Answer: is it supposed to be 2y+y=4?
Basically, what this asks you is to maximize the are A=ab where a and b are the sides of the recatangular area (b is the long side opposite to the river, a is the short side that also is the common fence of both corrals). Your maximization is constrained by the length of the fence, so you have to maximize subject to 3a+b=450 (drawing a sketch helps - again, b is the longer side opposite to the river, a are the three smaller parts restricting the corrals)
3a+b = 450
b = 450 - 3a
so the maximization max(ab) becomes
max(a(450-3a)=max(450a-3a^2)
Since this is in one variable, we can just take the derivative and set it equal to zero:
450-6a=0
6a=450
a=75
Plugging back into b=450-3a yields
b=450-3*75
b=450-225
b=215
Hope that helps!
That's a monomial; it has one variable, one coefficient, and one degree.
Answer:
8. Louis
9. Rose; Raymond
Step-by-step explanation:
8. An exponent represents the number of times the base appears as a factor in the product.
We use a coefficient to signify repeated addition: 3x means x+x+x.
We use an exponent to signify repeated multiplication. x³ means x·x·x.
So, the expression ...

You can see that the factor 4 appears 7 times in the product, so would be represented in exponential form as ...

Louis has correctly observed this fact. In general, we see that multiplying powers of the same base causes those powers to be added.
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9.
<u>Part A</u>. Rose is correct for the same reason as in problem 8.
5^5 · 5^2 = 5^(5+2) = 5^7
<u>Part B</u>. Raymond is correct. We know that division cancels similar terms from the numerator, so ...

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The rules of exponents we're using here are ...
(a^b)(a^c) = a^(b+c)
(a^b)/(a^c) = a^(b-c)
Answer:
99 in³
Step-by-step explanation:
volume of cone = ⅓πr²h = 33 in³
volume of cylinder = πr²h = 3(volume of cylinder) = 99 in³