Answer:
c) Length = 12, width = 8 and height = 23.
Step-by-step explanation:
Let the length be x, then the width = x - 4 and the height = 2x - 1.
a) The polynomial is x(x - 4)(2x - 1)
b) x(x - 4)(2x - 1) = 2208
c) x(x - 4)(2x - 1) - 2280 = 0
2x^3 - 9x^2 + 4x - 2280 = 0
I'll use graphical software to find a solution for this. Its easily obtained online.
There is one real root and its x = 12.
So the dimensions of the box are L = 12, W = 8 and H = 23 inches.
Answer:
2. a and b only.
Step-by-step explanation:
We can check all of the given conditions to see which is true and which false.
a. f(c)=0 for some c in (-2,2).
According to the intermediate value theorem this must be true, since the extreme values of the function are f(-2)=1 and f(2)=-1, so according to the theorem, there must be one x-value for which f(x)=0 (middle value between the extreme values) if the function is continuous.
b. the graph of f(-x)+x crosses the x-axis on (-2,2)
Let's test this condition, we will substitute x for the given values on the interval so we get:
f(-(-2))+(-2)
f(2)-2
-1-1=-3 lower limit
f(-2)+2
1+2=3 higher limit
according to these results, the graph must cross the x-axis at some point so the graph can move from f(x)=-3 to f(x)=3, so this must be true.
c. f(c)<1 for all c in (-2,2)
even though this might be true for some x-values of of the interval, there are some other points where this might not be the case. You can find one of those situations when finding f(-2)=1, which is a positive value of f(c), so this must be false.
The final answer is then 2. a and b only.
Answer:
3/4
Step-by-step explanation:
The slope of the line is given by
m= (y2-y1)/(x2-x1)
= (6-3)/(0 - -4)
= (6-3)/( 0+4)
3/4
Answer:
13 times 2
52 divided by 2
20 plus 6
Step-by-step explanation:
1 i think 1 is the answer
