6) Solve. x + 5 = 10 A) x = 2 B) x = 3 09 x = 4 D) X = 5
1 answer:
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Answer:
A. 35 ft.
B. 35 ft
Step-by-step explanation:
Please see attached photo for diagram.
A. Determination of the diagonal using pythagorean theorem.
A square has all sides equal. Thus, the diagonal of the square can be obtained as follow:
Ist leg (L₁) = 25 ft
2nd leg (L₂) = 25 ft
Diagonal (d) =?
d² = L₁² + L₂²
d² = 25² + 25²
d² = 625 + 625
d² = 1250
Take the square root of both side
d = √1250
d = 35 ft
B. Determination of the diagonal using trigonometry.
Since all the sides in a square are equal, the angle between each leg will be 90°. Thus, the diagonal will bisect the angle between the two leg equally i.e
Angle between Diagonal and each leg = 90/2 = 45°
Finally, we shall determine the length of the diagonal. This can be obtained as follow:
Angle θ = 45°
Opposite = 25 ft
Hypothenus = d
Sine θ = Opposite / Hypothenus
Sine 45 = 25 / d
0.7071 = 25 / d
Cross multiply
0.7071 × d = 25
Divide both side by 0.7071
d = 25 / 0.7071
d = 35 ft
The complete question in the attached figure
we know that
the equation of a sphere is
(x-h)²+(y-k)²+(z-l)²=r²
<span>let's assume that the center of the sphere is at the origin
</span>so
(h,k,l)-------> (0,0,0)
for r=16 m
(x-h)²+(y-k)²+(z-l)²=r²--------> (x)²+(y)²+(z)²=16²
for z=9 m
(x)²+(y)²+(9)²=16²--------> (x)²+(y)²=256-81--------> (x)²+(y)²=175
the radius of the circle is r=√175 m
so the area of the circle A=pi*r²-----> A=pi*175-----> A=549.5 m²
the answer is
the area of the circle is 549.5 m²
we know that
the equation of a sphere is
(x-h)²+(y-k)²+(z-l)²=r²
<span>let's assume that the center of the sphere is at the origin
</span>so
(h,k,l)-------> (0,0,0)
for r=16 m
(x-h)²+(y-k)²+(z-l)²=r²--------> (x)²+(y)²+(z)²=16²
for z=9 m
(x)²+(y)²+(9)²=16²--------> (x)²+(y)²=256-81--------> (x)²+(y)²=175
the radius of the circle is r=√175 m
so the area of the circle A=pi*r²-----> A=pi*175-----> A=549.5 m²
the answer is
the area of the circle is 549.5 m²