SPJ1


Related Questions

which function below has the smallest slope?
f(x)
f(x) = 2x - 3

Answers

Answer:

f(x)

Step-by-step explanation:

f(x) is a little represented number after solving for x but

f(x)=2x-3 is more bigger

Subtract 5x - 4 from the sum of -3x - 4 + y and 4x - y

Answers

Answer:

-4x

Step-by-step explanation:

((-3x-4+y) + (4x-y)) - (5x-4)
= (-3x-4+y+4x-y) - 5x+4
= (x-4) -5x+4
=x-4-5x+4
=-4x

What is the ratio of 338 and 508

Answers

RATIO OF 338 : 508

=> 169 : 254

When there is no traffic, it takes Rina 4 hours to get from Boston to New York. Once, Rina started her trip to New York at a speed of 60 mph, but after 2 1/3 hours of driving she stopped for 40 minutes. She had to drive at a speed of 45 mph for the rest of her trip. How long was her trip?

Answers

The whole trip was 0.185 Km or 185 m long.

What is speed ?

Speed is the time rate at which an object is moving along a path.

Given:

For 7/3 hours speed is = 60 mph = 0.06 kmph

For 40 minutes or 2/3 hours = 0 mph

for 1 hours = 45 mph  or 0.045 kmph

The total distance she travels

= 7/3*0.06+ 2/3*0+ 1*0.045

=0.185 Km or 185 m

Learn more about this concept here:

https://brainly.com/question/1293031

#SPJ1

What is 10 to the power of 3.

I would like to thank everyone that asked and answered questions I was stuck on. I graduated last week and couldnt have done it without Brainly.

Answers

Answer:

1000

Step-by-step explanation:

Hello!

10³ can be expanded to 10 x 10 x 10

Multiplying it out, we get 1000.

When multiplying by 10 you basically add a zero to the end, so we add 3 zeroes in total, which gives us 1000.

Exponents

Warning! [tex]x^y[/tex] is not [tex]x*y[/tex]. A very common error.

Instead, picture it as we are multiplying "x" by itself for "y" number of times.

I appreciate your kind comments!

Two balls are drawn without replacement from a box containing 2black and 3 red balls. What is the probability of drawing a black ball on the second draw? Draw a tree diagram

Answers

The probability that the second ball drawn is black is 4/10 = 2/5

How to find the probability?

There are two cases. The case where the first ball is red is the first one.

The probability of drawing a red ball is equal to the quotient between the number of red balls and the total number of balls.

p = 3/5

Then, the probability of drawing a black ball in the second attempt is computed in the same way, but because we already drew a ball, now the total number of balls is 4, so we have:

q = 2/4 = 1/2.

So the joint probability is:

P = (3/5)*(1/2) = 3/10.

Then we have the case where both balls are black, the probabilities now are:

p = 2/5

q = 1/4

So the joint probability is:

P = (2/5)*(1/4) = 1/10

The total probability is the sum of the two above:

probability = 3/10 + 1/10 = 4/10.

The probability that the second ball drawn is black is 4/10 = 2/5

If you want to learn more about probability:

https://brainly.com/question/251701

#SPJ1

If 30% of a number is 78 and 65% of the same number is 169, find 95% of that
number.

Answers

Answer:

let say the number is x, then 30x÷100=78, x=260...from this we can calculate 95 percent of 260 which is equal to 247

The 95 percentage of the number is A = 247

What is Percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.

Percentage change is the difference between the measured value and the true value , as a percentage of the true value

Percentage change =( (| Measured Value - True Value |) / True Value ) x 100

Given data ,

Let the number be represented as n

Now , We can set up two equations based on the given information

30 percentage of the number is 78 ,

So , 0.3 ( n ) = 78

0.65 ( n ) = 169

Solving for n in the first equation, we get:

n = 260

Substituting n = 260 into the second equation, we can check that it is true:

0.65(260) = 169

Now, we can find 95% of the number by multiplying it by 0.95

0.95 x 260 = 247

Hence , 95% of the number is 247

To learn more about percentage click :

https://brainly.com/question/12861068

#SPJ2

help pleaseeeeeeeeee

Answers

Put the answer choice numbers where the x’s are in the equation and then solve. The ones that are equal to 0 once solved will be your answer
Way to solve is to factor it.
(X-6)(X+4)=0
X= 6 or X =4

Drag and drop a power into each box to match its number.

