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spayn [35]
3 years ago
8

You have 64 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river

find the length and width of the plot will maximize the area.
A) length: 33 feet, width: 32 feet
B) length: 16 feet, width: 16 feet
C) length: 48 feet, width: 16 feet
D) length: 32 feet, width: 16 feet
Mathematics
2 answers:
DIA [1.3K]3 years ago
4 0

Answer:

D

Step-by-step explanation:

You don't need any real math to guess at the right answer.

Choice A requires at least 33+32+32=97 feet of fence, hence you  an rule it out because that is more fence than you have.

Choice B requires at least 16+16+16=48 feet, hence you can rule it out because it does not use all your fence and you can get more area by using it all.

Choice C requires at least 48+16+16=80 feet of fence, which is more than you have.

Choice D requires at least 32+16+16=64 feet of fence, so this is the right choice.

nordsb [41]3 years ago
4 0

Answer:

Step-by-step explanation:

2L+W=64\\ \\ W=64-2L\\ \\ A=LW\\ \\ A=64L-2L^2\\ \\ \frac{dA}{dL}=64-4L=0\\ \\ 4L=64\\ \\ L=16\\ \\ W=64-2(16)\\ \\ W=32\\ \\ \text{So the lengths are 32ft by 16ft}

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Musya8 [376]

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yes

Step-by-step explanation:

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3 years ago
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What is 23,718 rounded to the nearest ten thousand
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23,718<span>

The 2 is in the ten thousands place. There is a 3 in the thousands place. Since 3 is less than 5, 2 stays the same and everything after it turns into 0s.

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8 0
3 years ago
Which expression correctly displays the calculations to find the a^5b^4 term of (a+b)^8
LUCKY_DIMON [66]

Answer:

Step-by-step explanation:

THE BINOMIAL THEOREM shows how to calculate a power of a binomial -- (a + b)n -- without actually multiplying.

For example, if we actually multiplied out the 4th power of (a + b) --

(a + b)4 = (a + b)(a + b)(a + b)(a + b)

-- then on collecting like terms we would find:

(a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4 .  .  .  .  (1)

Note:  The literal factors are all possible terms in a and b where the sum of the exponents is 4:  a4,  a3b,  a2b2,  ab3,  b4.

The degree of each term is 4.

The first term is actually a4b0, which is a4 · 1.

Thus to "expand" (a + b)5, we would anticipate the following terms, in which the sum of all the exponents is 5:

(a + b)5 =  ? a5 +  ? a4b +  ? a3b2 +  ? a2b3 +  ? ab4 +  ? b5

The question is, What are the coefficients?

They are called the binomial coefficients.  In the expansion of

(a + b)4, the binomial coefficients are

1  4  6  4  1

line (1) above.

 Note the symmetry:  The coefficients from left to right are the same right to left.

The answer to the question, "What are the binomial coefficients?" is called the binomial theorem.  It shows how to calculate the coefficients in the expansion of (a + b)n.

The symbol for a binomial coefficient is The binomial theorem.  The upper index n is the exponent of the expansion; the lower index k indicates which term, starting with k = 0.

For example, when n = 5, each term in the expansion of  (a + b)5  will look like this:

The binomial theorema5 − kbk

k will successively take on the values 0 through 5.

(a + b)5 = The binomial theorema5  +  The binomial theorema4b  +  The binomial theorema3b2  +  The binomial theorema2b3  +  The binomial theorem ab4  +  The binomial theoremb5

Note:  Each lower index is the exponent of b.  The first term has k = 0 because in the first term, b appears as b0, which is 1.

Now, what are these binomial coefficients, The binomial theorem ?

The theorem states that the binomial coefficients are none other than the combinatorial numbers, nCk .

The binomial theorem  =  nCk

 (a + b)5  =  5C0a5 + 5C1a4b + 5C2a3b2 + 5C3a2b3 + 5C4ab4 + 5C5b5

  =  1a5 + The binomial theorema4b + The binomial theorema3b2 + The binomial theorema2b3 + The binomial theoremab4 + The binomial theoremb5

  =  a5  +  5a4b  +  10a3b2  +  10a2b3  +  5ab4  +  b5

The binomial coefficients here are

1  5  10  10  5  1.

8 0
2 years ago
Solve the formula for x<br>Gx +Hy=J​
ra1l [238]

Answer:

x = \frac{J-Hy}{G}

Step-by-step explanation:

This question is from the topic subject of formula. It implies expressing x in terms of G, H y and J.

Given that: Gx + Hy = J

Subtract Hy from both sides to have;

Gx + Hy - Hy = J - Hy

⇒  Gx = J - Hy

Then divide both sides by G, so that we have;

x = \frac{J-Hy}{G}

Therefore,

x = \frac{J-Hy}{G}

4 0
3 years ago
Look at the following math problem. 7 × 10 = 70 In this problem, you're multiplying 7 by 10. What is 10 called in this math prob
umka2103 [35]
For this case we have the following expression:
 7 × 10 = 70
 Where, by definition:
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Multiplier
3 0
3 years ago
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