I need Help ASAP please

A family wants to build a rectangular garden on one side of a barn. If 600 feet of fencing is available to use, then what is the

vovangra [49]

Answer: (A) $A=300l-l^{2}$

(B) Length varies between 1 and 150

(C) Largest area is 22500ft²

Step-by-step explanation: Suppose length is l and width is w.

The rectangular garden has perimeter of 600ft, which is mathematically represented as

$2l+2w=600$

Area of a rectangle is calculated as

$A=lw$

Now, we have a system of equations:

$2l+2w=600$

$A=lw$

Isolate w, so we have l:

$2w=600-2l$

w = 300 - l

Substitute in the area equation:

A = l(300 - l)

A = 300l - l²

(A) Function of area in terms of length is given by A = 300l - l²

(B) The practical domain for this function is values between 1 and 150.

(C) For the largest area, we need to determine the largest garden possible. For that, we take first derivative of the function:

A' = 300 - 2l

Find the values of l when A'=0:

300 - 2l = 0

2l = 300

l = 150

Replace l in the equation:

w = 300 - 150

w = 150

Now, calculate the largest area:

A = 150*150

A = 22500

The largest area the fence can enclose is 22500ft².

4 0

2 years ago

In a student government election, 6 seniors, 2 juniors, and 3 sophomores are running for election. Students elect four at-large

Harrizon [31]

4-0-0
2-1-1
1-2-1
1-0-3
0-1-3

Those are just the ones I can think of so about 5 ways

3 0

3 years ago

Read 2 more answers

For each part, give a relation that satisfies the condition. a. Reflexive and symmetric but not transitive b. Reflexive and tran

Vesnalui [34]

Answer:

For the set X = {a, b, c}, the following three relations satisfy the required conditions in (a), (b) and (c) respectively.

(a) R = {(a,a), (b,b), (c, c), (a, b), (b, a), (b, c), (c, b)} is reflexive and symmetric but not transitive .

(b) R = {(a, a), (b, b), (c, c), (a, b)} is reflexive and transitive but not symmetric .

(c) R = {(a,a), (a, b), (b, a)} is symmetric and transitive but not reflexive .

Step-by-step explanation:

Before, we go on to check these relations for the desired properties, let us define what it means for a relation to be reflexive, symmetric or transitive.

Given a relation R on a set X,

R is said to be reflexive if for every $a \in X, (a,a) \in R$ .

R is said to be symmetric if for every $(a, b) \in R, (b, a) \in R$ .

R is said to be transitive if $(a, b) \in R$ and $(b, c) \in R$ , then $(a, c) \in R$ .

(a) Let R = {(a,a), (b,b), (c, c), (a, b), (b, a), (b, c), (c, b)}.

Reflexive: $(a, a), (b, b), (c, c) \in R$

Therefore, R is reflexive.

Symmetric: $(a, b) \in R \implies (b, a) \in R$

Therefore R is symmetric.

Transitive: $(a, b) \in R \ and \ (b, c) \in R$ but but (a,c) is not in R.

Therefore, R is not transitive.

Therefore, R is reflexive and symmetric but not transitive .

(b) R = {(a, a), (b, b), (c, c), (a, b)}

Reflexive: $(a, a), (b, b) \ and \ (c, c) \in R$

Therefore, R is reflexive.

Symmetric: $(a, b) \in R \ but \ (b, a) \not \in R$

Therefore R is not symmetric.

Transitive: $(a, a), (a, b) \in R$ and $(a, b) \in R$ .

Therefore, R is transitive.

Therefore, R is reflexive and transitive but not symmetric .

(c) R = {(a,a), (a, b), (b, a)}

Reflexive: $(a, a) \in R$ but (b, b) and (c, c) are not in R

R must contain all ordered pairs of the form (x, x) for all x in R to be considered reflexive.

Therefore, R is not reflexive.

Symmetric: $(a, b) \in R$ and $(b, a) \in R$

Therefore R is symmetric.

Transitive: $(a, a), (a, b) \in R$ and $(a, b) \in R$ .

Therefore, R is transitive.

Therefore, R is symmetric and transitive but not reflexive .

4 0

3 years ago

Help with 16 and 17 please

Keith_Richards [23]

Answer:

16) b and 17) C

Step-by-step explanation:

8 0

3 years ago

Miriam buys 24 petunia plants and 40 azalea plants

Cloud [144]

Answer:

she buys 64 plants in total

5 0

3 years ago