Answer and Explanation:
You got the first one right!
2. You do the same as you did for the first one: to combine the exponents, you multiple 2 by 9 = 18, and now 18 is your new exponent.
, which is the answer
3. Here, you can split up the inside so that you have:
, which is the answer
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Answer:44
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
If the pieces were similar, the scale factor would be 16 / 8 = 2 so therefore, b = 5 * 2 = 10.
Answer:
Step-by-step explanation:
From the given information:
a)
Assuming the shape of the base is square,
suppose the base of each side = x
Then the perimeter of the base of the square = 4x
Suppose the length of the package from the base = y; &
the height is also = x
Now, the restriction formula can be computed as:
y + 4x ≤ 99
The objective function:
i.e maximize volume V = l × b × h
V = (y)*(x)*(x)
V = x²y
b) To write the volume as a function of x, V(x) by equating the derived formulas in (a):
y + 4x ≤ 99 --- (1)
V = x²y --- (2)
From equation (1),
y ≤ 99 - 4x
replace the value of y into (2)
V ≤ x² (99-4x)
V ≤ 99x² - 4x³
Maximum value V = 99x² - 4x³
At maxima or minima, the differential of
⇒ 198x - 12x² = 0
By solving for x:
x = 0 or x =
Again:
V = 99x² - 4x³
At x =
= -198
Thus, at maximum value;
Recall y = 99 - 4x
when at maximum x =
y = 33
Finally; the volume V = x² y is;
V = 8984.25 inches³