Answer:
The radius is 0.398 feet to produce a perfect lawn for the lawnmower.
It is given that the width of the lawnmower is 2.5 feet and the length of the rope is 25 feet.
It is required to calculate the radius (R) of the pole that will produce a perfect lawn.
What is a circle?
It is defined as the combination of points that and every point has an equal distance from a fixed point ( called the center of a circle).
We have,
Width of the lawnmower = 2.5 feet
Length of the rope = 25 feet
For the perfectly mowed lawn, it means the lawnmower width which is 2.5 feet must wrap the pole with radius R, mathematically:
The perimeter of the pole = width of the lawnmower
2πR = 2.5
R = 0.398 Feet ( π = 3.14 )
Thus, the radius is 0.398 feet to produce a perfect lawn for the lawnmower.
Answer:
ABCD is not a parallelogram
Step-by-step explanation:
Use the distance formula to determine whether ABCD below is a parallelogram. A(-3,2) B(-3,3) C (5,-3) D (-1.-5)
We have to find the length of the sides of the parallelogram using the formula below
= √(x2 - x1)² + (y2 - y1)² when given vertices (x1, y1) and (x2, y2)
For side AB
A(-3,2) B(-3,3)
= √(-3 -(-3))² + (3 -2)²
= √0² + 1²
= √1
= 1 unit
For side BC
B(-3,3) C (5,-3)
= √(5 -(-3))² + (-3 -3)²
= √8² + -6²
= √64 + 36
= √100
= 10 units
For side CD
C (5,-3) D (-1.-5)
= √(-1 - 5)² + (-5 - (-3))²
= √-6² + -2²
= √36 + 4
= √40 units
For sides AD
A(-3,2) D (-1.-5)
= √(-1 - (-3))² + (-5 -2)²
= √(2² + -7²)
= √(4 + 49)
= √53 units
A parallelogram is a quadrilateral with it's opposite sides equal
From the above calculation
Side AB ≠ CD
BC ≠ AD
Therefore, ABCD is not a parallelogram
<u>Answer:</u>
<h2>
ST = 44.54 ft</h2>
<u>Explanation:</u>
given:
∠T=90° , ∠R=39° and TR = 55 ft
ST = 55×tan(39)
ST = 55×0.80..
ST = 44.54 ft
Hi and hopes this helps:
Answer: 1/2
