The shape of this particular section of the rollercoaster is a half of a circle. Center the circle at the origin and assume the highest point on this leg of a roller coaster is 30 feet above the ground.

1. Write the equation that models the height of the roller coaster.

a. Start by writing the equation of the circle. (Remember that the general form of a circle with the center at the origin is x^2 + y^2 = r^2

b. Now solve this equation for y. (Remember the roller coaster is above ground, so you are only interested in the positive root.

2. Graph the model of the roller coaster using the graphing calculator. Either sketch by hand or take a picture and paste the image below.

Answer:

Amount contributed by Oscar = $8

Step-by-step explanation:

Given that:

Amount spent on gift = $36

Amount contributed by Moriah = $12

Let,

x be the amount contributed by each of them.

Thus,

Gift total = Contribution of all

36 = x+x+x+12

36 = 3x+12

3x+12 = 36

3x=36-12

3x=24

Dividing both sides by 3

[tex]\frac{3x}{3}=\frac{24}{3}\\x=8[/tex]

Hence,

Amount contributed by Oscar = $8

Answer:

11/36

Step-by-step explanation:

We have 36 possible outcomes when rolling a pair of dice.

Only 1 outcome gets both 3's. (3 3)

For the sum to be greater than 8, there are 10 outcomes.

(3 6) (4 5) (4 6) (5 4) (5 5) (5 6) (6 3) (6 4) (6 5) (6 6)

The probability is therefore (1+10)/36=11/36.

Answer:

Step-by-step explanation:

(a) [tex]\int x^n e^{5x^4+1} \ dx[/tex]

Suppose [tex]5x^4 + 1 = f[/tex]

by differentiation;

[tex]\implies \ 20 x^3 dx = df --- (1)[/tex]

Suppose n = 3

Then, the integral

[tex]I = \int x^ 3 e^{5x^4 + 1} \ dx[/tex]

[tex]= \int e^f \ \dfrac{df}{20}[/tex]

[tex]= \dfrac{1}{20} \int e^f \ dt[/tex]

[tex]= \dfrac{1}{20} e^f + C[/tex]

recall that [tex]f = 5x^4 + 1[/tex]

Then;

[tex]\mathbf{ I = \dfrac{1}{20}e^{5x^4+1}+C}[/tex]

(b) [tex]\int \dfrac{cos (\dfrac{1}{x^3})}{x^n } \ dx[/tex]

suppose; [tex]\dfrac{1}{x^3} = f[/tex]

[tex]x^3 = f[/tex]

[tex]\implies -3x^{-4} \ dx = df[/tex]

[tex]\implies \dfrac{1}{x^4} \ dx =-\dfrac{1}{3} df[/tex]

If n = u, then the integration is:

[tex]I = \int \dfrac{1}{x^4} \ cos (\dfrac{1}{x^4}) \ dx[/tex]

[tex]= \int -\dfrac{1}{3} \ cos \ f \ df[/tex]

[tex]= -\dfrac{1}{3} \int \ cos \ f \ df[/tex]

[tex]= -\dfrac{1}{3} \ sin \ f + C[/tex]

Since;  [tex]x^3 = f[/tex]

Then;

[tex]\mathbf {I = -\dfrac{1}{3} \ sin \ \Big( \dfrac{1}{x^3}\Big) + C}[/tex]

(c) [tex]\int \dfrac{x+n}{x^2 + 8x -4} \ dx[/tex]

Suppose  [tex]x^2 + 8x - 4 = f[/tex]

Then, by differentiation of both sides

[tex](2x + 8) \ dx = df[/tex]

[tex](x + 4) \ dx = \dfrac{1}{2} \ df[/tex]

Suppose n = 4 in integration, then:

[tex]I = \int \dfrac{(x + 4) }{x^2 +8x -4} \ dx[/tex]

By substitution;

[tex]I = \int \dfrac{1}{2}\dfrac{1}{f} \ df[/tex]

[tex]= \dfrac{1}{2} \ \ { In |f|} + C[/tex]

[tex]\mathbf{= \dfrac{1}{2} \ \ { In |x^2+8x -4|} + C}[/tex]

The suitable substitutions of n are 3,4,4 respectively.

The process of finding integrals is called integration.

a)[tex]f(x)=\int\limits {x^3e^{5x^4+1} } \, dx[/tex]

Suppose

[tex]5x^4+1 =t\\20x^3 dx =dt[/tex]

So, we need n=3 for easy integration.

[tex]f(x)=\int\limits {x^3e^{5x^4+1} } \, dx[/tex]

[tex]I = \frac{1}{20} \int\limits {e^{t} } \, dt[/tex]

[tex]I=\frac{e^{t} }{20}[/tex]

[tex]I = e^{5x^{4}+1 }/20 +c[/tex]

b)Similarly for [tex]f(x) = \int\limits\frac{cos(\frac{1}{x^3} )}{x^n} \, dx[/tex]

n=4 is needed for easy integration.

I = [tex]\frac{-1}{3} sin(\frac{1}{x^3} ) +c[/tex]

c)For [tex]f(x) = \int\limits \frac{x+n}{x^{2} +8x-4} \, dx[/tex]

n=4 is needed for easy integration.

[tex]I = \frac{1}{2} log(x^{2} +8x-4)[/tex]

Hence, the suitable substitutions of n are 3,4,4 respectively.

