The equation of the parabola with the given vertex and directrix in vertex form is y = (1/16)( x + 5 )² - 9.
Hence, option C is the correct answer.
<h3>What is the equation of the parabola?</h3>
Given the data in the question;
- Vertex of the parabola: ( -5, -9 )
- h = -5
- k = -9
- Directrix of the parabola: y = -13
To find the equation, we use the equation of the parabola that opens up or down since the directrix ( y = -13 ) is vertical.
The equation is expressed as;
( x - h )² = 4p( y - k )
First, we find the distance from the focus to the vertex.
|p| is the distance rom the focus to the vertex and from the vertex to the directrix.
p = -9 + 13
p = 4
We substitute the values into the equation;
( x - h )² = 4p( y - k )
( x - (-5) )² = 4(4)( y - (-9) )
( x + 5 )² = 16( y + 9 )
Multiply both side by 1/16
(1/16)( x + 5 )² = y + 9
Make y the subject of the formula
(1/16)( x + 5 )² - 9 = y
y = (1/16)( x + 5 )² - 9
The equation of the parabola with the given vertex and directrix in vertex form is y = (1/16)( x + 5 )² - 9.
Hence, option C is the correct answer.
Learn more about equation of parabola here: brainly.com/question/21685473
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The maximum possible volume of this type of box that can be made from a 20 cm by 20 cm square of paper is 512cm³.
<h3>How to calculate the volume?</h3>
From the information, when the side of 1cm are cut, this will become an open box. The volume will be:
= 18 × 18 × 1
= 324cm³
Also, when 2cm is cut, the volume will be:
= 16 × 16 × 2
= 512cm³
Learn more about volume on:
brainly.com/question/1972490
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Well if you get back to the definition of a division, diving X by Y is finding out how many Ys you can have in a X.
It is clear that you will have more than X times Y if Y is less than 1 since dividing X by 1 is exactly X.
If you think of 10 and 1, you can divide 10 in exactly 10 portions of 1.
But you can divide it into 100 portions of 0,1.
And 100 is bigger than 10 of course.
Hope this helps.
is differentiable across its domain, so the MVT says there is some value of
in the open interval
such that
You have
so the equation above becomes
Solve for
.
so
is indeed the average of the endpoints, i.e. the midpoint.
<h3>hey ....</h3>
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