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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Related Questions
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Answers
Answer:
17
Step-by-step explanation:
Given
3n - 4 = 8 ( add 4 to both sides )
3n = 12 ( divide both sides by 3 )
n = 4
Thus
5n - 3 = 5(4) - 3 = 20 - 3 = 17
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p -> ~q:_______________________________
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Answer:
P is you pass the class, so it's the hypothesis in the conditional. And Q is the conclusion, which ic you got to the next grade.
Step-by-step explanation:
In order to got to the next grade, you need to pass the class.
or
If you pass the class, you go to the next grade.
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
Answer:
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What is the equation of the line that is parallel to the line y = 2x + 6 and goes through point C (8, 1)?
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Answer:
y=2x-15
Step-by-step explanation:
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What is the location of H' after the image is rotated 180 degrees?
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Answer:
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Step-by-step explanation:
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Shannon's little brother is 7 weeks old. She is exactly
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Answers
Answer:
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Step-by-step explanation:
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In 2001, gold was priced at (0.5x + 300) dollars per ounce. Its price tripled in 2008 and then doubled in 2011. In 2016, its price dropped to 2 3 of the price in 2011.
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Answers
Answer:
[tex]2x + 1200[/tex]
Step-by-step explanation:
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Each new line represents the change stated in the question.
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Answers
Answer:
A
Step-by-step explanation:
Remember that parallel lines have the same slope.
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[tex]y=x+4[/tex]
And:
[tex]y=x-2[/tex]
The slope is the coefficient in front of the x.
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The slope of the second equation is also 1.
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Answers
Answer:
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Answers
Answer:
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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
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Step-by-step explanation:
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Answers
Hey mate here is your answer.
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image attached. Thank you!
Answers
Answer:
C
Step-by-step explanation:
We'll have to use trigonometry for this.
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[(√3)/2] * 18 = 9√3
Already, we can tell that the answer is likely C, but let's find y to make sure.
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:
Using the cosine/ sine ratio in the right triangle and the exact values
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----------------------------------------------------------
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Answer:
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Answer:
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Step-by-step explanation:
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Answers
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Step-by-step explanation:
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Answers
Answer:
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(-3, 2)
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Answers
Answer:
Part 1:
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Part 2:
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rrange the numbers in decreasing order.
a.
8.508
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Answers
Answer:
8.58
8.508
7.5
7.058
Step-by-step explanation:
Answer:
8.58, 8.508, 7.5, 7.058
Step-by-step explanation:
Um, I think this means greatest to least.
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Look at the place values.
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x(3) = 2(4)
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11.5) = 2(2)
x(0.5) = 2(0.5)
x(12) = 12
Answers
Answer:
the 2nd and 4th i think
Step-by-step explanation:
I’m pretty sure the answer would be
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Why is it that when comparing a squares area with a rectangles area, with the SAME PERIMETER, that the square has a greater area?
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
A = area of square = s^2
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
C = 0.25L^2-0.5LW+0.25W^2
C = 0.25(L^2-2LW+W^2)
C = 0.25(L-W)^2
Regardless of what we pick for L and W, the expression (L-W)^2 is always positive. Squaring a negative number leads to a positive result.
So C is always positive as long as [tex]L \ne W[/tex]
If C > 0, and C = A - B, then
C > 0
A-B > 0 .... replace C with A-B
A > B .... add B to both sides
This shows the square area is always larger than the rectangle.
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I NEED HELPP?!
Answers
Answer:
Slope of a line = rise/run
Your answer:
m = 8/5
help show work
assig 8
(a)solve the inequality
(b)graph the solution on the real number line.
(c)write the solution in interval notation.
29
30
31
32
33
Answers
Answer: see below
Step-by-step explanation:
29) -5x ≥ 30
÷ -5 ↓ ÷ -5
x ≤ -6
Graph: ←--------- ·
-6
Interval Notation: (-∞, 6]
30) -4x < -40
÷ -4 ↓ ÷ -4
x > 10
Graph: o---------→
10
Interval Notation: (10, ∞)
31) 2x - 5 ≥ -11
+5 +5
2x ≥ -6
÷ 2 ÷ 2
x ≥ -3
Graph: · ---------→
-3
Interval Notation: [-3, ∞)
32) 8 - 3x > 20
-8 -8
-3x > 12
÷ -3 ↓ ÷ -3
x < -4
Graph: ←---------o
-4
Interval Notation: (-∞, -4)
33) 4x - 11 < 7x + 4
-7x -7x
-3x - 11 < 4
+ 11 +11
-3x < 15
÷ -3 ↓ ÷ -3
x > -5
Graph: o---------→
-5
Interval Notation: (-5, ∞)
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?
Answers
Answer:
p[
Step-by-step explanation:
p[