If using the method of completing the square to solve the quadratic equation x2 −4x+13=0, which number would have to be added to
1 answer:
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The complete question in the attached figure
step 1
find the tree height for an angle of elevation of 55°<span>
tan 55</span>°=opposite side angle 55°/adjacent side angle 55°
opposite side angle 55°=the tree height h1
adjacent side angle 55°=10 ft
so
tan 55°=h/10-------> h=10*tan 55°-----> h=14.28 ft
step 2
find the tree height for an angle of elevation of 75°
tan 75°=opposite side angle 75°/adjacent side angle 75°
opposite side angle 75°=the tree height h2
adjacent side angle 75°=10 ft
so
tan 75°=h2/10-------> h2=10*tan 75°-----> h2=37.32 ft
therefore
<span>the height of the tree is within the range [14.26,37.32]
</span>
Part 1) 4.2 ft
<span>the value is not in the interval [14.26,37.32]
therefore
it is </span>Not Reasonable
Part 2) 14.7 ft
the value is in the interval [14.26,37.32]
therefore
it is Reasonable
Part 3) 24.4 ft
the value is in the interval [14.26,37.32]
therefore
it is Reasonable
Part 4) 33.9 ft
the value is in the interval [14.26,37.32]
therefore
it is Reasonable
Part 5) 39.1ft
the value is not in the interval [14.26,37.32]
therefore
it is Not Reasonable
Part 6) 58.7 ft
the value is not in the interval [14.26,37.32]
therefore
it is Not Reasonable
step 1
find the tree height for an angle of elevation of 55°<span>
tan 55</span>°=opposite side angle 55°/adjacent side angle 55°
opposite side angle 55°=the tree height h1
adjacent side angle 55°=10 ft
so
tan 55°=h/10-------> h=10*tan 55°-----> h=14.28 ft
step 2
find the tree height for an angle of elevation of 75°
tan 75°=opposite side angle 75°/adjacent side angle 75°
opposite side angle 75°=the tree height h2
adjacent side angle 75°=10 ft
so
tan 75°=h2/10-------> h2=10*tan 75°-----> h2=37.32 ft
therefore
<span>the height of the tree is within the range [14.26,37.32]
</span>
Part 1) 4.2 ft
<span>the value is not in the interval [14.26,37.32]
therefore
it is </span>Not Reasonable
Part 2) 14.7 ft
the value is in the interval [14.26,37.32]
therefore
it is Reasonable
Part 3) 24.4 ft
the value is in the interval [14.26,37.32]
therefore
it is Reasonable
Part 4) 33.9 ft
the value is in the interval [14.26,37.32]
therefore
it is Reasonable
Part 5) 39.1ft
the value is not in the interval [14.26,37.32]
therefore
it is Not Reasonable
Part 6) 58.7 ft
the value is not in the interval [14.26,37.32]
therefore
it is Not Reasonable
Answer:
45.82 square inches
Step-by-step explanation:
Use the formula for the surface area of a sphere, A = 4r²
If the diameter is 3.82 inches, the radius is 1.91 inches.
Plug in 3.14 as and 1.91 as r, and solve:
A = 4r²
A = 4(3.14)(1.91²)
A = 45.82
So, approximately 45.82 square inches of material are needed.