If f (x) = -3x+4 and g(x) =2,solve for the value of x for which f (x) =g(x) is true. X=
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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.
Answer:
ft³
Step-by-step explanation:
First, let's figure out how to get the <em>volume </em>of a sphere from its <em>surface area</em>. If r is the radius of our sphere, then
The formula for a sphere's surface area is
The formula for a sphere's volume is
So to get from area to volume, we have to <em>divide the area by 3 </em>and then <em>multiply it by r.</em> Mathematically:
Before we solve for V though, we need to find the radius of our sphere. Thankfully, we're given the surface area - ft² - so we can use the area formula to find that radius:
And now that we have our radius, we can put it into our volume formula to find
ft³