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prisoha [69]
3 years ago
6

1) El largo de un rectángulo mide el triple que su ancho. Si el ancho mide 12 cm, el perímetro del rectángulo es: Selecciona la

opción correspondiente: a) 86 cm b) 90 cm c) 96 cm d) 102 cm 2) ¿Cuál es el perímetro de un heptágono regular de 2,45 m de lado? Selecciona la opción correspondiente: a) 14,7 m b) 12,25 m c) 17,15 m d) 20 m 3) Si una cancha de fútbol mide 98 m de largo y su ancho equivale a la mitad de esta medida, su perímetro es: Selecciona la opción correspondiente: a) 304 m b) 284 m c) 294 m d) 354 m 4) Frente a la casa de Carolina hay un parque que tiene 45 m de largo y 38 000 mm de ancho. Si ella da dos vueltas alrededor de este, ¿qué distancia en metros recorre? Selecciona la opción correspondiente: a) 160 metros b) 330 metros c) 166 metros d) 332 metros
Mathematics
1 answer:
Wittaler [7]3 years ago
4 0

Answer:

1) c) 96 cm

2) c) 17,15 m

3) c) 294 m

4) d) 332 metros

Step-by-step explanation:

1)

La fórmula para el perímetro de un rectángulo = 2L + 2W

= 2 (largo + ancho)

L = longitud

W = ancho

Se nos dice en la pregunta que:

La longitud de un rectángulo es tres veces su ancho. Si el ancho es de 12 cm

Por lo tanto,

L = 3 W

L = 3 × 12

Largo = 36cm

Por lo tanto, el perímetro =

2 (largo + ancho) cm

= 2 (36 + 12) cm

= 2 (48) cm

= 96 cm

2)

La fórmula para el perímetro de un heptágono regular = 7a

Donde a = longitud de un lado

De la pregunta,

a = 2,45 m laterales

Por lo tanto, el perímetro de un Heptágono regular = 7 (2,45 m)

= 17,15 m

3)

La fórmula para el perímetro de un rectángulo = 2L + 2W

= 2 (largo + ancho)

L = longitud

W = ancho

Se nos dice en la pregunta que:

Si un campo de fútbol tiene 98 m de largo y su ancho es igual a la mitad de esta medida,

Por lo tanto,

L = 98 m

W = 1/2 de longitud

Ancho = 1/2 (98)

= 49

Por lo tanto, el perímetro =

2 (largo + ancho) m

= 2 (98 + 49) m

= 2 (147) m

= 294 m

4)

El parque es de forma rectangular.

Longitud = 45 m

Ancho = 38.000 mm

Convertir mm en m

1 milímetro = 0,001 metro

38.000 milímetro =

38.000 × 0,001 metros

= 38 metros (38 m)

La distancia alrededor del parque = perímetro del parque

Perímetro = 2 (L + W)

= 2 (45 + 38)

= 2 (83)

= 166 m

Distancia alrededor del parque una vez = 166 m

Pero nos dijeron que dio la vuelta al parque 2 veces, por lo tanto, la distancia que recorrió = 166 m × 2

= 332m

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Leona [35]

Answer:

a. 5 b. y = -\frac{3}{4}x + \frac{1}{2} c. 148.5 d. 1/7

Step-by-step explanation:

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Solution

a. f"(2)

f"(x) = df'(x)/dx = d(sin(πx) + x² +3)/dx = cos(πx) + 2x

f"(2) = cos(π × 2) + 2 × 2

f"(2) = cos(2π) + 4

f"(2) = 1 + 4

f"(2) = 5

b. Equation for the line tangent to the graph of y = 1/f(x) at x = 0

We first find f(x) by integrating f'(x)

f(x) = ∫f'(x)dx = ∫(sin(πx) + x² +3)dx = -cos(πx)/π + x³/3 +3x + C

f(0) = 2 so,

2 = -cos(π × 0)/π + 0³/3 +3 × 0 + C

2 = -cos(0)/π + 0 + 0 + C

2 = -1/π + C

C = 2 + 1/π

f(x) = -cos(πx)/π + x³/3 +3x + 2 + 1/π

f(x) = [1-cos(πx)]/π + x³/3 +3x + 2

y = 1/f(x) = 1/([1-cos(πx)]/π + x³/3 +3x + 2)

The tangent to y is thus dy/dx

dy/dx = d1/([1-cos(πx)]/π + x³/3 +3x + 2)/dx

dy/dx = -([1-cos(πx)]/π + x³/3 +3x + 2)⁻²(sin(πx) + x² +3)

at x = 0,

dy/dx = -([1-cos(π × 0)]/π + 0³/3 +3 × 0 + 2)⁻²(sin(π × 0) + 0² +3)

dy/dx = -([1-cos(0)]/π + 0 + 0 + 2)⁻²(sin(0) + 0 +3)

dy/dx = -([1 - 1]/π + 0 + 0 + 2)⁻²(0 + 0 +3)

dy/dx = -(0/π + 2)⁻²(3)

dy/dx = -(0 + 2)⁻²(3)

dy/dx = -(2)⁻²(3)

dy/dx = -3/4

At x = 0,

y = 1/([1-cos(π × 0)]/π + 0³/3 +3 × 0 + 2)

y = 1/([1-cos(0)]/π + 0 + 0 + 2)

y = 1/([1 - 1]/π + 2)

y = 1/(0/π + 2)

y = 1/(0 + 2)

y = 1/2

So, the equation of the tangent at (0, 1/2) is

\frac{y - \frac{1}{2} }{x - 0} = -\frac{3}{4}  \\y - \frac{1}{2} = -\frac{3}{4}x\\y = -\frac{3}{4}x + \frac{1}{2}

c. If g(x) = f (√(3x² + 4). Find g'(2)

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g'(2) = [6sinπ√(16) + 36(16) + 18]/√16)

g'(2) = [6sin4π + 576 + 18]/4)

g'(2) = [6 × 0 + 576 + 18]/4)

g'(2) = [0 + 576 + 18]/4)

g'(2) = 594/4

g'(2) = 148.5

d. If h be the inverse function of f. Find h' (2)

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then h'(x) = 1/f'(x)

h'(x) = 1/(sin(πx) + x² +3)

h'(2) = 1/(sin(π2) + 2² +3)

h'(2) = 1/(sin(2π) + 4 +3)

h'(2) = 1/(0 + 4 +3)

h'(2) = 1/7

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