can anyone please help me I am struggling?? It’s 9th grade algebra 1 average rate of change comparison
1 answer:
Answer:
a) 2 b) 1 c) 7/6
Function a(x) = 2x + 3 has the greatest rate of change
Step-by-step explanation:
a(x) = 2x + 3
2(-1) + 3 = 1 (-1,1)
2(2) + 3 = 7 (2,7)
= 6/3
=2
b(x) = x^2 - 1
(-1)^2 - 1 = 0 (-1, 0)
(2)^2 - 1 = 3 (2,3)
= 3/3
=1
c(x) = 2^x + 1
2^(-1) + 1 = 1.5 (-1, 1.5)
2^(2) + 1 = 5 (2,5)
= 3.5/3 or 7/6
=7/6
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The height of the smaller building is <u>94.63 feet</u>, computed using the trigonometric ratios.
In the question, we take AB to be the taller building, where A is its top and B is its base, CD to be the shorter building, where C is its top and D is its base, and CE to be the perpendicular from C to AB.
Given that the horizontal distance between the two buildings is 260 feet, we can say that BC = CE = 260 feet.
The angle of elevation from the top of the shorter building to the top of the taller building is 30°, that is, ∠ECA = 30°.
The angle of depression from the top of the shorter building to the base of the taller building is 20°, that is, ∠ECB = 20°.
When ∠ECB = 20°, then ∠CBD = 20°, as they are alternate angles.
We are asked to find the height of the shorter building, that is, we are asked to find CD.
In ΔCBD,
tan ∠CBD = CD/BD {perpendicular/base},
or, tan 20° = CD/260,
or, CD = 260*tan 20° = 260*0.36397023426 {∵ tan 20° = 0.36397023426},
or, CD = 94.6322609092.
Therefore, the height of the smaller building is <u>94.63 feet</u>, computed using the trigonometric ratios.
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