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3 years ago

The radius of a circle is 9 feet. What is the length of a 90° arc?

Mathematics

1 answer:

maks197457 [2]3 years ago

7 0

Answer:

$\frac{9\pi }{2}$ feet, or 14.14 feet

Step-by-step explanation:

Use the arc length formula:

s = rθ

To use the formula, we have to convert the central angle to radians.

90° is equivalent to $\frac{\pi }{2}$ radians, so plug this and the radius into the formula:

s = rθ

s = (9)( $\frac{\pi }{2}$ )

s = $\frac{9\pi }{2}$

So, the length of the arc is $\frac{9\pi }{2}\\$ feet, or approximately 14.14 feet

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The figure is made up of a cylinder and a sphere which has been cut in half. The radius of each half sphere is 5 mm. What is

alexgriva [62]

<h2>Answer:</h2>

<em>Rounded to the nearest hundredth the volume of the composite figure is:</em>

<em>1308 33 cubic millimeters</em>

<h2>Explanation:</h2>

Hello! I wrote the complete question in a comment above. The volume of a cylinder is defined as:

$V_{c}=\pi r^2 h \\ \\ r:radius \\ \\ h:height$

While the volume of half a sphere is:

$V_{hs}=\frac{2}{3}\pi r^3$

Since we have 2 half spheres, then the volume of these is the same as the volume of a sphere:

$V_{s}=\frac{4}{3}\pi r^3$

Then, the composite figure is:

$V=\pi r^2 h +\frac{4}{3}\pi r^3 \\ \\ V=\pi r^2(h+\frac{4}{3}r)$

The radius of the cylinder is the same of the radius of each half sphere. So:

$r=5mm \\ \\ h=10mm \\ \\ \\ V=(3.14) (5)^2((10)+\frac{4}{3}(5)) \\ \\ V=25(3.14)(10+\frac{20}{3}) \\ \\ \boxed{V\approx 1308.33mm^3}$

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3 years ago

Compare. >,< or = for each ? 7 yd 1 ft ? 25 ft , 38 in ? 3 ft

IceJOKER [234]

7 yd > 1 ft, 25 ft > 38 in. idk about that 3 ft there

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3 years ago

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Write an equation in slope-intercept form for the line

Art [367]

Answer:

Step-by-step explanation:

y - 2 = -4(x - 1)

y - 2 = -4x + 4

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3 years ago

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Monica [59]

1=51
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A line has a slope of $-\frac{3}{7},$ and its $y$-intercept is $(0,18)$. What is its $x$-intercept?

puteri [66]

Answer:

(42, 0)

Step-by-step explanation:

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0 = -3/7x + 18

-18 = -3/7x

x = 42

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3 years ago

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