Properly identifying and assigning the proper variables to each part of the problem before attempting to solve it
Synthetic division yields
See attachment for work
Answer:
Number 1 can form a right triangle. Numbers 2 & 3 cannot.
Step-by-step explanation:
To check if the sides are a right triangle, check if the sum of the squares of the two smaller sides equals the length of the square of the longest side. In other words, do the Pythagorean Theorem.
5² + 12² = 13²
25 + 144 = 169
169 = 169
<u><em>They are equal therefore Number 1 can form a right triangle.</em></u>
5² + 7² = 9²
25 + 49 = 81
74 = 81
<em>They are not equal, therefore Number 2 can't form a right triangle.</em>
<em />
10² + 12² = 30²
100 + 144 = 900
244 = 900
<em>They are not equal, therefore Number 3 can't form a right triangle.</em>
Newton's cooling model is ΔT = ΔTo * e ^ (-k t)
ΔTo = 200°F - 70°F = 130°F
k = 0.6
t = 2 hours
=> ΔT = 130 * e ^ (-0.6 t) = 130 * e^ (-0.6 * 2) = 130 * e ^ (-1.2)
ΔT = 39.15°F
ΔT = T - Tenvironment => T = ΔT + Tenvironment = 39.15°F + 70°F = 109.15°F ≈ 109 °F.
Answer: T = 109 °F
This is a proportion problem. Let the monument me x feet tall.
40/x=5/6
Cross multiply:
240=5x
x=48 ft.
So the monument is 48 ft tall,