1,000 --- ( )

10,000 --- ( )

1,000,000 --- ( )

(10^2) (10^3) (10^4) (10^5) (10^6)

Answers

The match of the expressions are:

1,000 --- (10^2) 10,000 --- (10^4) 1,000,000 --- (10^6)

How to rewrite the numbers as powers?

The numbers are products of 10.

This means that the numbers can be represented as exponents, where the base is 10 and the exponent is the number of zeros.

Using the above highlight, we have:

1,000 --- (10^2) 10,000 --- (10^4) 1,000,000 --- (10^6)

Read more about powers and exponents at:

https://brainly.com/question/11975096

#SPJ1

Bill is making a movie and needs to cast some actors. There are 5 actors ( Anne, Lisa, Diana, Maggie, and Susan ) interested in playing the female lead role, and 2 actors ( Jacob and Mark ) interested in playing the male lead role. Anne and Mark are Bill's siblings. What is the probability Bill will cast a family member in the movie?

Answers

Answer:

2 out of seven or 2/7 or 28.5%

Step-by-step explanation:

there are two "yeses" out of 7 total choices

Use Order of Operations
to solve. PEMDAS
9 + 6(2²+4)

Answers

Answer:

57

Step-by-step explanation:

9+6(2^2+4)

Calculate 2 to the power of 2 and get 4.

9+6(4+4)

Add 4 and 4 to get 8.

9+6×8

Multiply 6 and 8 to get 48.

9+48

Add 9 and 48 to get 57.

57

Please explain as well!​

Answers

Answer:

The height of the other book is 2 3/4 inches.

Step-by-step explanation:

From the information,we get:

Two stacks of books together are = 7 1/2 inches tall.

One stack is given,that is = 4 3/4 inches.

To Find:

The height of the other.

Solution:

Let us assume that the other height of the book be x.

Then the equation will be:

[tex] 4\cfrac{3}{4} + x = 7\cfrac{1}{2} [/tex]

Solve for x to get the other book's height.

Convert the mixed fractions to fractions:

[tex] \implies \: \cfrac{19}{4 } + x = \cfrac{15}{2} [/tex]

Subtract 19/4 from both sides:

[tex] \implies \: x + \cfrac{19}{4} - \cfrac{19}{4} = \cfrac{15}{2} - \cfrac{19}{4} [/tex]

[tex] \implies \: x = \cfrac{11}{4} =\boxed{ 2 \cfrac{3}{4} \rm \: inches}[/tex]

Hence, we can conclude that:

The height of the other book is 2 3/4 inches.

Which of the following functions best fits the data shown in the scatterplot below? y=100x+2y is equal to 100 x plus 2 y=20x2+10y is equal to 20 x squared plus 10 y=4x+8y is equal to 4 to the x th power plus 8 y=2x+5y is equal to 2 to the x th power plus 5

Answers

The equation of the scatter plot is (a) y = 100x + 2

How to determine the equation of the scatterplot?

The line of best fit of the scatter plot passes through the points

(x,y) = (0,2) and (1,102)

Start by calculating the slope using:

[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]

So, we have:

[tex]m = \frac{102 - 2}{1 - 0}[/tex]

m = 100

The equation is then calculated as:

y = m(x - x1) + y1

This gives

y = 100(x -0) + 2

Evaluate

y = 100x + 2

Hence, the equation of the scatter plot is (a) y = 100x + 2

Read more about scatter plot at:

https://brainly.com/question/6592115

#SPJ1

PLEASE HELP!!!!!! WHAT IS THE ANSWER

Answers

Answer:

B

Step-by-step explanation:

Divide y by x for each ordered pair:

2/4 = 1/2

3/6 = 1/2

5/10 = 1/2

7/14 = 1/2

All ratios are equal, so it is proportional.

Answer: B

Answer:

b

Step-by-step explanation:

mark brainliest

Pls Help I’m so confused how do you do this

Answers

Answer: A

Step-by-step explanation:

[tex]$$Given $m \angle A=9 x-7, \quad m \angle B=7 x-9, m \angle C=28-2 x$ \\For the triangle $m \angle A+m \angle B+m \angle c=180$$$\begin{aligned}&\Rightarrow(9 x-7)+(7 x-9)+(28-2 x)=180 \\&\Rightarrow 9 x+7 x-2 x-7-9+28=180 \\&\Rightarrow 14 x=180-28+16 \\&\Rightarrow 14 x=168 \\&\Rightarrow \quad x=12\end{aligned}[/tex]

