A delivery truck can transport packages weighing at most 3,800 pounds(lbs) and with a volume of no more than 400 cubic feet (ft^
1 answer:
Let's approach this problem by slowly eliminating choices.
First consider the keyword "at most" and "no more than". This means that the inequality should be less than or equal to the constant value stated. This will automatically eliminate two choices with the greater than symbol favoring the variables - choices A and D.
Next we associate the right constants to the right coefficients of variables. The two kinds of weight the truck transports are 30 and 65 lbs, and we know that this should not exceed 3,800 lbs. This is therefore our first inequality. The other inequality is for the volume. The combinations of the two volumes 4 and 9 cubic feet should not exceed 400 cubic feet when transported.
If you try to construct the inequality and miss it among the choices, don't worry! Let's try doing some simplifications first and see if it matches either B or C.
After simplification you can get
from dividing the equation by 5 and 
for leaving it as it is.
Looking carefully, we can see that this is equivalent to option B.
ANSWER: B.
First consider the keyword "at most" and "no more than". This means that the inequality should be less than or equal to the constant value stated. This will automatically eliminate two choices with the greater than symbol favoring the variables - choices A and D.
Next we associate the right constants to the right coefficients of variables. The two kinds of weight the truck transports are 30 and 65 lbs, and we know that this should not exceed 3,800 lbs. This is therefore our first inequality. The other inequality is for the volume. The combinations of the two volumes 4 and 9 cubic feet should not exceed 400 cubic feet when transported.
If you try to construct the inequality and miss it among the choices, don't worry! Let's try doing some simplifications first and see if it matches either B or C.
After simplification you can get
Looking carefully, we can see that this is equivalent to option B.
ANSWER: B.
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Answer:
- (-1, -32) absolute minimum
- (0, 0) relative maximum
- (2, -32) absolute minimum
- (+∞, +∞) absolute maximum (or "no absolute maximum")
Step-by-step explanation:
There will be extremes at the ends of the domain interval, and at turning points where the first derivative is zero.
The derivative is ...
h'(t) = 24t^2 -48t = 24t(t -2)
This has zeros at t=0 and t=2, so that is where extremes will be located.
We can determine relative and absolute extrema by evaluating the function at the interval ends and at the turning points.
h(-1) = 8(-1)²(-1-3) = -32
h(0) = 8(0)(0-3) = 0
h(2) = 8(2²)(2 -3) = -32
h(∞) = 8(∞)³ = ∞
The absolute minimum is -32, found at t=-1 and at t=2. The absolute maximum is ∞, found at t→∞. The relative maximum is 0, found at t=0.
The extrema are ...
- (-1, -32) absolute minimum
- (0, 0) relative maximum
- (2, -32) absolute minimum
- (+∞, +∞) absolute maximum
_____
Normally, we would not list (∞, ∞) as being an absolute maximum, because it is not a specific value at a specific point. Rather, we might say there is no absolute maximum.
You can divide a triangle using medians. Let's name triangle ΔABC shown in figure 1. So you must start at one of the vertices and then bisect the opposite side. Let's start with the point A and then we bisect the opposite side. Then the length from B to D is equal to the length from D to C. So let's take the point B and then we bisect the opposite side. Then the length from A to E is equal to the length from E to C. The same reasoning happens with the point C. So we have, in figure 2, the triangle ΔABC divided into six triangles which all have the same area.
