Extrusive molten rocks are formed from lava while the intrusive molten rocks are formed from magma.
<u>Explanation:</u>
Extrusive molten rocks originate from lava, framing at the outside of the Earth and cooling rapidly, which means they structure little precious stones. Intrusive volcanic rocks originate from magma, shaping profound underground and taking more time to cool, which means they structure bigger crystals.
Intrusive molten rocks are framed when magma cools gradually underneath the surface, while extrusive rocks are shaped when magma cools quickly at the surface.
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Imagine a right triangle where the legs represent the horizontal and vertical lengths of the string and the hypotenuse represents the length of the string.
Let us assign some values:
x = horizontal length in feet
50 = vertical length in feet
L = length of the string in feet
Because we are modeling these quantities with a right triangle, we can use the Pythagorean theorem to relate them with the following equation:
L² = x² + 50²
We want to find an equation for the change of L over time, so first differentiate both sides with respect to time t then solve for dL/dt:
2L(dL/dt) = 2x(dx/dt)
dL/dt = (x/L)(dx/dt)
First let's solve for x at the moment in time described in the problem using the Pythagorean theorem:
L² = x² + 50²
Given values:
L = 100ft
Plug in and solve for x:
100² = x² + 50²
x = 86.6ft
Now let's find dL/dt. Given values:
x = 86.6ft, L = 100ft, dx/dt = 4ft/sec
Plug in and solve for dL/dt:
dL/dt = (86.6/100)(4)
dL/dt = 3.46ft/sec