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4 years ago

A parabola can be drawn given a focus of (4,-8) and a directrix of x = -4. What can be said about the parabola?

Mathematics

1 answer:

Pani-rosa [81]4 years ago

6 0

Answer:

It opens to the right and the vertex is at (0, -8).

The axis of symmetry is y = -8.

Step-by-step explanation:

The vertex is halfway between the directrix and the focus.

The focus is to the right of the directrix so the curve will open towards the right. The axis of symmetry is the line y = -8.

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????help me please ??????????

poizon [28]

Answer:

$5.07

Step-by-step explanation:

1. Find the total cost of apples first

1.99 * 3 = $5.97

2. Price of the bread

.89 * 2 = 1.78

3. Price of the box of cereal

3.99

4. Gallon of milk

3.19

5. Add all together

And you come up with 14.93 dollars

6. Subtract by 20

20 - 14.93 = 5.07

8 0

3 years ago

Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a minimum. f(x,y)=xy; 6x y=10

Pepsi [2]

There is a maximum value of 7/6 located at (x, y) = (5/6, 7).

The function given to us is f(x, y) = xy.

The constraint given to us is 6x + y = 10.

Rearranging the constraint, we get:

6x + y = 10,

or, y = 10 - 6x.

Substituting this in the function, we get:

f(x, y) = xy,

or, f(x) = x(10 - 6x) = 10x - 6x².

To find the extremum, we differentiate this, with respect to x, and equate that to 0.

f'(x) = 10 - 12x ... (i)

Equating to 0, we get:

10 - 12x = 0,

or, 12x = 10,

or, x = 5/6.

Differentiating (i), with respect to x again, we get:

f''(x) = -12, which is less than 0, showing f(x) is maximum at x = 5/6.

The value of y, when x = 5/6 is,

y = 12 - 6x,

or, y = 12 - 6*(5/6) = 7.

The value of f(x, y) when (x, y) = (5/6, 7) is,

f(x, y) = xy,

or, f(x, y) = (5/6)*7 = 7/6.

Thus, there is a maximum value of 7/6 located at (x, y) = (5/6, 7).

Learn more about maximum and minimum at

brainly.com/question/2437551

#SPJ4

7 0

2 years ago

Anthony has a sink that is shaped like a half-sphere. The sink has a volume of 3000

IgorLugansk [536]

Answer:

a) 80
b) 56

Step-by-step explanation:

a) Calculate the volume of the the cup using volume of cylinder equation: $V = \pi r^{2} h$

Where V = Volume, r=radius, and h=height. Your answer should be in cubic inches ( $in^3$ ).
You're given diameter, so use equation $d/2 = r$ to find radius.
Substituting these equations will give you: $V = \pi (d/2)^2 h$
However, the given volume of the sink is 3000 $\pi$ , meaning that you should modify your results to match this value. Do not substitute $\pi$ for 3.14..., leave it as a symbolic value. Your final V of the cup should = 37.5 $\pi$
Divide the volume of the sink by the volume of the cup. This number will be the amount of cups needed to empty it. In equation form:
$Vsink / V cup =$ # of cups.
Note the the $\pi$ will cancel each other out, so there's not need to factor that in.
b) Repeat the steps above with the new d (diameter) value.