Answer:
x=3
Step-by-step explanation:
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Answer: the distance of the boat from the foot of the lighthouse is 290.5 feet.
Step-by-step explanation:
The right angle triangle ABC representing the scenario is shown in the attached photo.
Angle A is alternate to the angle of depression, hence, they are the same.
The height of the lighthouse represents the opposite side of the right angle triangle. The distance, x of the boat from the foot of the lighthouse represents the adjacent side of the right angle triangle.
To determine x, we would apply
the tangent trigonometric ratio.
Tan θ, = opposite side/adjacent side. Therefore,
Tan 11.1 = 57/x
x = 57/Tan 11.1 = 57/0.1962
x = 290.5 feet to the nearest tenth.
We know that
the equation of a sphere is
(x-h)²+(y-k)²+(z-l)²=r²
where (h,k,l) is the center and r is the radius
we have
x²+y²+z²<span>−2x−4y+8z+17=0
</span>
Group terms that contain the same variable, and move the
constant to the opposite side of the equation
(x²+2x)+(y²-4y)+(z²+8z)=-17
<span>Complete
the square. Remember to balance the equation by adding the same constants
to each side
</span>(x²+2x+1)+(y²-4y+4)+(z²+8z+16)=-17+1+4+16
(x²+2x+1)+(y²-4y+4)+(z²+8z+16)=4
Rewrite as perfect squares
(x+1)²+(y-2²)+(z+4)²=4
(x+1)²+(y-2²)+(z+4)²=2²
the center is the point (-1,2,-4) and the radius is 2 units
The answer is 14%
Cost of meal is 100%: $18.50 is 100%
Tip is x%: $2.59 is x
Make a proportion:
$18.50 : 100% = $2.59 : x
x = 100% * $2.59 : $18.50
x = 14%
We have y - 2 = m(x + 5), where m = (-1 - 2)/(10 + 5) = -3/15 = -1/5;
Then y - 2 = (-1/5)(x + 5);
5y - 10 = (-1)(x + 5);
5y - 10 = -x - 5;
x + 5y - 5 = 0 is the equation of the line.