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3 years ago

15

A rope from the top of a mast on a sailboat is attached to a point 6 feet from the base of the mast. If the rope is 24 feet long

, about how high is the mast?

1 answer:

Zanzabum3 years ago

3 0

Answer: It is about 23 feet.

Step-by-step explanation:

1. Let's call <em>x</em> the height of the mast.

2. You know that the rope is attached to a point 6 feet from the base of the mast and the rope is 24 feet long, therefore, you can draw the right triangle shown in the figure attached.

3. To calculate <em>x</em>, you must apply the Pythagorean Theorem as you can see below:

$x=\sqrt{(24ft)^{2}-(6ft)^{2}}\\x=\sqrt{540ft^{2}}$

$x$ ≈ $23ft$

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3 years ago

F(x) = x − 8, g(x) = |x + 8|<br> Find <br> (f ∘ g)(x).

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3 years ago

Need to find volume, step by step explanation pls <br><br><br><br>

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Given:

A figure of combination of hemisphere, cylinder and cone.

Radius of hemisphere, cylinder and cone = 6 units.

Height of cylinder = 12 units

Slant height of cone = 10 units.

To find:

The volume of the given figure.

Solution:

Volume of hemisphere is:

$V_1=\dfrac{2}{3}\pi r^3$

Where, r is the radius of the hemisphere.

$V_1=\dfrac{2}{3}(3.14)(6)^3$

$V_1=\dfrac{6.28}{3}(216)$

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Volume of cylinder is:

$V_2=\pi r^2h$

Where, r is the radius of the cylinder and h is the height of the cylinder.

$V_2=(3.14)(6)^2(12)$

$V_2=(3.14)(36)(12)$

$V_2=1356.48$

We know that,

$l^2=r^2+h^2$ [Pythagoras theorem]

Where, l is length, r is the radius and h is the height of the cone.

$(10)^2=(6)^2+h^2$

$100-36=h^2$

$\sqrt{64}=h$

$8=h$

Volume of cone is:

$V_3=\dfrac{1}{3}\pi r^2h$

Where, r is the radius of the cone and h is the height of the cone.

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$V_3=301.44$

Now, the volume of the combined figure is:

$V=V_1+V_2+V_3$

$V=452.16+1356.48+301.44$

$V=2110.08$

Therefore, the volume of the given figure is 2110.08 cubic units.

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2 years ago