Answer:
Ok soo.
Step-by-step explanation:
sum of two adjacent angles of parallelogram is 180
so angle K + angle L = 180
as AK bisects angle K and LA bisects angle L
so, angle AKL + angle ALK = 180 /2 = 90
in triangle AKL,
angle AKL + angle ALK+angle KAL = 180(sum of all angles in triangle = 180)
so, from above two equations,
angle KAL = 90
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Answer:
A) Radius: 3.44 cm.
Height: 6.88 cm.
B) Radius: 2.73 cm.
Height: 10.92 cm.
Step-by-step explanation:
We have to solve a optimization problem with constraints. The surface area has to be minimized, restrained to a fixed volumen.
a) We can express the volume of the soda can as:
This is the constraint.
The function we want to minimize is the surface, and it can be expressed as:
To solve this, we can express h in function of r:
And replace it in the surface equation
To optimize the function, we derive and equal to zero
The radius that minimizes the surface is r=3.44 cm.
The height is then
The height that minimizes the surface is h=6.88 cm.
b) The new equation for the real surface is:
We derive and equal to zero
The radius that minimizes the real surface is r=2.73 cm.
The height is then
The height that minimizes the real surface is h=10.92 cm.
Answer:
a. x/3.
Step-by-step explanation:
You divide to find a quotient so it is x / 3.
(x+6)(x+2)
Simplifying
(x + 6)(x + 2)
Reorder the terms:
(6 + x)(x + 2)
Reorder the terms:
(6 + x)(2 + x)
Multiply (6 + x) * (2 + x)
(6(2 + x) + x(2 + x))
((2 * 6 + x * 6) + x(2 + x))
((12 + 6x) + x(2 + x))
(12 + 6x + (2 * x + x * x))
(12 + 6x + (2x + x2))
Combine like terms: 6x + 2x = 8x
(12 + 8x + x2)