Helpppppp pleaseeeee
1 answer:
Step-by-step explanation:
1. Given angles are,
40°, 3x+8° , 10x+42°
Therefore, by the problem,
=> 40° + 3x+8° + 10x+42° = 180° [Angle sum property of triangle]
=> 3x + 10x = 180° - (40°+42°+8°)
=> 13x = 180° - 90°
=> 13x = 90°
<u>Hence required value of x is (90/13)°</u>
2. Given,
12x - 18° = 5x +19° [Alternate angles]
=> 12x - 5x = 19 + 18
=> 7x = 37
<u>Hence required value of x is (37/7)°</u>
3. Given,
Exterior angle 132°
So it's paired interior angle will be = 180° - 132° (linear pair) = 48°
Hence the angles we get are = 42° , 87° , 20x - 10°
Therefore, by the problem,
48° + 87° + 20x - 10° = 180° [Angle sum property of triangle]
=> 20x = 180 - 48 - 87 + 10
=> 20x = 55
=> x = 2.75
<u>Hence required value of x is </u><u>2.75</u>
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Answer:
The receiver must be placed at a distance of 6.125 ft from the center.
Step-by-step explanation:
The dish is of parabola shape with the length of 14 feet and 2 feet deep from the center.
A parabola is a curve which is a set of all points in the plane which are at equal distance away from a given point called focus and given line called directrix.
We have to find out the point at which all the waves comes to one point where the receiver must be placed is the focus of the parabola.
The above scenario is shown in the image which can be converted in mathematical graphical representation of the parabolic curve.
The extreme two end points becomes, (-7,2) and (7,2)
The general equation for such parabola is:
x² = 4ay
where, a is the distance from the center and the focus.
Since, (7,2) satisfy the equation so,
7² = 4a×2
a = 49 /8
Thus,
<u>The receiver must be placed at a distance of 6.125 ft from the center.</u>
