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lakkis [162]
2 years ago
5

\sqrt[n]{x} \\ x^{2} \sqrt[n]{x}" alt="\sqrt[n]{x} \\ x^{2} \sqrt[n]{x}" align="absmiddle" class="latex-formula">Ms. Sanchez is purchasing a car for $14,000. The tax rate in the state where she is buying the car is 7%. What is the total amount she will pay for the car including the tax?
Mathematics
1 answer:
I am Lyosha [343]2 years ago
4 0
My answer to what is the total amount she will pay with 7% tax is $14,980
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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
I need help on these questions pls
Lady bird [3.3K]
3a. Megan's car has more gas
3b. 2/3=66.666% and 3/5= 60% so 6 2/3 gallons

5. 108.09-15.45= 92.64


3 0
3 years ago
You deposit $300 in a savings account. The account earns 2% simple interest per year.
Anit [1.1K]
300x .02= 6

6x10=60

Therefore the answer is $360
6 0
3 years ago
Can someone PLZZ help me!!!?
Luda [366]

Answer:elect the scenarios that are related to providing clarity in a research survey.

The survey’s research question analyzes a loss of market share.

A company uses an online survey.

A company surveys customers at all locations.

The survey contains a rating scale and rank order questions.

A focus group field-tests the survey.

A company creates an overview of topics to address.

The survey contains ten items.

5 0
3 years ago
.............................................................
Len [333]

Answer:

0.058863

Step-by-step explanation:

5 0
2 years ago
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