What is the value of k? k=

Derive the equation of the parabola with a focus at (0, −4) and a directrix of y = 4.

Goshia [24]

$\sqrt{(x_{0} - 0)^{2} + (y_{0} - (-4))^{2}} = |y_{0} - 4|$
 $\sqrt{(x_{0} - 0)^{2} + (y_{0} + 4)^{2}} = |y_{0} - 4|$
 $(x_{0} - 0)^{2} + (y_{0} + 4)^{2} = (y_{0} - 4)^{2}$
$(x_{0})^{2} + (y_{0} + 4)^{2} = (y_{0} - 4)^{2}$
$x_{0}^{2} + (y_{0}^{2} + 4y_{0} + 4y_{0} + 16) = y_{0}^{2} - 4y_{0} - 4y_{0} + 16$
$x_{0}^{2} + (y_{0}^{2} + 8y_{0} + 16) = y_{0}^{2} - 8y_{0} + 16$
$x_{0}^{2} + y_{0}^{2} + 8y_{0} + 16 = y_{0}^{2} - 8y_{0} + 16$
$x_{0}^{2} + 16y_{0} = 0$
$16y_{0} = -x_{0}^{2}$
$\frac{16y_{0}}{16} = \frac{-x_{0}^{2}}{16}$
$y_{0} = -\frac{1}{16}x_{0}^{2}$
$y = -\frac{1}{16}x^{2}$

The answer is C.

5 0

3 years ago

Matt is given 9/10 hours to shovel a driveway. He only uses 2/3 of the given time to shovel the driveway. How much time is left?

ser-zykov [4K]

Answer:

0.23333333333

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Find the coordinates of the missing endpoint if P is midpoint of NQ

Annette [7]

So wat are the answer choices

6 0

3 years ago

How many solutions does this equation have?

iogann1982 [59]

<h3>Explanation</h3>

Solve the equation for s-term.

$- 4s = - 10 - 5s \\ - 4s + 5s = - 10 \\ s = - 10$

Answer Check by substituting s = -10 in the equation.

$- 4( - 10) = - 10 - 5( - 10) \\ 40 = - 10 + 50 \\ 40 = 40 \: \: \tiny \boxed{ \green \checkmark}$

Solutions

No Solutions

When both sides of equation are different. For example, 3 = 4 which makes the equation false. That means the equation is false for all real numbers, thus having no solutions.

One Solution

A common type solution because you see this type of solution a lot. If you can solve the equation for a variable like x = 2 or s = 0. That's one solution.

Infinitely Many Solutions

When both sides are same like 3 = 3 or 7 = 7. That means the equation is true for all real numbers. You can see this type of solution by solving the equation with same both sides like 3x+2 = 3x+2.

<h3>Answer</h3>

Because we can solve the equation for s-term. Therefore the answer is one solution

6 0

3 years ago

A distributor ships DVDs to several stores. The shipping boxes contain several DVDs (in their cases) plus a layer of padding at

Snowcat [4.5K]

Answer:

Option B.

Step-by-step explanation:

It is given that,

Thickness of Each DVD case = 14 mm

Thickness of each layer of padding = 10 mm

Length of the interior of the box = 132 mm

Let d represents the number of DVDs that the distributor can fit into one box with two layers of padding.

Thickness of d DVD cases = 14d mm

Thickness of two layers of padding = 10×2=20 mm

Total thickness of d DVD cases and 2 layers of padding = 14d+20

Total thickness must be less than or equal to 132.

$14d+20\leq 132$

Therefore, the correct option is B.

7 0

3 years ago

What is the value of k?k=​

What is the value of k?k=