Camilo practica tiro al blanco. En cada disparo acertado puede obtener 5, 8, o 10 puntos. En su última práctica, su puntuación t
1 answer:
Answer:
20 disparos
Step-by-step explanation:
Primera etapa es de determinar cuantos tiros de Camilo acertaron al blanco.
Sabemos que en su última práctica, obtuvo 99 puntos con una mezcla de 5, 8 y 10 puntos. Eso puedo se exprimir así:
5x + 8y + 10x = 99
Sabemos también que el obtuvo tantos tiros de 8 puntos que de 10 puntos, entonces
y = z
Podemos mezclar las 2 ecuaciones y substituir y por z:
5x + 8y + 10y = 99
5x +18y = 99
Una ecuación, dos variables... no es fácil... pero son números pequeños y se puede intentar soluciones. Entonces, cuantas veces podemos multiplicar 5 y 18 para obtener 99?
El más simple es de hacer la tabla de multiplicación de 18 y ver cual número nos deja con un multiple de 5.
18 x 1 = 18 (99 - 18 = 81, no un multiple e 5)
18 x 2 = 36 (99 - 36 = 63, no un multiple de 5)
18 x 3 = 54 (99 - 54 = 45, SI, un multiple de 5)
18 x 4 = 72 (99 - 72 = 27, no un multiple de 5)
18 x 5 = 90 (99 - 90 = 9, no un multiple de 5)
Entonces, sabemos que y = 3 y z = 3
5x + 18 (3) = 99
5x + 54 = 99
5x = 45
x = 9
El tiró 9 veces por 5 puntos, 3 veces por 8 puntos y 3 veces pour 10 puntos.
En total tiró 15 veces.
Si acertó 75% (3/4) de las veces, cuantos tiros total?
Camilo tiró 20 veces en total.
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Half the area is the circular sector PTQ (with center P, arc TQ) minus the right triangle PUT.
A/2 = area(sector PTQ) - area(triangle PUT)
The triangle is half of equilateral triangle PQT, so a 30/60/90 right triangle so we know the sides are in ratio 1:√3:2 so
TU = (7/2)√3
area(PUT) = (1/2) (7/2)(7/2)√3 = (49/8)√3
area(sector PTQ) = (angle TQP / 360°) πr^2
We know angle TQP is 60° because TQP is equilateral. r=7.
area(sector PTQ) = (60°/360°) π (7²) = 49π/6
Putting it together,
A/2 = area(sector PTQ) - area(triangle PUT)
A = 2(49π/6 - (49/8)√3)
A = 49(π/3 - √3/4) square cm
I hate ruining a nice exact answer with an approximation, but they seem to be asking.
A ≈ 30.095057615914535
Check:
I'm not sure how to check it. I'd estimate it's about 25% bigger than equilateral triangle PQT with area (√3/4)7² ≈ 21.2, so around 27. 30 seems reasonable.
Now the real area we seek is the big square PQRS minus A, so
area = 7² - 30.095057615914535 = 18.904942384086 sq cm
They want square meters for some reason; we scale by (1/100)²
Answer: 0.00189 square meters
The answer is 1.12% decrease
Explanation in image
Explanation in image
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