Answer:
4445.18 pulgadas cúbicas
Step-by-step explanation:
Paso 1
La fórmula para la circunferencia de una esfera = 2πr
Circunferencia de una esfera = 64 pulgadas
Por eso,
64 = 2πr
Por lo tanto, encontramos r
Dividir ambos lados por 2π
64 / 2π = 2πr / 2π
r = 10.185916358 pulgadas
Radio r = 10.2 pulgadas
Paso 2
Volumen de una esfera
= 4/3 × π × r³
r = 10.2 pulgadas
Por lo tanto, 4/3 × π × (10.2) ³
= 4445.18 pulgadas cúbicas
Por lo tanto, el volumen en pulgadas cúbicas de una esfera = 4445.18 pulgadas cúbicas
Step-by-step explanation:
y = 3 + 8x^(³/₂), 0 ≤ x ≤ 1
dy/dx = 12√x
Arc length is:
s = ∫ ds
s = ∫₀¹ √(1 + (dy/dx)²) dx
s = ∫₀¹ √(1 + (12√x)²) dx
s = ∫₀¹ √(1 + 144x) dx
If u = 1 + 144x, then du = 144 dx.
s = 1/144 ∫ √u du
s = 1/144 (⅔ u^(³/₂))
s = 1/216 u^(³/₂)
Substitute back:
s = 1/216 (1 + 144x)^(³/₂)
Evaluate between x=0 and x=1.
s = [1/216 (1 + 144)^(³/₂)] − [1/216 (1 + 0)^(³/₂)]
s = 1/216 (145)^(³/₂) − 1/216
s = (145√145 − 1) / 216
Answer:
D
Step-by-step explanation:
answers B and D are both true but box plots compare medians more often than means
Answer:
θ = 
(60° )
Step-by-step explanation:
Using the identity
sin²x + cos²x = 1 ⇒ sin²x = 1 - cos²x
Given
cos²θ - sin²θ = 2 - 5cosθ
cos²θ - (1 - cos²θ) = 2 - 5cosθ
cos²θ - 1 + cos²θ = 2 - 5cosθ
2cos²θ - 1 = 2 - 5cosθ ( subtract 2 - 5cosθ from both sides )
2cos²θ + 5cosθ - 3 = 0 ← in standard form
(cosθ + 3)(2cosθ - 1) = 0 ← in factored form
Equate each factor to zero and solve for θ
cosθ + 3 = 0
cosθ = - 3 ← not possible as - 1 ≤ cosθ ≤ 1
2cosθ - 1 = 0
cosθ = 
, so
θ = 
( ) = ( or 60° )
