(picture) is this the correct way to solve 19?

Mathematics

1 answer:

goldfiish [28.3K]2 years ago

8 0

I cant see your work very clearly so I'll work it out below:-

f(x + Δx) = (x + Δx)^2 - 2(x + Δx) - 3

= x^2 + 2x(Δx) + (Δx)^2 - 2x - 2(Δx) - 3

= x^2 - 2x + (Δx)^2 + 2x(Δx) - 2(Δx) - 3

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The solid block below is shaped so that it will interlock with another solid block to form a cube.

jeka57 [31]

Answer:

Your didnt explain enough this isnt possible to solve

6 0

1 year ago

A parabola has a focus of F(2, -0.5) and a directrix of y=-1.5 P(x,y) represents any point on the parabola, while D(x, -1.5) rep

prohojiy [21]

The sketch of the parabola is attached below

We have the focus $(a,b) = (2, -0.5)$
The point $P(x,y)$
The directrix, c at $y=-1.5$

The steps to find the equation of the parabola are as follows

Step 1
Find the distance between the focus and the point P using Pythagoras. We have two coordinates; $(2, -0.5)$ and $(x,y)$ .
We need the vertical and horizontal distances to find the hypotenuse (the diagram is shown in the second diagram).
The distance between the focus and point P is given by
$\sqrt{ (x-a)^{2}+ (y-b)^{2} }$

Step 2
Find the distance between the point P to the directrix $c$ . It is a vertical distance between y and c, expressed as $y-c$

Step 3
The equation of parabola is then given as
$\sqrt{ (x-a)^{2}+ (y-b)^{2} }$ = $y-c$
$(x-a)^{2}+ (y-b)^{2}= (y-c)^{2}$ ⇒ substituting a, b and c
$(x-2)^{2}+ (y--0.5)^{2} = (y--1.5)^{2}$
$(x-2)^{2}+ (y+0.5)^{2}= (y+1.5)^{2}$ ⇒Rearranging and making $y$ the subject gives

$y= \frac{ x^{2} }{2} -2x+1$