The standard height from the floor to the bull's-eye at which a standard dartboard is hung is 5 feet 8 inches. A standard dartboard is
18 inches in diameter.
Suppose a standard dartboard is hung at standard height so that the bull's-eye is 11 feet from a wall to its left.
Samuel throws a dart at the dartboard that lands at a point 11.5 feet from the left wall and 5.5 feet above the floor.
Does Samuel's dart land on the dartboard?
Answers
Answer:
Yes, Samuel dart does land on the dart board
Step-by-step explanation:
The given parameters are;
The height from the floor to the bulls eye = 5 feet 8 inches
The size of the standard board = 18 inches diameter
The distance of the bulls eye from the wall to the left = 11 feet
The distance the dart Samuel throws land from the left wall = 11.5 feet
The distance above the ground, the dart Samuel throws land = 5.5 feet
Whereby Samuel throws the dart directly at the dartboard, we have;
The location of the bulls eye = (11, 5.67)
The equation of the circle representing the dart board = (x - 11)² + (y - 5.67)² = 0.75² = 0.5625
The unit of the radius is in feet
The position of Samuel's dart is represented by the coordinate, (11.5, 5.5)
Plugging in the coordinates of the position of Samuel's dart into the equation of the circle of the dart board gives;
(11.5 - 11)² + (5.5 - 5.67)² = 0.2789 ≈ 0.528²
Therefore, given that the square of the distance of the position of Samuel's dart is less than the square of the radius of the dart board, we have;
Yes, Samuel dart does land on the dart board.
From the parameters given to find out if Samuel's dart landed on the dartboard, we can say that;
Samuel's dart does not land on the dartboard.
We are given;
Height from the floor to the bulls eye = 5 ft 8 in = 5.67 ft
Diameter of the standard dartboard = 18 in = 1.5 ft
Thus, radius; r = 1.5/2 = 0.75 ft
Distance of the bulls eye from the wall to the left = 11 ft
Distance of dart thrown by Samuel from the left wall = 11.5 ft
Height of dart thrown by Samuel above the ground = 5.5 ft
We know that general equation of a circle is;
(x - a)² + (y - b)² = r²
Since Height from the floor to the bulls eye is 5.67ft,then a = 5.67 ft
And also since Distance of the bulls eye from the wall to the left = 11 ft, then b = 11 ft
Thus;
(x - 11)² + (y - 5.67)² = 0.75²
(x - 11)² + (y - 5.67)² = 0.5625
Now, since he throws a dart at the dartboard that lands at a point 11.5 feet from the left wall and 5.5 feet above the floor. Thus;
r² = (11.5 - 11)² + (5.5 - 5.67)²
r² = 0.2789
r² of 0.2789 gotten here is lesser than 0.5625 gotten earlier, we can conclude that Samuel's dart does not land on the dart board.
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Answer:
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Step-by-step explanation:
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Answer:
A
Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answers
Answer:
y=2x-15
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△PQR is rotated 180° about the origin. What is the coordinate for Q' ?
(3, 2)
(2, -3)
(-3, 2)
(-2, 3)
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(-3, -4)
(-4, 3)
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(3, 4)
Answers
Answer:
Part 1:
Q’ = (2, -3)
Part 2:
R’ = (-3, -4)
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the farm covers an area of 13square miles. The farm is divided into 4 equal sections, as shown in this diagram. What is the area, in square miles, of each section?
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Answer:
p[
Step-by-step explanation:
p[
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Answers
Answer:
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Step-by-step explanation:
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3n = 12 ( divide both sides by 3 )
n = 4
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5n - 3 = 5(4) - 3 = 20 - 3 = 17
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assig 8
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(c)write the solution in interval notation.
29
30
31
32
33
Answers
Answer: see below
Step-by-step explanation:
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Graph: ←--------- ·
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Interval Notation: (10, ∞)
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÷ 2 ÷ 2
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x < -4
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Answers
Answer:
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Step-by-step explanation:
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Answers
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Answer:
5(m+9) = 5m+25
Step-by-step explanation:
durrrrrrrrrrrrrrr
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a.
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Answers
Answer:
8.58
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7.5
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Step-by-step explanation:
Answer:
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Answers
Answer:
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image attached. Thank you!
Answers
Answer:
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Step-by-step explanation:
We'll have to use trigonometry for this.
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We will use cosine to find y because cos = adjacent/hypotenuse.
cos(A) = cos(60) = adjacent/hypotenuse = y/18
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~ an aesthetics lover
Answer:
C
Step-by-step explanation:
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----------------------------------------------------------
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Answers
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or
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Answers
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Step-by-step explanation:
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Answers
Answer:
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Since positive times negative is equal to negative, we can multiply -5.5 by an addition symbol, making it an addition problem, and making it the same expression.
To evaluate the expression, we can do 33.6-5.5.
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Answers
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Answer:
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Step-by-step explanation:
Answer:
6! Hope this helps have a great night!!!!
Step-by-step explanation:
May I plz have brainliest?
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Answers
s = side length of square
4s = perimeter of square
L = length of rectangle
W = width of rectangle
P = 2L+2W = perimeter of rectangle
4s = 2L+2W .... since we want the perimeters the same
4s = 2(L+W)
s = 0.5(L+W)
s^2 = (0.5(L+W))^2 ... square both sides
s^2 = 0.25(L+W)^2
The last equation shows the area of the square, s^2, in terms of L and W. This way we can connect the square to the rectangle.
-----------------------------------
The area of the rectangle is LW
Let's subtract this from the area of the square and see what we get
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B = area of rectangle = LW
C = difference in area
C = A - B
C = s^2 - LW
C = 0.25(L+W)^2 - LW
C = 0.25(L^2+2LW+W^2) - LW
C = 0.25L^2+0.5LW+0.25W^2-LW
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C = 0.25(L^2-2LW+W^2)
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Answers
Answer:
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Answer:
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it was on a mathcounts competition
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Answer:
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Answers
Answer:
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Answers
Hey mate here is your answer.
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Add my snaq k1nglean if anyone wants to ttrade you gotta be 16+
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Which point lies on the graph of the function shown below y=-x^2+5x-3
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C.(2,3)
D.(-2,2)
Answers
Answer:
C: (2,3)
Step-by-step explanation:
to solve this algebraically just plug in the x and y values of the points and see if they are true, but here is the graph to juse show you