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posledela
3 years ago
10

a rectanular field is 65 meters wide and 115 meters long. a coach asks players to run from one corner to the opposite corner dia

gonally across field, then run back to where they started. how far do they have to run altogether

Mathematics
1 answer:
Eddi Din [679]3 years ago
8 0

Answer:

Players ran 264.20 m altogether.

Step-by-step explanation:

Diagram is attached for reference

Given:

Length of rectangular field (BC) = 115 m

Width of rectangular field (AB) = 65 m

a coach asks players to run from one corner to the opposite corner diagonally across field.

i.e In diagram from point A to Point C

So we will first find the length of diagonal AC.

Now we know that all angles of rectangle is 90°

Hence by Pythagoras theorem we get;

AC^2=AB^2+BC^2

Substituting the value we get;

AC^2 = 115^2+65^2 = 17450

Now taking square root on both side we get;

\sqrt{AC^2} = \sqrt{17450} \\\\AC \approx 132.10\ m

Now Players run back from where they started.

So players ran = 132.10 m + 132.10 m = 264.20 m

Hence Players ran 264.20 m altogether.

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Brand A = 21 heart-rate watches.

Brand B = 13 heart-rate watches.

Step-by-step explanation:

Let A be the number of Brand A heart watches and B be the number of Brand B heart watches.

We have been given that a nonprofit community health organization purchased 34 ​heart-rate watches for use at a wellness center.

We can represent this information in an equation as:

A+B=34...(1)

We have been given that in a certain​ year, brand A of​ heart-rate watch cost ​$39.99 and brand B cost ​$59.99 and the organization spent ​$1619.66 for the​ watches.

We can represent this information in an equation as:

39.99*A+59.99*B=1619.66...(2)

We will use substitution method to solve our system of equations.

From equation (1) we will get,

A=34-B

Substituting A=34-B in equation(2) we will get,

39.99*(34-B)+59.99*B=1619.66

1359.66-39.99*B+59.99*B=1619.66

-39.99*B+59.99*B=1619.66-1359.66

20*B=260

B=\frac{260}{20}

B=13

Therefore, the organisation purchased 13 heart-rate watches of brand B.

Now let us substitute B=13 in equation (1).

A+13=34

A+13-13=34-13

A=21

Therefore, the organisation purchased 21 heart-rate watches of brand A.

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3 years ago
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