1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Aleks04 [339]
3 years ago
5

Justin wants to use 188ft of fencing to,fence off the greatest possible retangular area for a garden .What dimensions should he

use? What will be the area of the garden?
Mathematics
1 answer:
marshall27 [118]3 years ago
4 0
The greatest area that can be enclosed by a given amount of material will always be a square...

M=2L+2W  so we can say:

2L=M-2W

L=(M-2W)/2

area is:

A=LW  and using L from above:

A=W(M-2W)/2

A=(MW-2W^2)/2

dA/dW=(M-4W)/2 

d2A/dW2=-4

Since acceleration, d2A/dW2, is a negative constant, when velocity, dA/dW=0, it is at an absolute maximum for A(W).

dA/dW=0 only when M-4W=0, 4W=M, W=M/4

from earlier we found L=(M-2W)/2 and using W from above we get:

L=(M-M/2)/2

L=(2M-M)/4

L=M/4

So L=W=M/4, thus it is a square.

That's the proof, anyway...

188=2x+2y

94=x+y

y=94-x

A=xy and using y from above:

A=94x-x^2

dA/dx=94-2x, d2A/dx2=-2, as explained earlier, since acceleration is a negative constant, when dA/dx=0, it is at an absolute maximum for A(x).

dA/dx=0 only when 94-2x=0, 2x=94, x=47

and from earlier, y=94-x, so y=94-47

y=47

So the dimensions that produce the greatest area are:

47ft by 47ft

And thus the greatest area is:

47^2=2209 ft^2
You might be interested in
Hannah and Dawson have both invested money in savings accounts with APYs of 3.2%. If Hannah's account has a balance of $31,000 a
9966 [12]

Answer:

$341.07

Step-by-step explanation:

Hanna and Dawson both invested at 3.2% = 0.032

Hannah has balance of 31,000 in account

Dawson has balance of 42000 in account

Interests earned by both are

1)Hannah -P(1+i)^-n

=31000(1+0.032)^-1

=31000(1.032)^-1

=31000(0.968992)

=$30038.752

=$30038.75

Interest earned by Dawson is $31,000 - $30038.75 = $961.25

2)Dawson-  P(1+i)^-n

=42000(1+0.032)^-1

=42000(1.032)^-1

=42000(0.968992)

=$40697.664

=$$40697.664

Interest earned by Dawson is $42,000 - $40697.66= $1302.32

3) Hence the amount that Dawson earns than is:

=$1302.32-$961.25

= $341.07

3 0
3 years ago
John collected 17 leaves to feed his caterpillar collection if he wanted to split the leaves equally amongst the four cages how
Papessa [141]

Answer:

It lies between the numbers 4 and 5

Step-by-step explanation:

If John has 17 leaves and 4 cages then he should put 17/4, or 16/4+1/4 which is 4+0.25, or 4.25 in each cage.

3 0
3 years ago
Read 2 more answers
The question is in the picture
aleksandr82 [10.1K]

Answer: 140

Step-by-step explanation: since 4 = 40 then 2 would also be 40 because they are the same angle (Keep in mind that a line is 180 degrees) 180-40=140! Good luck! :D

5 0
2 years ago
Determine whether the set of vectors is a basis for ℛ3. Given the set of vectors , decide which of the following statements is t
schepotkina [342]

Answer:

(A) Set A is linearly independent and spans R^3. Set is a basis for R^3.

Step-by-Step Explanation

<u>Definition (Linear Independence)</u>

A set of vectors is said to be linearly independent if at least one of the vectors can be written as a linear combination of the others. The identity matrix is linearly independent.

<u>Definition (Span of a Set of Vectors)</u>

The Span of a set of vectors is the set of all linear combinations of the vectors.

<u>Definition (A Basis of a Subspace).</u>

A subset B of a vector space V is called a basis if: (1)B is linearly independent, and; (2) B is a spanning set of V.

Given the set of vectors  A= \left(\begin{array}{[c][c][c][c]}1 & 0 & 0 & 0\\ 0 & 1 & 0 & 1\\ 0 & 0 & 1 & 1\end{array} \right) , we are to decide which of the given statements is true:

In Matrix A= \left(\begin{array}{[c][c][c][c]}(1) & 0 & 0 & 0\\ 0 & (1) & 0 & 1\\ 0 & 0 & (1) & 1\end{array} \right) , the circled numbers are the pivots. There are 3 pivots in this case. By the theorem that The Row Rank=Column Rank of a Matrix, the column rank of A is 3. Thus there are 3 linearly independent columns of A and one linearly dependent column. R^3 has a dimension of 3, thus any 3 linearly independent vectors will span it. We conclude thus that the columns of A spans R^3.

Therefore Set A is linearly independent and spans R^3. Thus it is basis for R^3.

8 0
3 years ago
The questions on a test consist of 10 multiple choices, 3 essays, and 9 free responses. If the questions are ordered randomly, w
stepladder [879]

Answer:

\frac{9}{22}

Step-by-step explanation:

add all qestions together 10+3+9=22

and put the number of free responces on top of the total number of qestions

\frac{9}{22\\}

and you cant simplify it so its in its simplist form

3 0
2 years ago
Other questions:
  • What is a benefit of health Insurance?
    9·1 answer
  • brllie rides her bike 176.25 miles in three weeks. she averaged 11.75 miles per hour each tim she ride. hiw many hours did it ta
    15·1 answer
  • Which expression can be used to find the volume of the sphere​
    5·1 answer
  • What is greater, 3/5r 4/10?
    12·1 answer
  • Evaluate the integral. (Use C for the constant of integration.) x2 − 3x + 12 (x2 − 4x + 11)2 dx
    15·1 answer
  • 48oz sprite for $1.39 or 32 oz dr. pepper for $0.89?
    13·1 answer
  • The tigers football team had a 2 yard loss followed by a 4 yard loss what was the total change?
    11·2 answers
  • In a group of students the ratio of the number of students who liked music and sport is 9:7. out of which 25 liked both the acti
    8·1 answer
  • Suppose you have six quarters, nine dimes, and four pennies. Explain how you find the total value of all the coins.
    11·1 answer
  • Evaluet 2-(4-x) when x=-5​
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!