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forsale [732]
3 years ago
14

The directrix of a parabola is y=9. The focus of the parabola is (2,5).

Mathematics
1 answer:
GrogVix [38]3 years ago
4 0
The distance from any point P (x,y) on the parabola to the focus = the distance of this point from the directrix.

distance between P to focus:-

= sqrt ( x - 2)^2 + (y - 5))^2

distance from the point to directrix = ( 9 - y)

so sqrt( x - 2)^2 + (y-5)^2  = 9 -y
(x - 2)^2+ (y - 5)^2 = (9-y)^2
x^2 -4x + 4 + y^2 - 10y + 25 = 81 - 18y + y^2
x^2 - 4x + 4 +25 - 81 = -18y + 10y
-8y = x^2 - 4x -52 

y =  (-1/8)^2 + 1/2 x + 6 1/2    is the required equation


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2 years ago
If a certain cannon is fired from a height of 8.8 meters above the​ ground, at a certain​ angle, the height of the cannonball ab
Dennis_Churaev [7]

Answer:

It would take approximately 6.50 second for the cannonball to strike the ground.

Step-by-step explanation:

Consider the provided function.

h(t)=-4.9t^2+30.5t+8.8

We need to find the time takes for the cannonball to strike the ground.

Substitute h(t) = 0 in above function.

-4.9t^2+30.5t+8.8=0

Multiply both sides by 10.

-49t^2+305t+88=0

For a quadratic equation of the form ax^2+bx+c=0 the solutions are: x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}

Substitute a = -49, b = 305 and c=88

t=\frac{-305+\sqrt{305^2-4\left(-49\right)88}}{2\left(-49\right)}=-\frac{-305+\sqrt{110273}}{98}\\t = \frac{-305-\sqrt{305^2-4\left(-49\right)88}}{2\left(-49\right)}= \frac{305+\sqrt{110273}}{98}

Ignore the negative value of t as time can't be a negative number.

Thus,

t=\frac{305+\sqrt{110273}}{98}\approx6.50

Hence, it would take approximately 6.50 second for the cannonball to strike the ground.

6 0
2 years ago
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Answer:

B. 24d + 4; $76

Step-by-step explanation:

Part 1: If the online store charges $24 per DVD, this is the same as saying "24 multiplied by the number of DVDs bought".

It's given that "d" represents the number of DVDs

  • So the first part of the variable expression is: 24d

If the online store also charges an additional $4 per <em>order,</em> that means that it's only $4 extra for the whole order. NOT per DVD you buy.

  • Result: 24d + 4

Part 2: If someone were to buy 3 DVDs, that would mean that d = 3.

To find the total cost, substitute 3 for d into the expression.

  • 24d + 4
  • 24(3) + 4
  • 72 + 4 = 76
  • Result: $76
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