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Diano4ka-milaya [45]
3 years ago
8

Which shows the length of the darkened arc? (The wierd symbol next to the answers is Pi)​

Mathematics
2 answers:
SashulF [63]3 years ago
8 0

Answer: 15 π

Step-by-step explanation:

The formula for determining the circumference of a circle is expressed as

Circumference = 2πr

Looking at the circle,

Diameter = 18 inches

Radius = diameter/2 = 18/2

Radius = 9 inches

Circumference = 2 × 9 × π = 18π

The formula for determining the length of an arc is expressed as

Length of arc = θ/360 × 2πr

Where

θ represents the central angle.

r = 9 inches

θ = 60 degrees

Length of arc = 60/360 × 2 × π × 9

Length of arc = 3π

The length of the darkened arc is the circumference of the circle - the arc formed by 60 degrees. Therefore,

length of the darkened arc = 18π - 3π = 15π

fgiga [73]3 years ago
3 0

Answer:

15 pi

Step-by-step explanation:

The circumference of the circle is given by

C = pi * d

C = pi *18

We are subtracting part of the circumference that covers 60 degrees

The entire circle is 360 degrees

60/360 = 1/6

We are subtracting 1/6 of the circumference

1/6 *18pi = 3pi

We have 18pi and subtract 3pi = 15pi

The dark shaded arc is 15pi

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Write an exponential function in the form y = ab that goes through points (0,19)<br>and (5,4617).​
gtnhenbr [62]

Answer:

y = 1/2 (2)x

     Step-by-step explanation:

Using the equation y = abx , substitute both of your given points into that equation.

2 = ab2 and 4 = ab3   Solve each equation for a.

2⁄b2    and 4⁄b3 = a     Therefore, 2⁄b2 = 4⁄b3

                             

Cross multiply: 2b3 = 4b2     Divide both sides by b2

2b = 4      a = 2/4 = 1/2

b = 2

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3 years ago
According to the empirical rule, if the data form a bell-shaped normal distribution, __________ of the observations will fall wi
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Answer:

95%

Step-by-step explanation:

The empirical rule states that if data follows normal distribution then the percentage of observations falls within one, two and three standard deviation around the mean are

i) 68% falls within one standard deviation

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iii) 99.7% falls within three standard deviation.

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After a party there were 2 and 2/3 pepperoni pizzas and 1 and 5/6 cheese pizzas left. How much pizza was left
Harlamova29_29 [7]
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Ms. Hatcher bought the pencil decoration shown below for her bulletin board.
Gre4nikov [31]

Answer:

335.5 in^2

Step-by-step explanation:

The area is a rectangle and a triangle

The area of the rectangle is

A = a*b where a is 11 and b is 25

A = 11*25 =275

The area of the triangle is

A = 1/2 b*h  where b is 11 and h is 11

A = 1/2 (11) * 11

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The total area is 275+60.5=335.5

7 0
3 years ago
Read 2 more answers
3.
loris [4]

(a) It looks like the ODE is

<em>y'</em> = 4<em>x</em> √(1 - <em>y </em>^2)

which is separable:

d<em>y</em>/d<em>x</em> = 4<em>x</em> √(1 - <em>y</em> ^2)   =>   d<em>y</em>/√(1 - <em>y</em> ^2) = 4<em>x</em> d<em>x</em>

Integrate both sides. On the left, substitute <em>y</em> = sin(<em>t </em>) and d<em>y</em> = cos(<em>t</em> ) d<em>t</em> :

∫ d<em>y</em>/√(1 - <em>y</em> ^2) = ∫ 4<em>x</em> d<em>x</em>

∫ cos(<em>t</em> ) / √(1 - sin^2(<em>t</em> )) d<em>t</em> = ∫ 4<em>x</em> d<em>x</em>

∫ cos(<em>t</em> ) / √(cos^2(<em>t</em> )) d<em>t</em> = ∫ 4<em>x</em> d<em>x</em>

∫ cos(<em>t</em> ) / |cos(<em>t</em> )| d<em>t</em> = ∫ 4<em>x</em> d<em>x</em>

Since we want the substitutiong to be reversible, we implicitly assume that -<em>π</em>/2 ≤ <em>t</em> ≤ <em>π</em>/2, for which cos(<em>t</em> ) > 0, and in turn |cos(<em>t</em> )| = cos(<em>t</em> ). So the left side reduces completely and we get

∫ d<em>t</em> = ∫ 4<em>x</em> d<em>x</em>

<em>t</em> = 2<em>x</em> ^2 + <em>C</em>

arcsin(<em>y</em>) = 2<em>x</em> ^2 + <em>C</em>

<em>y</em> = sin(2<em>x</em> ^2 + <em>C </em>)

(b) There is no solution for the initial value <em>y</em> (0) = 4 because sin is bounded between -1 and 1.

7 0
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