[tex]$$Therefore,\\&m \angle A=9 x-7=9 \times 12-7=101^{\circ}\\&m \angle B=7 x-9=7 \times 12-9=75^{\circ} \\&m \angle C=28-2 x=28-2 \times 12=28-24=4^{\circ}\\[/tex]

[tex]$$Since $m \angle A=101^{\circ}$ so $B C$ is the longest side of a triangle $\triangle A B C$ \\\\Since $m \angle C=4^{\circ} S 0$ SB is the shortest side of a triangle $\triangle A B C$\\\\So listing the sides in $\triangle A B C$ from shortest to longest is: (a) $\overline{A B}, \overline{A C}, \overline{B C}$[/tex]

7x^2+3y^2+12x+2y-6=0 Help me find the value of a,b,c and the discriminant number

Answers

Answer:

b o a h d

Step-by-step explanation:

1*5 3%9 46% &45 that is the answer

What is the radius of the circle with center at (-6, -4) that goes through the point (1, -7) rounded to the nearest tenth?

Answers

Answer:

dhususbdgdg

Step-by-step explanation:

hdhakuxtsjwkbevdvsiw in e

what is the solution to the trigonometric inequality 2sin(x)+3>sin ^2(x) over the interval

Answers

The intervals that satisfy the given trigonometric Inequality are; 0 ≤ x < 3π/2 and 3π/2 < x ≤ 2π

How to solve trigonometric inequality?

We are given the trigonometric Inequality;

2 sin(x) + 3 > sin²(x)

Rearranging gives us;

sin²(x) - 2 sin(x) - 3 < 0

Factorizing this gives us;

(sin(x) - 3)(sin(x) + 1) < 0

Thus;

sin(x) - 3 = 0 or sin(x) + 1 = 0

sin(x) = 3 or sin(x) = -1

sin(x) = 3 is not possible because sin(x) ≤ 1.

Thus, we will work with;

sin(x) = -1 for the interval 0 ≤ x ≤ 2π radians.

Then, x = sin⁻¹(-1)

x = 3π/2.

Now, if we split up the solution domain into two intervals, we have;

from 0 ≤ x < 3π/2, at x = 0. Then;

sin²(0) - 2 sin(0) - 3

= 0² - 0 - 3

= -3 < 0

Thus, the interval 0 ≤ x < 3π/2 is true.

From 3π/2 < x ≤ 2π, take x = 2π. Then;

sin²(2π) - 2 sin(2π) - 3

= 0² - 0 - 3

= -3 < 0

Thus, the interval 3π/2 < x ≤ 2π is also true.

Read more about trigonometric inequality at; https://brainly.com/question/27862380

#SPJ1

The Smith family pays a rate of 27 mills in property tax. The assessed value of their home is $98,000. What is their property tax?

Answers

Their property tax would be =$ 26,460

Calculation of property tax

A mill is one-thousandth of a dollar, and in property tax terms is equal to $1.00 of tax for each.

Therefore 27 mills = $27 for every $1,000 of assessed value, or 2.7%.

To calculate the property tax would

= 27/100× 98,000

= 2646000/100

=$ 26,460

Therefore, Their property tax would be =$ 26,460

Learn more about percentage here:

https://brainly.com/question/24304697

#SPJ1

Use the net to determine the total surface area.


134.4 in
92.8 in
103.2 in
72 in

Answers

D 72 for lateral surface area

hello fellow indians Question: Lawrence poured 27.328 L of water into a right rectangular prism- shaped tank. The base of the tank is 40 cm by 28 cm. When he finished pouring the water, the tank was ⅔ full. ( 1L=1,000 cm 3).

Answers

Answer: andres is 5 years old pls banned him he called e a mean word like the N word

Step-by-step explanation:

what is the median of the data set represented by the box plot shown below? 38,45,50,60,75

Answers

Answer:

50

Step-by-step explanation:

The graph of the function f(x)=−4(x−3)2+9 will be a parabola opening in which direction?

Answers

Answer:

downwards

Step-by-step explanation:

the equation of a parabola in vertex form is

f(x) = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

• if a > 0 then parabola opens upwards

• if a < 0 then parabola opens downwards

for

f(x) = - 4(x - 3)² + 9 with a = - 4 < 0 , then

the parabola opens downwards

PLEASE ILL GIVE 25 POINTS ANS MARK BRAINIEST IF SOMEONE GIVES ME THE RIGHT ANSWER PLEASE PLEASE PLWASE

Answers

Answer:

Circumference: 25.12m

Area: 50.24 [tex]m^{2}[/tex]

Step-by-step explanation:

Formula for circumference of a circle: C=[tex]\pi d[/tex] or C=[tex]2\pi r[/tex] since the diameter is double the radius

C=3.14*2*4=3.14*8=25.12

Formula for area of a circle: A=[tex]\pi r^{2}[/tex]

A=3.14*[tex]4^{2}[/tex]=3.14*4*4=3.14*16=50.24

Q: Wilma estimates that she’ll drive about 18,000 miles during the year. The car she wants to purchase gets an average of 24 miles per gallon, and the average cost per gallon of gas in her neighborhood is $2.72. Locate the error in her calculations, and select the correction.

