Find the volume of the sphere.

What is the ratio of quarts in a carton of milk

rjkz [21]

4:1
4 quarts are equal to 1 gallon (i think i am correct)

8 0

3 years ago

Use the given information to write the equation of the parabola.

m_a_m_a [10]

Answer:

x² = -2y

Step-by-step explanation:

The focus is p away from the vertex, and so is the directrix.

To find the equation of the parabola, we must first determine if the parabola is horizontal or vertical.

Horizontal parabola [Standard form]: (y – k)² = 4p(x – h)
Vertical parabola [Standard form]: (x – h)² = 4p(y – k)

If the parabola is vertical, the directrix, and focus will have the same x value but different y value compared to the vertex (h, k). You can also tell if the directrix in in the form y = k – p, and if the focus is in the form (h, k + p).

Likewise, if the parabola is horizontal, the directrix, and focus will have the same y value but different x value compared to the vertex (h,k) . You can also tell if the directrix is in the form x = h – p, and if the focus is in the form (h + p, k).

For this problem, given that the vertex is at the origin (0,0), and that the focus is at the point (0, -½).

You can tell that the x value is the same for the vertex, and focus so this must be a vertical parabola. Because this is a vertical parabola, we can use the form mentioned as earlier (x – h)² = 4p(y – k).

If h = 0, and k = 0, the p value must be the difference between the k of the vertex, and the k of the focus: -½ - 0 → -½.

Now we can just plug in our known information to derive the equation!

h = 0, k = 0, p = -½ → (x - h)² = 4p(y - k) →

(x - 0)² = 4(-½)(y - 0) → x² = -2(y - 0) →

x² = -2y.

Also p = 1/4a, if you are wondering.

So because this is a vertical parabola, x² = -2y is generally the same as y = -1/2x² in standard quadratic form. I just like to think of the horizontal parabola as an inverse quadratic because it is like reflecting over the line y = x.

8 0

3 years ago

Read 2 more answers

A soldier started patrolling around his camp at 22 30 . His patrol lasted 3 hours and 20 minutes .What time did his patrol end

baherus [9]

Answer:01 50 Hrs

Step-by-step explanation:

If the soldier started patrol at 2230 hrs and his petrol lasted for 3 hours and 20 minutes, that means he was on patrol for that time.

The time he finished was therefore:

= 2230 + 320

= 2550

At 24 you begin at 0:00am so:

= 2550 - 2400

= 150

Patrol ended at 0150 hrs

4 0

3 years ago

14. The maximum capacity for seating in a theater is 500 people. The theater sells two types of

Eva8 [605]

Taking into account the definition of a system of linear equations, the amount of adult tickets sold is 356 and the amount of child tickets sold is 144.

<h3>System of linear equations</h3>

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.

<h3>Amount of ticket sold</h3>

In this case, a system of linear equations must be proposed taking into account that:

"x" is the amount of adult tickets sold.
"y" is the amount of child tickets sold.

The maximum capacity for seating in a theater is 500 people. If they sold out on a certain showtime, this is represented by x+y=500.

On the other side, the theater sells two types of tickets, adult tickets for $7.25 each and child tickets for $4 each and the made a total of $3,157. This is represented by 7.25x +4y=3157.

So, the system of equations to be solved is

$\left \{ {{x+y=500} \atop {7.25x+4y=3157}} \right.$

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable x from the first equation you get:

x=500 - y

Substituting this expression in the second equation you get:

7.25× (500 -y) +4y=3157

7.25×500 - 7.25y +4y=3157

3625 - 7.25y +4y=3157

- 7.25y +4y=3157 -3625

-3.25y= -468

y= (-468)÷ (-3.25)

Substituting this value in the expression x=500 - y you get:

x=500 - 144

Remembering that "x" is the amount of adult tickets sold and "y" is the amount of child tickets sold, you get that the amount of adult tickets sold is 356 and the amount of child tickets sold is 144.

Learn more about system of equations:

<u>brainly.com/question/14323743</u>

<u>brainly.com/question/1365672</u>

<u>brainly.com/question/20533585</u>

<u>brainly.com/question/20379472</u>

5 0

2 years ago

The question is in the picture. (Alegbra 1)

Nady [450]

OPTION D = 2q is right answer

6 0

3 years ago