a shoe store has a sale in which all shoes are priced at $33.00. the original price was $44. what is the percent of discount.
1 answer:
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The reasonable estimate for the length of side DE is 3 units
Find the diagram of the question attached. The given triangle ABC and BDE are similar triangles.
Using the similarity theorem of a triangle, this is expressed as:
AC = DE
Using the pythagoras theorem to get the length of AC:
AB^2 = AC^2 + BC^2
5^2 + AC^2 + 4^2
AC^2 = 25 - 16
AC^2 = 9
AC= 3
Since AC = DE, hence the reasonable estimate for the length of side DE is 3 units
Learn more on similar shapes here: brainly.com/question/14285697
Answer:
the absolute maximum value is 89.96 and
the absolute minimum value is 23.173
Step-by-step explanation:
Here we have cotangent given by the following relation;
so that the expression becomes
f(t) = 9t +9/tan(t/2)
Therefore, to look for the point of local extremum, we differentiate, the expression as follows;
f'(t) = =
Equating to 0 and solving gives
Where n is an integer hence when n₁ = 0 and n₂ = 1 we have t = π/4 and t = 3π/2 respectively
Or we have by chain rule
f'(t) = 9 -(9/2)csc²(t/2)
Equating to zero gives
9 -(9/2)csc²(t/2) = 0
csc²(t/2) = 2
csc(t/2) = ±√2
The solutions are, in quadrant 1, t/2 = π/4 such that t = π/2 or
in quadrant 2 we have t/2 = π - π/4 so that t = 3π/2
We then evaluate between the given closed interval to find the absolute maximum and absolute minimum as follows;
f(x) for x = π/4, π/2, 3π/2, 7π/2
f(π/4) = 9·π/4 +9/tan(π/8) = 28.7965
f(π/2) = 9·π/2 +9/tan(π/4) = 23.137
f(3π/2) = 9·3π/2 +9/tan(3·π/4) = 33.412
f(7π/2) = 9·7π/2 +9/tan(7π/4) = 89.96
Therefore the absolute maximum value = 89.96 and
the absolute minimum value = 23.173.