A: Wilma made a mistake in step 2. Instead of dividing by 12, she should have divided by 24. She should budget $170 per month for fuel expenses.

Answers

The mistake is made in the second step. The correct steps are given below.

What is Algebra?

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Wilma estimates that she’ll drive about 18,000 miles during the year.

The car she wants to purchase gets an average of 24 miles per gallon, and the average cost per gallon of gas in her neighbourhood is $2.72.

Locate the error in her calculations, and select the correction.

Step - 1

18000 miles/year

18000 miles / 12 months = 1500 miles/month

Step 2

1500 miles/month

1500 miles/month / 24 miles per gallon = 62.5 gallons/month

62.5 gallons/month

Step 3

(62.5 gallons/month) x ($2.72/gallons) = $170 cost/month

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ1


What is the answer to this

Answers

if you are adding them the answer would be
2/4 or 1/2 if you simplify it

I need help with question 24

Answers

Answer:

D

Step-by-step explanation:

angle ABC=angle ADC

angle BAC=angle DCA

AC=CA

Which graph represents exponential decay?
ty
80
60
40
20
80
60
40
20
2
1 2
3
80
60
40
20
ty
O
2 3
x
80
60
40
20
ty
1
2
3

Answers

Using exponential function concepts, it is found that the first graph to the similar problem represents an exponential decay.

What is an exponential function?

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

A(0) is the initial value.r is the decay rate, as a decimal.

As x goes to positive infinity, a exponential function approaches a constant, hence a graph similar to the first one of the similar problem linked below represents exponential decay.

More can be learned about exponential functions at https://brainly.com/question/17747948

#SPJ1

I donot understand what so ever but brainly has def been helping

Answers

Answer:

what happened to you brooooooooo

32 of the 49 8th Graders said that they
prefer dogs over cats.
22 of the 38 9th Graders said that they
prefer dogs.
Did a higher percentage of 8th Graders or
9th Graders prefer dogs?
8th Graders
9th Graders

Answers

Answer:

8th graders i think is the answer

Step-by-step explanation:

Answer:

The 9th grades had given a higher percentage because even without converting to a percent, you can tell just by seeing that there is a 1 number difference if you would try to add.

Other Questions
Factor 60-36w6036w60, minus, 36, w to identify the equivalent expressions. In 1997 the U.S. population was approxiamately 266,667,000 people. At the rate of 440 prisoners per 100,000 population, about how many prisoners were inthe system The figure shows two identical metal bars are different temperatures. What is thecoefficient of linear expansion for the metal from which the bars are made?(A) 1.6 10 (*C).(B) 1.4 x 10(*C)-L - 1.000 m42-1.001 m(C) 1.2 x 10-5 (C)-(D) 1.1 x 10 (C)-T=0.0CT-70.0Cut.luce Probability and statistics please help me out What do you think the significance of the fisherman catching a dead donkey is? Which statement would the information presented in this population pyramid best justify? Three girls are chasing a black dog circle adjectives and underline verbs Choose the correct form of the imperfect.Ruth _________ (encender) la menora. What were the causes championed by Enlightenment thinkers? X^2-6x+5=0 solve with quadratic formula The hard disk that is mounted inside the system unit sometimes is called a(n) ____________________ disk because it is not portable. What is the volume, in cubic meters, if the prism below? Read the quotation by adam smith. according to this quote, what motivates most individuals? desire for power concern for others competition for jobs sense of self-interest What does x= please help AD are tangent to OC. Find the value of x.NEED HELP WITH THIS QUESTION QUICK!!! pls answer I will give brainliest ???? Do yall understand What changes the color of the pastels? An arithmetic sequence has this recursive formula:{ A1=5{An= An-1-4What is the explicit formula for this sequence?A. an= (-1) + (n - 5)(-4)B. an=5+ (n 1)(-4)C. an= 5+ (n-4)(-1)D. an= (-4) + (n 1)5 AMSWER ASAP PLEASE PLEASE PLEASE