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sergij07 [2.7K]
2 years ago
7

For two days, your boss decides to double the amount you make if on day 1, you make $70 dollars and on day 2, you make$80 dollar

s, write an expression for the total commission you earn?
Mathematics
1 answer:
Hoochie [10]2 years ago
6 0

Answer:

300

Step-by-step explanation:

Day 1: $70

Day 2: $80

Total commission = day 1 × 2 + day 2 × 2

= 70 × 2 + 80×2

= 140 + 160

= 300

Or

Total commission = 2(day 1 + days 2)

= 2(70 + 80)

= 2(150)

x = 300

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A rectangular field with one side along a river is to be fenced. Suppose that no fence is needed along the river, the fence on t
Andreas93 [3]

Answer:

a) Side Parallel to the river: 200 ft

b) Each of the other sides: 400 ft

Step-by-step explanation:

Let L represent side parallel to the river and W represent width of fence.

The required fencing (F) would be F=L+2W.

We have been given that field must contain 80,000 square feet. This means area of field must be equal to 80,000.

LW=80,000...(1)

We are told that the fence on the side opposite the river costs $20 per foot, and the fence on the other sides costs $5 per foot, so total cost (C) of fencing would be C=20L+5(2W)\Rightarrow 20L+10W.

From equation (1), we will get:

L=\frac{80,000}{W}

Upon substituting this value in cost equation, we will get:

C=20(\frac{80,000}{W})+10W

C=\frac{1600,000}{W}+10W

C=1600,000W^{-1}+10W

To minimize the cost, we need to find critical points of the the derivative of cost function as:

C'=-1600,000W^{-2}+10

-1600,000W^{-2}+10=0

-1600,000W^{-2}=-10

-\frac{1600,000}{W^2}=-10

-10W^2=-1,600,000

W^2=160,000

\sqrt{W^2}=\pm\sqrt{160,000}  

W=\pm 400

Since width cannot be negative, therefore, the width of the fencing would be 400 feet.

Now, we will find the 2nd derivative as:

C''=-2(-1600,000)W^{-3}

C''=3200,000W^{-3}

C''=\frac{3200,000}{W^3}

Now, we will substitute W=400 in 2nd derivative as:

C''(400)=\frac{3200,000}{400^3}=\frac{3200,000}{64000000}=0.05

Since 2nd derivative is positive at W=400, therefore, width of 400 ft of the fencing will minimize the cost.

Upon substituting W=400 in L=\frac{80,000}{W}, we will get:

L=\frac{80,000}{400}\\\\L=200

Therefore, the side parallel to the river will be 200 feet.

4 0
3 years ago
A rectangle had a length of 2x-7 and a with of 3x+8y. Write and simplify an expression for the perimeter of that rectangle?
wel

Answer:

Step-by-step explanation:

A rectangle had a length of 2x-7 and a width of 3x+8y

Perimeter P = 2(l + w)

P = 2(2x - 7 + 3x + 8y)

P = 2(5x + 8y - 7)

P= 10x + 16y - 14

4 0
3 years ago
Mario is constructing a wall around a rectangular area which will cover a maximum of 60 square feet. The length of the wall will
Feliz [49]

Answer:

W \le 6

Step-by-step explanation:

Given

Area = 60ft^2\ (max)

Length = 10ft

Required

Represent the width as an inequality

First, we represent the area as an inequality.

Area = 60ft^2\ (max)

max as used above means less than or equal to.

So, we have:

Area \le 60

The area of a rectangle is:

Area = L * W

So, we have:

L * W \le 60

Substitute 10 for L

10 * W \le 60

Divide both sides by 10

\frac{10 * W}{10} \le \frac{60}{10}

W \le \frac{60}{10}

W \le 6

7 0
3 years ago
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