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: -2 and 4

Step-by-step explanation:

Let \(t=x/2\).

\(f(t)=0 \longrightarrow t=-1, 2\\\\\therefore x=-2, 4\)

Answer:

I'm not sure if you mean (2/3)x +6 or 2/(3x+6) so I'm going to answer (2/3)x+6.

Step-by-step explanation:

let's just make f(x)=y real quick.

Then,

1. Switch the x and y in the equation

So you would get   x=(2/3)y+6

2. Solve for y

So you would get    

x-6=2/3y

3(x-6)=2y

(3x-18)/2=y

3. Refine and State

So the answer is f(x)= (3x-18)/2

Answer:

-17m/-6 , 4m/3

Step-by-step explanation:

Im not sure what the question is regarding but if its what im doing in school now that is the answer

Answer:

A line that is parallel to y = 3x - 9 will have the same slope as the given line. The slope of y = 3x - 9 is 3. Therefore, the equation of the line that passes through (1, 2) and is parallel to y = 3x - 9 is:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is the point (1, 2)

Substituting the values we get:

y - 2 = 3(x - 1)

Simplifying the equation we get:

y - 2 = 3x - 3

y = 3x - 1

Therefore, the equation of the line that passes through (1, 2) and is parallel to y = 3x - 9 is y = 3x - 1 .

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Answer:

-1 7/10 and -1.7

Step-by-step explanation:

The standard deviation of the probability distribution is approximately 13703.91.

To calculate the standard deviation of a probability distribution, we need to follow these steps:

Calculate the expected value (mean) of the probability distribution. This is done by multiplying each value (x) by its corresponding probability (p(x)) and summing them up.

Expected value (mean) = (10 * 27) + (20 * 28) + (30 * 45) = 270 + 560 + 1350 = 2180.

Calculate the squared deviation for each value. This is done by subtracting the expected value from each value, squaring the result, and then multiplying by the corresponding probability.

Squared deviation for 10: (10 - 2180)^2 * 27 = 212080 * 27 = 5726160.

Squared deviation for 20: (20 - 2180)^2 * 28 = 1998800 * 28 = 55982400.

Squared deviation for 30: (30 - 2180)^2 * 45 = 2815200 * 45 = 126684000.

Calculate the variance of the probability distribution. This is done by summing up the squared deviations.

Variance = (5726160 + 55982400 + 126684000) = 187692560.

Calculate the standard deviation by taking the square root of the variance.

Standard deviation = sqrt(187692560) ≈ 13703.91.

As a result, the probability distribution's standard deviation is around 13703.91.

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Answer:

Angle A=60

Step-by-step explanation:

If ABC is approximately equal to DEF, A=D.

So x+30=2x

x+30=2x -> 30=x

If A=x+30 and x=30 then 30+30=60.

Answer:

Melissa needs to drive 325 miles for the two plans to cost the same

Step-by-step explanation:

Plan A

Initial Fee = 65

Additional cost per mile = 0.50 per mile

Plan B

Initial Fee = 0

Additional cost per mile = 0.70 per mile

Required

Mile both plans will cost the same

Let

\(y \to cost\)

\(x \to miles\)

So, we have:

\(y = Initial\ Fee + Additional * x\)

For plan A

\(y = 65+ 0.50* x\)

\(y = 65+ 0.50x\)

For plan B

\(y = 0 + 0.70*x\)

\(y = 0.70x\)

So, we have:

\(y = 65+ 0.50x\) --- plan A

\(y = 0.70x\) --- plan B

Both plans will cost the same when

\(y = y\)

\(0.70x = 65 +0.50x\)

\(0.70x -0.50x= 65\)

\(0.20x= 65\)

Divide by 0.20

\(x= 325\)

Answer

using y = mx+c

where m is the slope and c

6 = 3(2)+c

6 = 6 + c

c= 0

Y-intercept is where the line passes through the y-axis, which is where x = 0

So, when x = 0, y = 0

Another point on the line, then, is {0,0}

Answer:

9 7/8

Step-by-step explanation:

1. 4 3/8 can be converted into the improper fraction 35/8, and 5 1/2 can be converted into 11/2.

2. Now that we have 35/8 + 11/2, we have to find a common denominator. Since 2 goes into 8 four times, we can turn 11/2 into 44/8 by multiplying the numerator and denominator (the top and the bottom numbers) by 4.

3. Now we have 35/8 + 44/8. At this point, the all we have to do is add the numerators (the top numbers). 35+44=79, so our answer is 79/8, which we can simplify to 9 7/8.

Answer:  Do you have a pic

Step-by-step explanation:

Answer:

a² + 2ab + b² + ac + bc

Step-by-step explanation:

(a + b + c) * (a + b) = aa + ab + ac + ba + bb + bc

= a² + 2ab + b² + ac + bc

The trick you use here is called the distributive property.

