Firstly expand (x - 3)(ax^2 + bx + c):
ax^3 + bx^2 + cx - 3ax^2 - 3bx - 3c
Now rearrange it so that it's in the form ax^3 + bx^2 + cx + d:
ax^3 + (b-3a)x^2 + (c-3b)x - 3c
Now we can compare both equations:
ax^3 + (b-3a)x^2 + (c-3b)x - 3c = 2x^3 - x^2 - 19x + 12
We get:
(1) a = 2
(2) b - 3a = -1
(3) c - 3b = -19
(4) -3c = 12
If we substitute (1) into (2) we get:
b - 3*2 = -1
b - 6 = -1
b = 5
Now if we solve (4) we get:
-3c = 12
c = -4
Therefor a = 2, b = 5 and c = -4
Answer:
I cant see a table, but go ahead and pick c
Volume of cube, V = edge^3
Let edge of cube#1 = (x-4) m, therefore volume of cube#1, v1 = (x-4)^3 m
Let edge of cube#2 = x m, therefore volume of cube#2, v2 = x^3 m
Diff. in volume (in m) = 1216 = v2-v1 = [ x^3 - (x-4)^3 ]
= x^3 - [(x-4)(x-4)(x-4)]
= x^3 - [<span>x^2 - 8x +16(x - 4)]
= </span> x^3 - [ x^3 - 12x^2 + 48x - 64 ]
= 12x^2 - 48x + 64
= 4 (3x^2 - 12x + 16)
Therefore 4 (3^2 - 12x + 16) = 1216
3x^2 - 12x + 16 = 1216/4 = 304
3x^2 - 12x - 288 = 0
3 (x^2 - 4x - 96) = 0
(x^2 - 4x - 96) = 0
(x - 12) (x + 8) =0
(x-12) = 0
Therefore x = 12 m
Edge of cube#2 = x m = 12m
Edge of cube#1 = (x-4) m = 8m
Answer:
The door should be 1.6cm wide on the drawing.
Step-by-step explanation:
1 meter is 100 centimeters.
Elena's bedroom door is 80 centimeters wide.
To find how wide it should be on the drawing, divide by 50.
= 1.6cm
The door should be 1.6cm wide on the drawing.
