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OleMash [197]
3 years ago
12

A person jogged 10 times along the perimeter of a rectangular field at the rate of 12 kilometers per hour for 30 minutes. If fie

ld has a length that is twice its width, find the area of the field in square meters.
Mathematics
1 answer:
balu736 [363]3 years ago
4 0

Answer:

20,000m²

Step-by-step explanation:

If they jog 12 km/h for half an hour, they have covered.

12 X 0.5 = 6km in 10 circuits. Making 1 perimeter

6 / 10 =0.6 km (600 m).

To determine area we need to convert this perimeter to length and width. We know that it is a rectangle, with 2 equal widths and 2 equal lengths, and the length is twice the width.

So L = 2W

Perimeter = 2W + 2L

600 m = 2W + 2(2W)

600 m = 6W

W = 100 m

L = 200 m

Area = 100 X 200 = 20,000 m²

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The rate of growth of profit​ (in millions) from an invention is approximated by Upper P prime (x )equals x e Superscript negati
Alecsey [184]

Answer:

The function is  P(x) =  \frac{1}{2} e^{-x^2} +0.016

Step-by-step explanation:

From the question we are told that

    The rate of growth  is  P'(x) =  xe^{x} - x^2

     The total profit is P(2)  =$25,000

      The time taken to make the profit is x =  2 \ years

         

From the question

     P'(x) =  xe^{-x^2}  is the rate of growth

  Now here x represent the time taken

Now the total profit is mathematically represented as

       P(x) =  \int\limits {P'(x)} \,  =   \int\limits {xe^{-x^2}} \,

So using substitution method

   We have that

                      u =  - x^2

                      du =  2xdx

  So  

        p(x) =  \int\limits {\frac{1}{2} e^{-u}} \, du

       p(x) =  {\frac{1}{2} [ e^{-u}} +c ]

       p(x) =  {\frac{1}{2}  e^{-x^2}} + \frac{1}{2} c      recall  u =  - x^2   and  let  \frac{1}{2} c =  Z

       

At  x =  2 years  

     P(x)  =$25,000

So

       Since the profit rate is in million

    P(x)  =$25,000 = \frac{25000}{1000000} =$0.025 millon dollars

So  

       0.025 =  {\frac{1}{2}  e^{-2^2}} + Z  

=>    Z = 0.025 - {\frac{1}{2}  e^{-2^2}}  

       Z = 0.016  

So the profit function becomes

         P(x) =  \frac{1}{2} e^{-x^2} +0.016

     

       

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4 years ago
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Answer:

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