To get more about integration visit:

https://brainly.com/question/2633548





Step-by-step explanation:

Sum of interior angles in a polygon

= 180°(n - 2), where n is the number of sides.

Hence a convex polygon with 6 sides

=> 180°(6 - 2) = 720°.

Answer:

Hey

Step-by-step explanation:

Write the fraction in simplest form

[tex] - \frac{29}{18} [/tex]

[tex] \frac{8}{9} - \frac{5}{2} [/tex]

Find the difference between 8/9 and 5/-2

[tex] \frac{8}{9} - \frac{5}{2} [/tex]

[tex] \frac{8 \times 2}{9 \times 2} - \frac{5 \times 9}{2 \times 9} [/tex]

[tex] \frac{16}{18} - \frac{45}{18} [/tex]

[tex] \frac{16 - 45}{18} [/tex]

[tex] \frac{ - 29}{18} [/tex]

[tex] - \frac{29}{18} [/tex]

Answer:

8

Step-by-step explanation:

Answer: the answer is 8

Step-by-step explanation: hope this helps :)

Answer:

a smart person is not me clearly lol

Step-by-step explanation:

Answer:

im sure its D.)

Step-by-step explanation:

Answer:

Solve for the first variable in one of the equations, then sub the result into the other equation.

point form- (4,-1)

equation form- x=4, y=-1

Step-by-step explanation:

I HIGHLY recommend math-way to help you with problems like this :)

hope this helps!

Answer:

The measurement of the width is 10cm.

Answer:

Look at the graph below, hope this helped.

Step-by-step explanation:

Answer:

-0.88

Step-by-step explanation:

(f/g)(9)=(x+7)/-2x and the 9 brackets is the value of x with which you have to substitute. after u do that you get (9+7)/-18=16/-18=-0.88(8)

Answer:

C not sure though

Step-by-step explanation:

Answer:

These two corners are [tex]\sqrt{13}[/tex] units apart.

Step-by-step explanation:

Distance between two points:

Suppose we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Approximately how far apart are the two corners?

We have to find the distance between the points (-5,-2) and (-8-3). So

[tex]D = \sqrt{(5-(-8))^2+(-2-(-3))^2} = \sqrt{13}[/tex]

These two corners are [tex]\sqrt{13}[/tex] units apart.

Answer:

Answer is B

Step-by-step explanation:

P(x<2) - P(x<-2) = .9772 - .0228 = .9544

= 95%

Answer:

15

Step-by-step explanation:

18 ÷ 3 = 6

6+3 =15

hope this helps

Answer:

The fare ride was 11 miles.

Step-by-step explanation:

So it says that for the first mile the taxi charged $4.00 okay? so then it says for each additional mile he charges $1.25 so what i did was add the $4.00 and then kept on adding $1.25. so $4.00 plus $1.25 equals $5.25 so continue adding $1.25 till you get to exactly $16.50.. Count up exactly how many           "$1.25's" it took to get to $16.50 so it would be exactly 10 times you had to add $1.25 to it and we cant forget the first mile which was $4.00 so thats an additional mile so then it would 11 miles !

Answer:

88°

Step-by-step explanation:

Connect A to O, you'll have 2 same right triangles and angle COB is going to be split in half.

Answer:

88

Step-by-step explanation:

Step-by-step explanation:

When m > -3.1, the line should extend towards the right and the point at 3.1 should be an empty circle. (as m = 3.1 is not included in the solution set)

Hence the answer is Option D.

P.S. The reason why A is wrong is because the number line is wrongly labelled. -3.3, -3.2 and -3.1 are all less than -3 and should be on the left of the number line.

Answer:

weird questions but...

May I have 4 cups of water please?

Answer:

deciliter of water

Step-by-step explanation:

a unit of capacity equal to 1/10 of a liter.

Answer:

Step-by-step explanation:

I'm not sure about number 3, but I have the answer for number. The answer is 1:32.

3: 69

3/69

Then we reduce the fraction to the lowest term

3/69 = 1/32

1:32

Just divide 96/3 and you can see that one bus can hold 32 students

Answer:

gravitational force or  A the first one

Step-by-step explanation:

Answer:

Step-by-step explanation:

it a

Answer:

2?

Step-by-step explanation:

Answer:

In four minutes Heather can ring up 52 maybe even 53 customers.

Step-by-step explanation:

To find this answer you would have to find how many customers Heather can rind up in one minute. To do this you can do 121 divided by 9 which equals about 13 so you can use 13. And then you would do 13 times 4 because that's how many minutes the question is asking for, and your answer would be about 52, so your answer is about 52 close to 53, you might not get an exact answer for a problem like this. :)

Answer:

They each got 1/10th of the bag

Step-by-step explanation:

you just divide 1/5th by 2 which is 1/10

Answer:

50 m²

Step-by-step explanation:

2 cm for length = 5 m. 4 cm for width = 10 m. Area = width • length. 10•5=50

Answer:

14.66 or 14.7

Step-by-step explanation:

if we solve the equation we get 14.6666 but since it goes on and on we round and put it on 14.7

Answer:

Step-by-step explanation:

11 ÷ 3/4 = [tex]11 * \frac{4}{3}[/tex]

             [tex]=\frac{44}{3}\\\\=14\frac{2}{3}[/tex]