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3 years ago

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A water park charges $5 for entry into the park and an additional $2 for each of the big water slides. Steven spent $17 on his v

isit to the water park. Which equation can be used to find the number of big water slides, x, that Steven went on?

2 answers:

trapecia [35]3 years ago

7 0

5+3x=17 where x=2 ...

german3 years ago

4 0

2x+5=17
2x For the cost of every ride, 5 is the entry -&& 17 is the total amount he spent

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13. Wind farms are a source of renewable energy found around the world. The power P (in kilowatts) generated by a wind turbine v

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Since the Power is directly proportional to the velocity, their ratio $\frac{P}{v^{3} }$ is constant.

<span>Therefore </span> $\frac{500}{ 10^{3} } = \frac{x}{ 12^{3} }$ which is a proportion:

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that can be easily solved:

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3 years ago

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The planets in our solar system do not travel in circular paths. Rather, their orbits are elliptical. The Sun is located at a fo

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1. The distance between the perihelion and the aphelion is 116 million miles

2. The distance from the center of Mercury’s elliptical orbit and the Sun is 12 million miles

3. The equation of the elliptical orbit of Mercury is $\frac{x^{2}}{3364}}+\frac{y^{2}}{3220}=1$

4. The eccentricity of the ellipse is 0.207 to the nearest thousandth

5. The value of the eccentricity tell you that the shape of the ellipse is near to the shape of the circle

Step-by-step explanation:

Let us revise the equation of the ellipse is

$\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ , where the major axis is parallel to the x-axis

The length of the major axis is 2a
The coordinates of the vertices are (± a , 0)
The coordinates of the foci are (± c , 0) , where c² = a² - b²

∵ The Sun is located at a focus of the ellipse

∴ The sun located ate c

∵ The perihelion is the point in a planet’s orbit that is closest to the

Sun ( it is the endpoint of the major axis that is closest to the Sun )

∴ The perihelion is located at the vertex (a , 0)

∵ The closest Mercury comes to the Sun is about 46 million miles

∴ The distance between a and c is 46 million miles

∵ The aphelion is the point in the planet’s orbit that is furthest from

the Sun ( it is the endpoint of the major axis that is furthest from

the Sun )

∴ The aphelion is located at the vertex (-a , 0)

∵ The farthest Mercury travels from the Sun is about 70 million miles

∴ The distance from -a to c is 70 million miles

∴ The distance between the perihelion and the aphelion =

70 + 46 = 116 million miles

1. The distance between the perihelion and the aphelion is 116 million miles

∵ The distance between the perihelion and the aphelion is the

length of the major axis of the ellipse

∵ The length of the major axis is 2 a

∴ 2 a = 116

- Divide both sides by 2

∴ a = 58

∴ The distance from the center of Mercury’s elliptical orbit to the

closest end point to the sun is 58 million miles

∵ The distance between the sun and the closest endpoint is

46 million miles

∴ The distance from the center of Mercury’s elliptical orbit and

the Sun = 58 - 46 = 12 million miles

2. The distance from the center of Mercury’s elliptical orbit and the Sun is 12 million miles

∵ The major axis runs horizontally

∴ The equation is $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$

∵ a = 58

∵ c is the distance from the center to the focus of the ellipse

∴ c = 12

∵ c² = a² - b²

∴ (12)² = (58)² - b²

- Add b² to both sides

∴ (12)² + b² = (58)²

- Subtract (12)² from both sides

∴ b² = (58)² - (12)² = 3220

- Substitute these values in the equation

∴ $\frac{x^{2}}{3364}}+\frac{y^{2}}{3220}=1$

3. The equation of the elliptical orbit of Mercury is $\frac{x^{2}}{3364}}+\frac{y^{2}}{3220}=1$

The eccentricity (e) of an ellipse is the ratio of the distance from the

center to the foci (c) and the distance from the center to the

vertices (a) ⇒ $e=\frac{c}{a}$

∵ c = 12

∵ a = 58

∴ $e=\frac{12}{58}$ = 0.207

4. The eccentricity of the ellipse is 0.207 to the nearest thousandth

If the eccentricity is zero, it is not squashed at all and so remains a circle.

If it is 1, it is completely squashed and looks like a line

∵ The eccentricity of the ellipse is 0.207

∵ This number is closed to zero than 1

∴ The shape of the ellipse is near to the shape of the circle

5. The value of the eccentricity tell you that the shape of the ellipse is near to the shape of the circle

Learn more:

You can learn more about conics section in brainly.com/question/4054269

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3 years ago

Every day, the Scott Pet Store uses 3 bags of dog food to feed the dogs. For how many days will 1/2 of a bag of dog food last?

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If you would like to know for how many days will 1/2 of a bag of dog food last, you can calculate this using the following steps:

1 day ... 3 bags of dog food
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1/2 = 3 * x /3
x = 1/2 * 1/3
x = 1/6 of a day

The correct result would be 1/6 of a day.

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3 years ago

Use complete sentences to explain the relationship between tan 5pi/4 and tan pi/4. In your answer, reference specific values on

Kisachek [45]

Remark
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5*pi / 4 is between pi and 3/2 pi which means that the angle is in the third quadrant.

So you are talking about one two angles that are in the first and third quadrants.

Step One
Find the Tangent of pi/4 using the unit circle as a reference.

Since pi/4 is 1/2 way between 0 and pi/2 you are referring to something that has and x value of 0.707 for an x value and 0.707 for a y value. (They are equal)

That is the point where the opposite / adjacent = 0.707/0.707 = 1

Step Two
Find the tangent of 5pi/4 using the unit circle.
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3 years ago

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topjm [15]

Answer:

Below.

Step-by-step explanation:

1. The common difference is 3 so the next 2 terms are 12 and 15.

2.. The common difference is 2 so the next 2 terms are 4 and 6.

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2 years ago

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