Marie made a model (shown below) of the square pyramid she plans to build when she grows up. Find the surface area of the model.
\text{ m}^2 m 2 start text, m, end text, squared
1 answer:
Answer:
144m²
Step-by-step explanation:
The the model made by Marie is attached in the diagram below.
The square pyramid model that Marie has in mind of building has 4 congruent triangular faces on the four sides of the square pyramid, and 1 base square. Therefore the surface area of the square pyramid = area of the square + area of 4 triangles = b² + 4(1/2*b*h)
Given that b = 8, and h = 5, we have:
Surface area = 8² + 4(1/2*8*5)
= 64 + 4(20)
= 64 + 80
SA of the square pyramid = 144m²
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Answer:
(1, 2) and (- 1, - 2)
Step-by-step explanation:
Given the 2 equations
x² + y² = 5 → (1)
y = 2x → (2)
Substitute y = 2x into (1)
x² + (2x)² = 5, that is
x² + 4x² = 5
5x² = 5 ( divide both sides by 5 )
x² = 1 ( take the square root of both sides )
x = ± = ± 1
Substitute these values into (2) for corresponding values of y
x = 1 → y = 2(1) = 2 ⇒ (1, 2)
x = - 1 → y = 2(- 1) = - 2 ⇒ (- 1, - 2)
Answer:
Per hour decay of the isotope is 0.96%.
Step-by-step explanation:
Amount of radioactive element remaining after t hours is represented by
where a = initial amount
t = duration of decay (in hours)
Amount remaining after 1 hour will be,
y = 0.9904a
So amount of decay in one hour = a - 0.9904a
= 0.0096a gms
Percentage decay every hour =
=
= 0.958 %
≈ 0.96 %
Therefore, per hour decay of the radioactive isotope is 0.96%.