A analog clock (with hour and minute hands) is set to 5:00 P.M. After 30 min, what will the measure of the major arc formed by h
1 answer:
Answer:
180 degrees
Step-by-step explanation:
Given
Required
The measure of the major arc, 30 minutes after
First, we calculate the time after 30 minutes
At 5:30pm, the hour and the minute hand will be directly opposite each other.
In other words, the hands divide the time into two equal parts (180 degrees each)
At this point, there is no major or minor arc as both sides have the same measurement
<em>Hence, the measure of the arcs is 180 degrees</em>
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Answer:
The missing dimension is 4 units.
Step-by-step explanation:
In the given prism,
Of all the surfaces,
There are three rectangular surfaces and two triangular surfaces
<h2>Analyzing areas of rectangular surfaces:</h2>1)The two rectangles with dimensions of 15 units and 5 units:
The area of each rectangle = Length of rectangle Breadth of rectangle
From the diagram,
Length of rectangle = 15 units,
Breadth of rectangle = 5 units.
Area of each rectangle = 15 5 ;
Area of each rectangle = 75 square units.
Sum of areas of the two rectangles = 2 75
Sum of areas of the two rectangles = 150 square units (equation 1)
2) The rectangle with the dimensions 15 units and 6 units:
The area of thus rectangle= Length of rectangle Breadth of rectangle
From the diagram,
Length of rectangle = 15 units,
Breadth of rectangle = 6 units.
Area of the rectangle = 15 6 ;
Area of the rectangle = 90 square units. (equation 2)
From equation 1 and equation 2,
Therefore sum of areas of all rectangles in the prism = 150 + 90
Sum of areas of rectangles = 240 square units.
We also know,
Total surface area of the prism = Sum of areas of triangles + Sum areas of rectangles
Given, Total surface area of prism = 264 square units.
Therefore from the formula,
Sum of areas of triangles = Total surface area - sum of areas of reactangles
Sum of areas of triangles = 264 - 240
Sum of areas of triangles = 24 square units. (equation 3)
Let the missing dimension be 'h units'
<h2>Calculating sum of areas of triangles:</h2>From diagram,both triangles are congruent,hence have the same area
Area of a triangle =
From diagram,
Base = 6 units,
Height = h units.
Area of a triangle = = 3h square units.
Sum of the areas of both triangles = 3h+3h = 6h square units.
Using equation 3, we get
6h = 24;
h =
Therefore,
h = 4 units.
Therefore,
The missing dimension is 4 units.