1. The shape of the top surface of a table is a trapezium. Find its area
if its parallel sides are 1 m and 1.2 m and perpendicular distance
between them is 0.8 m.
0.8 m
1.2 m
H
Answers
Step-by-step explanation:
Answer:
First, draw the graphs of f(x) mentioned in the question.
Acc. to the question,
f(x) = min { sin (x), cos (x) }
Let us first draw the graphs of sin (x) and cos (x). Since the interval is given to be ( -π, π ), it's enough to plot the graph between this interval.
The graph looks like the image attached (1).
Now we are required to find the min { sin (x), cos (x) }.
Min function refers to the graph which only has the minimum values between the two.
For example, in the interval between ( -π, -3π/4 ), the graph of cos (x) [Blue line] has minimum value than the sin (x) graph.
Hence in that interval, we plot only the graph of cos (x).
Coming to the next interval, which is ( - 3π/4, π/4 ), the graph of sin (x) [Red line] has minimum value than the cos (x) graph.
Hence in this interval, we plot the graph of sin (x) alone.
Coming to the final interval, ( π/4, π ), we see that the graph of cos (x) [Blue line] has the minimum value.
Hence in this interval, we plot the graph of cos (x).
Joining the graph of all intervals, we get a graph like Image 2.
Now we see two corner points or sharp edges in the graph. We know that, these points are non-differentiable. Hence,
⇒ S = { -3π/4 , π/4 } are points which are non-differentiable.
Since Option (1) has these options, Set S is the subset of Option (1)/
Hence Option (1) is the correct answer.
Answer ⤵️
Step-by-step explanation:
Parallel sides=1m and 1.2m
height=0.8m
Area of table top==\frac{1}{2}\times\left(sum\ of\ parallel\ sides\right)\times\left(dis\tan ce\ between\ them\right)\ =
2
1
×(sum of parallel sides)×(distance between them)
=\frac{1}{2}\times\left(1+1.2\right)\ \left(0.8\right)=
2
1
×(1+1.2) (0.8)
=\frac{2.2\times0.8}{2}=
2
2.2×0.8
==\frac{2.2\times0.8}{2}=
2
2.2×0.8
==\frac{2.2\times0.8}{2}=
2
2.2×0.8
=0.88\ m^20.88 m
2