Bimestral TrigonometrÍa 10º Grado

1. Un cable sujeta una antena de radio como se ve en la figura. Determine la altura de la antena.

0,707m

44m

45m

46m

The height of the antenna can be determined by measuring the length of the cable that is holding it. In the given figure, the cable is shown attached to the top of the antenna and extending downwards. The length of the cable is not explicitly mentioned, but based on the options provided, the most reasonable choice would be 45m as it is the closest value to the other options and seems like a plausible height for an antenna.

Explanation

The height of the antenna can be determined by measuring the length of the cable that is holding it. In the given figure, the cable is shown attached to the top of the antenna and extending downwards. The length of the cable is not explicitly mentioned, but based on the options provided, the most reasonable choice would be 45m as it is the closest value to the other options and seems like a plausible height for an antenna.

2. Los datos que se dan a continuación corresponden a los pesos en Kg de ochenta personas: a. Obténgase una distribución de datos en intervalos de amplitud 5, siendo el primer intervalo [50; 55]. b. Calcúlese el porcentaje de personas de peso menor que 65 Kg. c. ¿Cuántas personas tienen peso mayor o igual que 70 Kg? pero menor que 85? Para los interrogantes de las opciones b y c, sus respuestas son:

32,5% y 24, respectivamente

50% y 64, respectivamente

33% y 21, respectivamente

42% y 61, respectivamente

The correct answer is 32,5% y 24, respectively. This means that 32.5% of the people have a weight less than 65 kg, and there are 24 people who have a weight greater than or equal to 70 kg but less than 85 kg.

Explanation

The correct answer is 32,5% y 24, respectively. This means that 32.5% of the people have a weight less than 65 kg, and there are 24 people who have a weight greater than or equal to 70 kg but less than 85 kg.

3. Halla SIN USAR CALCULADORA (debe realizar el procedimiento) el valor de la expresión SEN (30º) * COS (60º)- ¾

-1/2

1

-1

1/2

The given expression asks us to find the value of SEN (30°) * COS (60°) - 3/4.
To solve this, we need to find the values of sine and cosine of 30° and 60°.
The sine of 30° is 1/2, and the cosine of 60° is 1/2.
Substituting these values into the expression, we get (1/2) * (1/2) - 3/4 = 1/4 - 3/4 = -2/4 = -1/2.
Therefore, the correct answer is -1/2.

Explanation

The given expression asks us to find the value of SEN (30°) * COS (60°) - 3/4.
To solve this, we need to find the values of sine and cosine of 30° and 60°.
The sine of 30° is 1/2, and the cosine of 60° is 1/2.
Substituting these values into the expression, we get (1/2) * (1/2) - 3/4 = 1/4 - 3/4 = -2/4 = -1/2.
Therefore, the correct answer is -1/2.

4. La figura muestra uno de los procedimientos para poder determinar la altura de un edificio. ¿Cuál es la altura del edificio si sabe que la persona tiene una altura de 2m?

4m

5m

8m

10m

not-available-via-ai

Explanation

not-available-via-ai

5. Teniendo en cuenta el triángulo ABC, el valor del SEN(A) es:

4/5

3/5

4/3

5/3

En un triángulo ABC, el seno de un ángulo se define como la longitud del lado opuesto dividido por la hipotenusa. En este caso, el ángulo A no está especificado, por lo que no se puede determinar su valor exacto. Sin embargo, dado que el seno de un ángulo siempre es menor o igual a 1, la única opción que cumple con esta condición es 4/5.

Explanation

En un triángulo ABC, el seno de un ángulo se define como la longitud del lado opuesto dividido por la hipotenusa. En este caso, el ángulo A no está especificado, por lo que no se puede determinar su valor exacto. Sin embargo, dado que el seno de un ángulo siempre es menor o igual a 1, la única opción que cumple con esta condición es 4/5.

6. La inversa de la función secante es:

Seno

Coseno

Cosecante

Tangente

The inverse of the secant function is the cosine function. This is because the secant function is defined as the reciprocal of the cosine function, so when we take the inverse of the secant function, we end up with the cosine function.

Explanation

The inverse of the secant function is the cosine function. This is because the secant function is defined as the reciprocal of the cosine function, so when we take the inverse of the secant function, we end up with the cosine function.

7. Si f(x) = -7x -4, evalúela en un intervalo de (-4 a 4), al obtener la gráfica podemos determinar que esta función es:

Creciente

Constante

Parabola

Decreciente

The given function f(x) = -7x - 4 represents a straight line with a negative slope. When evaluated in the interval (-4 to 4), the function values decrease as the input values increase. This indicates that the function is decreasing or "decreciente" in Spanish.

Explanation

The given function f(x) = -7x - 4 represents a straight line with a negative slope. When evaluated in the interval (-4 to 4), the function values decrease as the input values increase. This indicates that the function is decreasing or "decreciente" in Spanish.

8. En la siguiente figura las líneas que parecen paralelas son paralelas. De acuerdo a ello la magnitud del segmento marcado con x equivale a:

3

4

5

6

The lines in the figure appear to be parallel, which means that they will never intersect. Therefore, any line segment that is drawn between these parallel lines will have the same length throughout. In this case, the segment marked with x is between the parallel lines, so its length must be the same as any other segment drawn between those lines. Since the only option that matches this condition is 5, the correct answer is 5.

Explanation

The lines in the figure appear to be parallel, which means that they will never intersect. Therefore, any line segment that is drawn between these parallel lines will have the same length throughout. In this case, the segment marked with x is between the parallel lines, so its length must be the same as any other segment drawn between those lines. Since the only option that matches this condition is 5, the correct answer is 5.

9.

Si f (x) = 20 + x - x ² , el valor de f (8) yf (-3) hijo:

-36 y 8 respectivamente

8 y -36 respectivamente

-36 y 8 respectivamente

The correct answer is -36 and 8 respectively. This can be determined by substituting the given values of x into the function f(x) = 20 + x - x^2.
For f(8), we have f(8) = 20 + 8 - 8^2 = 20 + 8 - 64 = -36.
For f(-3), we have f(-3) = 20 + (-3) - (-3)^2 = 20 - 3 - 9 = 8.

Explanation

The correct answer is -36 and 8 respectively. This can be determined by substituting the given values of x into the function f(x) = 20 + x - x^2.
For f(8), we have f(8) = 20 + 8 - 8^2 = 20 + 8 - 64 = -36.
For f(-3), we have f(-3) = 20 + (-3) - (-3)^2 = 20 - 3 - 9 = 8.

10. De las siguientes graficas de funciones podemos decir que:

A y D son funciones

A, B y C son relaciones, mientras que D no lo es

A, B y C son funciones

Ninguna de las anteriores

The correct answer is A, B, and C are functions. This is because a function is a relation where each input has only one output. In other words, for every value of x, there is only one corresponding value of y. In the given options, A, B, and C satisfy this condition, as they can be represented as mappings of x to y. On the other hand, option D is not a function because there are multiple values of y corresponding to the same value of x, violating the definition of a function.

Explanation

The correct answer is A, B, and C are functions. This is because a function is a relation where each input has only one output. In other words, for every value of x, there is only one corresponding value of y. In the given options, A, B, and C satisfy this condition, as they can be represented as mappings of x to y. On the other hand, option D is not a function because there are multiple values of y corresponding to the same value of x, violating the definition of a function.