What are the solutions of 2x2 - 6x + 5 = 0 ?
2 answers:
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Answer:
(a) The volume of the pyramid 440.44 cube units
(b) No she doesn't
(c) The volume of the larger pyramid is 1,486.485 cube units
Step-by-step explanation:
The given parameters are;
The scale factor of the pyramids, S.F. = 2:3
The base area of the small pyramid, = 110.11 square units
The height of the small pyramid, h₁ = 12 units
(a) The volume of a pyramid, V = (1/3) × Area of base × The height of the pyramid
Therefore;
The volume of the small pyramid, V₁ = (1/3) × 110.11 square units × 12 units
V₁ = 440.44 cube units
The volume of the small pyramid, V₁ = 440.44 cube units
(b) No she does not have to go through all the hard work again to find the volume of the larger pyramid
She only has to make use of the scale factor relationships of the two pyramid to calculate the volume of the larger pyramid
The volume scale factor = (The linear scale factor)³
(c) The linear scale factor of the pyramids = 2:3 = 2/3
Therefore;
The volume scale factor of the pyramids = (2/3)³ = 8/27
To find the volume of the larger pyramid, V₂, from the volume of the smaller pyramid, V₁, we multiply the volume of the smaller pyramid, V₁, by 27/8 as follows;
V₂ = V₁ × (27/8)
Therefore;
The volume of the larger pyramid, V₂ = 440.44 cube units × (27/8) = 1,486.485 cube units
The volume of the larger pyramid, V₂ = 1,486.485 cube units.
Answer:
Given: Line p is parallel to line r.
Alternate exterior angles states that two angles in the exterior of the parallel lines, and on opposite sides of the transversal.
Alternate exterior angles are non-adjacent and congruent.
[ Alternate exterior angles]
Since, Angles are congruent if they have the same angle measure in degrees
....[1] [by definition of congruent Angles]
Linear pair states that a pair of adjacent angles formed when two lines intersect.
therefore, by definition and
forms a linear pair.
Since, linear pair are always supplementary.
is supplementary to
Supplementary angles states that two angles are supplementary that means they add up to measure 180 degree.
Substitute the equation [1] in above equation we get;
then, by the definition of supplementary angle ;
is supplementary to
