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29 Jan 2020, 04:24
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The points (0,3) and (4,0) are joined to find a triangle with x-axis and y-axis as the other sides of the triangle. The area of this triangle overlaps with approximately what percentage of the area of a circle with equation x^2 + y^2 = 25 ?
A. 4%
B. 8%
C. 12%
D. 16%
E. 20%
Are You Up For the Challenge: 700 Level Questions
A. 4%
B. 8%
C. 12%
D. 16%
E. 20%
Are You Up For the Challenge: 700 Level Questions
29 Jan 2020, 04:46
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The points (0,3) and (4,0) are joined to find a triangle with x-axis and y-axis as the other sides of the triangle. The area of this triangle overlaps with approximately what percentage of the area of a circle with equation \(x^2 + y^2 = 25\) ?
--> The area of the triangle -\(\frac{3*4}{2}= 6\)
circle with equation \(x^2 + y^2 = 25=R^{2}\)
--> R=5
The area of circle = \(πR^{2}= 25π\) (\(π=\frac{22}{7}\))
\(25π -100%\)
\(6 --x % \)
-->\( x= \frac{6*100}{25π}= \frac{24}{π}= \frac{24}{(22/7)}= \frac{84}{11} ≈ 8%\)
The answer is B.
--> The area of the triangle -\(\frac{3*4}{2}= 6\)
circle with equation \(x^2 + y^2 = 25=R^{2}\)
--> R=5
The area of circle = \(πR^{2}= 25π\) (\(π=\frac{22}{7}\))
\(25π -100%\)
\(6 --x % \)
-->\( x= \frac{6*100}{25π}= \frac{24}{π}= \frac{24}{(22/7)}= \frac{84}{11} ≈ 8%\)
The answer is B.
29 Jan 2020, 06:31
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The points (0,3) and (4,0) are joined to find a triangle with x-axis and y-axis as the other sides of the triangle. The area of this triangle overlaps with approximately what percentage of the area of a circle with equation x^2 + y^2 = 25 ?
A. 4%
B. 8%
C. 12%
D. 16%
E. 20%
Area of Triangle = 1/2(base) * (height)
We are given --The points (0,3) and (4,0) are joined to find a triangle with x-axis and y-axis
So area of triangle = 1/2 (4)(3)= 6
Equation of circle x^2 + y^2 = 25 , from this equation we know center of circle must be at origin and radius=5
(The center-radius form of the circle equation is in the format (x – h)^2 + (y – k)^2 = r^2, with the center being at the point (h, k) and the radius being "r".)
Area of circle we can calculate since we know radius of circle= II r^2= (3.14) 25 apx =75
Remember we are asked apx value so we can make our cal easy by approximating.
Triangle overlaps what percent of circle area. Since both originate from origin, also circle has radius 5 , which is longer than any of the angle, we can very well think that triangle is within circle.
6/75*100=8%
So triangle overlaps 8% of the area of circle.
Ans choice B
Please hit kudos ,if it helped you
A. 4%
B. 8%
C. 12%
D. 16%
E. 20%
Area of Triangle = 1/2(base) * (height)
We are given --The points (0,3) and (4,0) are joined to find a triangle with x-axis and y-axis
So area of triangle = 1/2 (4)(3)= 6
Equation of circle x^2 + y^2 = 25 , from this equation we know center of circle must be at origin and radius=5
(The center-radius form of the circle equation is in the format (x – h)^2 + (y – k)^2 = r^2, with the center being at the point (h, k) and the radius being "r".)
Area of circle we can calculate since we know radius of circle= II r^2= (3.14) 25 apx =75
Remember we are asked apx value so we can make our cal easy by approximating.
Triangle overlaps what percent of circle area. Since both originate from origin, also circle has radius 5 , which is longer than any of the angle, we can very well think that triangle is within circle.
6/75*100=8%
So triangle overlaps 8% of the area of circle.
Ans choice B
Please hit kudos ,if it helped you
