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erastova [34]
2 years ago
7

A fence must be built to enclose a rectangular area of 45 comma 000 ftsquared. Fencing material costs $ 3 per foot for the two s

ides facing north and south and ​$6 per foot for the other two sides. Find the cost of the least expensive fence.
Mathematics
1 answer:
Tatiana [17]2 years ago
6 0

Answer:

150 feet by 300 feet.

Step-by-step explanation:

The fence is to enclose a rectangular area of 45,000 ft squared.

If the dimensions of the rectangle are x and y

Area of a rectangle = xy

  • xy=45000
  • x=\frac{45000}{y}

Perimeter of the Rectangle =2x+2y

Fencing material costs $ 3 per foot for the two sides facing north and south and ​$6 per foot for the other two sides.

  • Cost of Fencing, C=$(6*2x+3*2y)=$(12x+6y)

Substitute x=\frac{45000}{y} into the Cost to get C(y)

C=12x+6y

C(y)=12(\frac{45000}{y})+6y\\C(y)=\frac{540000+6y^2}{y}

The value at which the cost is least expensive is at the minimum point of C(y), when the derivative is zero.

C^{'}(y)=\dfrac{6y^2-540000}{y^2}

\dfrac{6y^2-540000}{y^2}=0\\6y^2-540000=0\\6y^2=540000\\y^2=\frac{540000}{6} =90000\\y=\sqrt{90000}=300

Recall,

x=\frac{45000}{y}=\frac{45000}{300}=150

Since x=150, y=300

The dimensions that will be least expensive to build is 150 feet by 300 feet.

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A metal rod will be cut into pieces that are each 1/56 meters long. The rod is 7/8 meters long. How many pieces will be made fro
S_A_V [24]

The number of pieces made from rod is 49

<h3><u>Solution:</u></h3>

Given that A metal rod will be cut into pieces that are each 1/56 meters long

The rod is 7/8 meters long.

<em><u>To find: number of peices made from rod</u></em>

The number of peices made from rod can be calculated by dividing the total length of rod by length of each piece

\text {number of pieces made }=\frac{\text {total length of rod }}{\text { length of each piece}}

Here total length of rod = \frac{7}{8} meters

length of each piece to be made = \frac{1}{56} meters

Substituting the values in above formula, we get

\text {number of pieces made }=\frac{\frac{7}{8}}{\frac{1}{56}}=\frac{7}{8} \times \frac{56}{1}

\text {number of pieces made }=7 \times 7=49

So the number of pieces made from rod is 49

7 0
3 years ago
Which statements about the relationship between the two triangles below are true? Check all that apply. Triangle A C D. Angle D
Karolina [17]

Answer:

Which statements about the relationship between the two triangles below are true

- Angle C is congruent to angle S (true)

- Angle D is congruent to angle T (true)

- Triangle D C A is similar to triangle T S R (true)

The rest are false.

Complete question;

Which statements about the relationship between the two triangles below are true? Check all that apply. Triangle A C D. Angle D is 60 degrees and angle A is 74.9 degrees. Triangle R S T. Angle R is 74.9 degrees and angle S is 45.1 degrees.

- Angle C is congruent to angle T

- Angle C is congruent to angle S

- Angle D is congruent to angle T

- Triangle D C A is congruent to triangle T S R

- Triangle D C A is similar to triangle T S R

- Triangle C A D is similar to triangle T R S

- Triangle C A D is congruent to triangle T R S

Step-by-step explanation:

See attached image for more information;

Angle C = 180 - (60+74.9) = 45.1°

Angle T = 180 - (74.9+45.1) = 60°

Therefore;

Angle C = Angle S = 45.1°

Angle D = Angle T = 60°

And

Triangle D C A is similar to triangle T S R

(Note the order of the letters)

The two triangles are not congruent because the length of their sides are not the same.

3 0
2 years ago
How do I simplify 9^7 × 9^2?
almond37 [142]

Answer: 420

387420489

Step-by-step explanation:

9^7: 4782969

9^2: 81

81 x 47 = 387420489

5 0
2 years ago
❤please help on math thanksssss
WARRIOR [948]

Answer:

the answer to the first one would be: 4/3

the second problem's answer: 20/36, which can be reduced to 5/9

3 0
3 years ago
I need help with writing the equation​
cricket20 [7]

Answer:

y=-1/8y+1

Step-by-step explanation:

flip the equation, then add -8 to both sides to cancel out the +8 on the left, then divide sides by -8Let's solve for x.

y=−8x+8

Step 1: Flip the equation.

−8x+8=y

Step 2: Add -8 to both sides.

−8x+8+−8=y+−8

−8x=y−8

Step 3: Divide both sides by -8.

6 0
3 years ago
Read 2 more answers
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