Answer:

\(a^2+b^2+2ab+ac+bc\)

Step-by-step explanation:

\((a+b+c(a+b)=\\a^2+ab+ac+ab+b^2+bc=\\a^2+b^2+ab+ab+ac+bc=\\a^2+b^2+2ab+ac+bc\)

The number the spinner is most likely to land on is 2

From the question, we have the following parameters that can be used in our computation:

The spinner

From the spinner, we have the number that covers the largest area to be 2

i.e.

Largest area = 2

This means that the number it is most likely to land on is 2 and it has the highest probability

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Answer: -0.25

Step-by-step explanation:

Start by undoing with PEMDAS (order of operations, P-parenthesis, E-exponents, etc)

+3 on both sides of equal sign, which gives you

8n=-2

then divide by 8 on both sides (undo the times 8)

n=-0.25

Answer: -0.25

Step-by-step explanation:

Start by undoing with PEMDAS (order of operations, P-parenthesis, E-exponents, etc)

+3 on both sides of equal sign, which gives you

8n=-2

then divide by 8 on both sides (undo the times 8)

n=-0.25

Answer:

Find 0% of 60: 0

Find 100% of 60: 60

Find 50% of 60: 30  

Find 25% of 60: 15

Find 75% of 60: 45

Step-by-step explanation:

The rate of change is measured by the slope m.

In case of y=3x-6, the slope is the coefficient of x, that is, the slope m is

Now, in the case of the table, we must find the slope m by choosing two points. The slope formula in this case is

where we chose:

Then, by substituting these values into the slope formula, we have

By comparing the slopes, we can see that the function represented in the table has the greatest rate of chance because 3.5>3

Answer:

it's 800 ft

Step-by-step explanation:

because again when you want to find the area of anything you mulipuly so

10 x 20= 200 then you get the 200 and times it by 4 so 200 x 4 = 800

hope this helps!

To determine the area of the remaining piece of cardboard expressed in terms of x when a square of side length x inches is cut out from a rectangular piece of cardboard having a length of 6x+2 inches and a width of 2x-4 inches, use the following steps.

Draw and label a diagram of the problem. The rectangle should be labeled as 6x+2 inches by 2x-4 inches, and the square cut out should be labeled as x inches by x inches. This is how the diagram looks like: Determine the area of the rectangle, Arect.

The area of the rectangle is given by the product of its length and width. Thus, Arect = (6x + 2)(2x - 4) Determine the area of the square, Asq. The area of the square is given by the square of its side length. Thus, Asq = x²Step 4: Determine the area of the remaining cardboard after the square is cut out, Ar.

This is the difference between the area of the rectangle and the area of the square. Thus, Ar = Arect - Asq= (6x + 2)(2x - 4) - x²= 12x² - 20x - 16

Simplify the expression. The final answer is given in terms of x. Thus, Ar = 12x² - 20x - 16.The area of the remaining piece of cardboard is expressed in terms of x as 12x² - 20x - 16.

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Answer:

120

Step-by-step explanation:

12 x 10 = 120

Answer:

\(\displaystyle \frac{75}{2}\) or \(37.5\)

Step-by-step explanation:

We can answer this problem geometrically:

\(\displaystyle \int^6_{-4}f(x)\,dx=\int^1_{-4}f(x)\,dx+\int^3_1f(x)\,dx+\int^6_3f(x)\,dx\\\\\int^6_{-4}f(x)\,dx=(5*5)+\frac{1}{2}(2*5)+\frac{1}{2}(3*5)\\\\\int^6_{-4}f(x)\,dx=25+5+7.5\\\\\int^6_{-4}f(x)\,dx=37.5=\frac{75}{2}\)

Notice that we found the area of the rectangular region between -4 and 1, and then the two triangular areas from 1 to 3 and 3 to 6. We then found the sum of these areas to get the total area under the curve of f(x) from -4 to 6.

Answer:

\(\dfrac{75}{2}\)

Step-by-step explanation:

The value of a definite integral represents the area between the x-axis and the graph of the function you’re integrating between two limits.

\(\boxed{\begin{minipage}{8.5 cm}\underline{De\:\!finite integration}\\\\$\displaystyle \int^b_a f(x)\:\:\text{d}x$\\\\\\where $a$ is the lower limit and $b$ is the upper limit.\\\end{minipage}}\)

The given definite integral is:

\(\displaystyle \int^6_{-4} f(x)\; \;\text{d}x\)

This means we need to find the area between the x-axis and the function between the limits x = -4 and x = 6.

Notice that the function touches the x-axis at x = 3.

Therefore, we can separate the integral into two areas and add them together:

\(\displaystyle \int^6_{-4} f(x)\; \;\text{d}x=\int^3_{-4} f(x)\; \;\text{d}x+\int^6_{3} f(x)\; \;\text{d}x\)

The area between the x-axis and the function between the limits x = -4 and x = 3 is a trapezoid with bases of 5 and 7 units, and a height of 5 units.

