Answer:
Change the equation to the slope intercept form (y = mx + b)
2y = 6x + 8
Divide equation by 2
y = 3x + 4
Therefore
The line as a y intercept of 4
:
Parallel lines have the same slope;
Find the slope by putting in the equation in the point/intercept form
4x + 4y = 20
4y = -4x + 20
Divide equation by 4, results
y = -1x + 5
:
Now we know the slope (-1) and the y intercept (+4) if the line
y = -1x + 4
or just
y = -x + 4 is "the line"
Step-by-step explanation:
Answer:
Flux = 16π
Step-by-step explanation:
The outward flux of F across the solid cylinder and z = 0 is
∫∫F*ds = ∫∫∫ DivF*dv
F = 2xy²i + 2x²yj + 2xyk
DivF = D/dx (2xy²) + D/dy (2x²y )
DivF = 2y² + 2x²
In cylindrical coordinates dV = rdrdθdz and as z = 0 the region is a surface ds = rdrdθ
Parametryzing the surface equation
x = rcosθ y = r sinθ and z = z
Div F = 2r²sin²θ + 2r²cos²θ
∫∫∫ DivF*dv = ∫∫ [2r²sin²θ + 2r²cos²θ]* rdrdθ
∫∫ 2r² [sin²θ + cos²θ]* rdrdθdz ⇒ ∫∫ 2r³ drdθ
Integration limits
0 < r < 2 0 < θ < 2π
2∫₀² r³ ∫dθ
(2/4)(2)⁴ 2π
Flux = 16π
How many meters is the peak of Orizaba higher than Popocatepetl?
Answer:
Popocatépetl: 5426 m and 17,802 ft
Orizaba: 18,491 meters
Step-by-step explanation:
How long does it take to climb Pico de Orizaba?
about 15 hours
Most ascents of Pico de Orizaba will take about 15 hours from the mountain hut to the summit and back. You will usually wake up and begin climbing by 1 a.m. to reach the summit by 10 a.m. and return to the starting mountain hut by 4 p.m.
How long does it take to climb Popocatépetl?
4 hours
What is Popocatépetl?
Popocatepetl is currently a very active volcano with forested slopes and a large crater. It is the second-highest peak in Mexico, behind Pico de Orizaba (5636 meters/18,491 feet), and is generally considered to be the fifth highest mountain in North American. The name Popocatepetl is Aztec for Smoking Mountain; it is often shortened to Popo. Popo and its neighboring volcano Iztaccihuatl (17,343 ft) dominate the sky east of Amecameca. They are located less than 80 km from Mexico City and are separated from each other by ten miles of high grounds referred to as Paso de Cortes. I had the pleasure of climbing the mountain on December 18, 1992, when the volcano was still considered dormant. This is no longer the case. In the 20th century, Popo had an eruption in 1947, but on December 21, 1994, it awakened from dormancy, spewing gas and ash, which was carried by the wind as far as Puebla, 25 miles east. Surrounding towns were evacuated, and scientists have since been closely monitoring Popo for signs of a possible eruption. Ever since then the mountain has been closed to climbing. In December 2000, the mountain came alive with the biggest eruption in 1200 years and with the biggest display of "fireworks" (lava shot ~400 meters/1300 feet into the air) that has been. 30,000 people were evacuated. The first documented ascent of Popocatepetl was by the Tecuanipas tribe in 1289, but this ascent has been disputed by historians. The first Spanish ascent of the mountain was an expedition led by Diego de Ordaz in 1519. Emperor Montezuma sent ten warriors to climb the mountain sometime between 1502 and 1519. Only two of these warriors survived the climb.
Answer:
Step-by-step explanation:
we know that
Applying the Intersecting Secant-Tangent Theorem
square root both sides
