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dimaraw [331]
3 years ago
6

A farmer wants to enclose a rectangular field that borders a river with 400 feet of fencing material. if the farmer does not fen

ce the side along the river, find the dimensions that will yield the maximum area. show all your equations.
Mathematics
1 answer:
ICE Princess25 [194]3 years ago
3 0
Let each side perpendicular to the river be "x".Then the side parallel to the river is "400-2x".
The formula for Area = width*length
A(x) = x(400-2x)
A(x) = 400x - 2x^2
You have a quadratic with a = -2 and b = 400
Maximum Area occurs where x = -b/2a = -400/(2*-2) = 100 ft. (width)
length = 400-2x = 400-2*100 =  200 ft (length)
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Identify the lateral area and the surface area of a right rectangular prism with an 8 cm by 9 cm base and a height of 13 cm.
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3 years ago
Determine which gym's membership grows faster from Month 2 to Month 4 by calculating the average rates of change.
nlexa [21]

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Gym A is growing faster

Gym A gained 13 members between months 2 and 4

Gym B gained 10 members between months 2 and 4

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Gym A:  (2,20) (4,46)

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8 0
2 years ago
Discrete Math
andrezito [222]

Answer:

Part c: Contained within the explanation

Part b: gcd(1200,560)=80

Part a: q=-6         r=1

Step-by-step explanation:

I will start with c and work my way up:

Part c:

Proof:

We want to shoe that bL=a+c for some integer L given:

bM=a for some integer M and bK=c for some integer K.

If a=bM and c=bK,

then a+c=bM+bK.

a+c=bM+bK

a+c=b(M+K) by factoring using distributive property

Now we have what we wanted to prove since integers are closed under addition.  M+K is an integer since M and K are integers.

So L=M+K in bL=a+c.

We have shown b|(a+c) given b|a and b|c.

//

Part b:

We are going to use Euclidean's Algorithm.

Start with bigger number and see how much smaller number goes into it:

1200=2(560)+80

560=80(7)

This implies the remainder before the remainder is 0 is the greatest common factor of 1200 and 560. So the greatest common factor of 1200 and 560 is 80.

Part a:

Find q and r such that:

-65=q(11)+r

We want to find q and r such that they satisfy the division algorithm.

r is suppose to be a positive integer less than 11.

So q=-6 gives:

-65=(-6)(11)+r

-65=-66+r

So r=1 since r=-65+66.

So q=-6 while r=1.

3 0
3 years ago
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