The area between the x-axis and the function between the limits x = 3 and x = 6 is a triangle with base of 3 units and height of 5 units.

Using the formulas for the area of a trapezoid and the area of a triangle, the definite integral can be calculated as follows:

\(\begin{aligned}\displaystyle \int^6_{-4} f(x)\; \;\text{d}x & =\int^3_{-4} f(x)\; \;\text{d}x+\int^6_{3} f(x)\; \;\text{d}x\\\\& =\dfrac{1}{2}(5+7)(5)+\dfrac{1}{2}(3)(5)\\\\& =30+\dfrac{15}{2}\\\\& =\dfrac{75}{2}\end{aligned}\)

Answer:

The answer is 11.8

Step-by-step explanation:

The value of x and y is 12.2 and 11.8 respectively.

The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.

The sine (sin) of an acute angle in a right angled triangle is the ratio between the side opposite the angle and the hypotenuse of the triangle.

According to the given question.

We have a right angled triangle.

In which one angle is 44 degrees and hypotenuse is 17 units.

Here,

With respect to angle 44 degrees the adjacent side is x and the opposite side is y.

Therefore,

Sine of 44 degrees is given by

\(sin44^{o} = \frac{opposite\ side }{Hypotenuse}\)

\(\implies sin44^{o} = \frac{y }{17}\)

\(\implies 0.6946 = \frac{y}{17}\)

\(\implies 0.6946 \times 17 = y\)

\(\implies y = 11.80\)

\(\implies y = 11.8\)

And, tangent of 44 degrees is give by

\(tan 44^{o} = \frac{opposite \ side }{adjacent \ side }\)

\(\implies tan44^{o} = \frac{y}{x}\)

\(\implies tan44^{o} = \frac{11.8}{x}\)

\(\implies 0.9657 = \frac{11.8}{x}\)

\(\implies x = \frac{11.8}{0.9657}\)

\(\implies x = 12.22\)

\(\implies x = 12.2\)

Therefore, the value of x and y is 12.2 and 11.8 respectively.

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Answer:

A, B and D

Step-by-step explanation:

√5 x √5 x √4 is basically 5 x 5 x 4 = 100, but the 100 still has the root sign

The sqrt of 100 is 10, since 10 x 10 = 100

Like said on the first line, it makes √100 and this is valid since the question does not say to simplify it

Answer:

a1 is 1/6

r is -1/10

S2 is 3/20

S3 is 91/600

Step-by-step explanation:

is good

Answer:

What is a1? 1/6

What is r? -1/10

S2 = ✔ 3/20

S3 = ✔ 91/600

The series converges to a value that is ✔ less than

the initial term.

Evaluate the infinite geometric series.

✔ 5/33

Step-by-step explanation:

A graph may or may not represent a function.

The true statement is: (b) Yes, the graph passes the vertical line test.

The vertical line test is used to determine if a graph represents a function or not.

When a vertical line is drawn through the graph, the line would only intersect with the curve at a point.

This means that:

The graph represents a function.

Hence, option (b) is true

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One whole unit circle has an angle of 2π. So, if our angle is 5π, this would be two revolutions and a half. This means that the terminal ray of this angle lies in Quadrant II at the x-axis.

The angle has an x-value of -1, a y-value of 0, and an r-value of 1.

So, the value of the six trigonometric functions are:

Step-by-step explanation:

=sin (17*180/3)

=sin (17*60]

=sin (1020)

=sin (1080 - 60)

=sin (-60)

=-sin (60)

=-√3/2

Where the above relations are given, note that Options A,  D, and E are the relations that represents a function. The others are just relations.

To distinguish a function from a relation, look to see if any of the x values are repeated; if not, the relationship is a function. If some x values are repeated but the accompanying y values differ, we have a relation rather than a function.

Note that where you are given domain and range, only the range is represented on the x-axis.

Some of the x values may be seen repeated in B, and C.

How is this so?

B) In a coordinate system, values are represented as (x, y). so

In relations, B 2 is repeated twice to in connection with -5, and -6. That is:

(2, -5) , (2, -6)

Since two is x, then its repetition nullified the relation as a function.

C) On table indicated on C, it is much easier to identify the x and y values. As is seen, -3 is repeated twice in connection with 4 and 2. Thus, its repetition nullified the relation as a function.

As a result, Options A,  D, and E are the relations that represent a function.

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Answer:

0.66 melones por niño o 2/3

Step-by-step explanation:

10/15=2/3=0.66

Answer:

she can paint 17  statues (with  some paint left,but not enough for another statue)

Step-by-step explanation:

7/8 divided into  1/20

is the same as   7/8 multiplied by 20/1

7/8 x 20/1  = 140/8  = 17.5