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Olegator [25]
3 years ago
12

Jerome burns 4 cal/min walking and 10 cal/min running. He walks between 10 and 20 min each day and runs between 30 and 45 min ea

ch day. He never spends more than an hour running and walking together. How much time should he spend on each activity to maximize his calorie burning?

Mathematics
1 answer:
erik [133]3 years ago
5 0

Answer:

20 minutes should spend on walking and 30 minutes on running.

Step-by-step explanation:

Let x represents the minutes spent on walking and y represents the minutes spent on running,

∵ He burns 4 cal/min walking and 10 cal/min running,

So, the total calories burnt,

Z = 4x + 10y

Which has to be maximised.

Now, he walks between 10 and 20 min each day,

i.e. 10 < x < 20,

Also, he runs between 30 and 45 min each day,

i.e. 30 <  y < 45,

By graphing 10 < x < 20 and 30 <  y < 45,

We obtained the vertices of feasible region,

(10, 45), (20, 45), (10, 30) and (20, 30)

At (10, 45),

Z = 4(10) + 10(45) = 40 + 450 = 490,

At (20, 45),

Z = 4(20) + 10(45) = 80 + 450 = 530,

At (10, 30),

Z = 4(10) + 10(30) = 40 + 300 = 340,

At (20, 30)

Z = 4(20) + 10(30) = 80 + 300 = 380

Hence, maximum calories is 530 when 20 minutes spent on walking and 30 minutes spent on running.

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Step-by-step explanation:

7 0
3 years ago
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jeyben [28]
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3 0
3 years ago
In 2000 the median size of a new single family house was 2057 square feet in 2010 the median size was 2169 square feet.
nalin [4]

Answer:

<h2>        d.)  11.2 square feet per year</h2>

Step-by-step explanation:

The difference in sizes:

2169 - 2057 = 112 square feet

It is 10 years from 2000 to 2010

112:10 = 11.2

6 0
3 years ago
Al abrir su alcancía Beatriz encontró que entre monedas de 5, 10 y 25 centavos completaba $ 9.50. Encontró igualmente que el núm
vladimir2022 [97]

Answer:

67 monedas de 5, 34 de 10 y 11 de 25.

Step-by-step explanation:

Representemos el primer enunciado de manera algebraica:

5x+10y+25z =950  (1)

Donde:

  • x es el numero de monedas de 5
  • y es el numero de monedas de 10
  • z es el numero de monedas de 25

Ahora, el número de monedas de 10 centavos era el triple de las de 25 centavos y que las de 5 centavos era el doble de las de 10 centavos, se puede representar como:

y=3z  (2)              

x=2y  (3)    

     

Combinado las eacuaciones (1), (2) y (3) tenemos:

5(2y)+10y+25(\frac{y}{3}) =950

10y+10y+\frac{25}{3}y =950

\frac{85}{3}y =950  

y =34

Por lo tanto el valor de x y z seran:

x=2(34)          

x=68          

z=11    

Si ponemos cada valor en la equacion (1), tenemos:

5(68)+10(34)+25(11) =955

Como el resultado da 955 hay un excedente de 5 pesos, asi que finalmente tendremos.

x = 67

y = 34

z = 11  

Espero te haya serrvido!

4 0
3 years ago
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Natalka [10]

Answer:

98

Step-by-step explanation:

u + xy

u = 18

x = 10

y =8

18 + 10*8 = 18 +80

= 98

5 0
2 years ago
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