3 years ago

Find the unknown angle measure by solving for the given variable

Mathematics

1 answer:

tiny-mole [99]3 years ago

3 0

A straight line is 180°. So you can do:

(15x - 4) + (5x - 8) = 180 Simplify

20x - 12 = 180

20x = 192 Find the value of x

x = 9.6

m∠ABD = 15x - 4 Plug in x = 9.6

m∠ABD = 15(9.6) - 4 = 144 - 4 = 140°

m∠DBC = 5x - 8 Plug in 9.6

m∠DBC = 5(9.6) - 8 = 48 - 8 = 40°

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The base of a solid in the xy-plane is the circle x2 + y2 = 16. Cross sections of the solid perpendicular to the y-axis are semi

Alexus [3.1K]

Answer:

The volume of the solid will be = 134.1 cubic units.

Step-by-step explanation:

The base of a solid has the equation of a circle x² + y² = 16 in the xy-plane. Cross-sections perpendicular to the y-axis of the solid are semicircles.

Therefore, the solid will be the shape of a hemisphere.

Now, the radius of the hemisphere will be 4 units.

{Since the base of the hemisphere is on the xy-plane and have equation

x² + y² = 4²}

Therefore, the volume of the solid will be = $\frac{2}{3}\pi r^{3} = (\frac{2}{3})\times (\frac{22}{7}) \times (4^{3}) = 134.1$ cubic units. (Answer)