1.
the x value of the vertex in form
ax^2+bx+c=y
is
-b/2a
so
-2x^2+8x-18
x value of vertex is
-8/(2*-2)=-8/-4=2
plug it in to get y value
-2(2)^2+8(2)-18
-2(4)+16-18
-8-2
-10
vertex is at (2,-10)
or you could complete the square to get into y=a(x-h)^2+k, where the vertex is (h,k)
so as follows
y=(-2x^2+8x)-18
y=-2(x^2-4x)-18
y=-2(x^2-4x+4-4)-18
y=-2((x-2)^2-4)-18
y=-2(x-2)^2+8-18
y=-2(x-2)^2-10
vertex is (2,-10)
5.
vertex is the time where the speed is the highest
at about t=10, the speed is at its max
5/9* 32
= (5*32)/9
= 160/9
= (153+ 7)/9
= 153/9+ 7/9
= 17+ 7/9
= 17 7/9
The final answer is 17 7/9~
take your compass on a point on your line. then draw a circle. take the 2 points in which the circle hit the line and draw 2 circles larger than half the distance between he 2 points. take the point that they intersect and and connect it to the line and you point M and it is purpendicular. does that make sense?
(v+4)t=66
t=66/(v+4)
...
(v-4)t=42, using t found above in this equation gives you:
66(v-4)/(v+4)=42 perform indicated multiplication on the left side
(66v-264)/(v+4)=42 multiply both sides by (v+4)
66v-264=42v+168 add 264 to both sides
66v=42v+432 subtract 42v from both sides
24v=432 divide both sides by 24
v=18
So his normal bicycling speed with no wind is 18 mph.
