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4 years ago

Use the arc length formula and the given information to find r. Show your work for full credit. s = 8.1 ft θ = (3.14/3)rad r = ?

2 answers:

4 0

This question is simple I'm a little confused on the specifics so I will try my best to help.

s=θ(r)
arc length = angle x radius
2.46888m(or 8.1 ft) = (π/3) x r
$r = (\pi /3)/2.46888$
$r = .425m$

marysya [2.9K]4 years ago

4 0

Answer:

The length of the radius is 7.74 ft.

Step-by-step explanation:

It is given that the length of arc is s=8.1 and central angle of arc is $\theta=\frac{3.14}{3}$ in radian.

The formula for arc length is

$s=r\theta$

Where, s is length of arc, θ is central angle of arc in radian and r is the radius of the circle.

Substitute s=8.1 and $\theta=\frac{3.14}{3}$ in the above formula.

$8.1=r\times \frac{3.14}{3}$

$8.1=r\times 1.0467$

Divide both sides by 1.0467.

$\frac{8.1}{1.0467}=r$

$7.73860705073=r$

$r\approx 7.74$

Therefore the value of r is 7.74 ft.

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Write the equation of the line that passes through (1 5) and (-2 14) in slope intercept form

Kryger [21]

To deliver what is being asked of the given above, solve first for the slope of the line. Given two points the slope is calculated by,

m = (y2 - y1) / (x2 -x1)

m = (14 - 5) / (-2 - 1) = -3

Use the point - slope to write the equation of the line,

y - y2 = m(x - x2)

y - 14 = -3(x - -2)

<em> y = -3x + 8</em>

Therefore, the answer is letter D.

5 0

3 years ago

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Babaganoush’s electricity supply company charges him a fixed quarterly sum plus a rate per unit for electricity used. In the mos

Brilliant_brown [7]

Answer:

14,848.25

Step-by-step explanation:

2400+800=3200

320+144=464

25 3200 464

---- ------ ----= 14,848.25

100 x x

25x3200x464 divided by 100

Hope this helped and have a great day!

4 0

3 years ago

A well known pharmaceutical manufacturer is manufacturing a newly developed vaccine, and is concerned about variability in the i

Lana71 [14]

Answer:

The null hypothesis is $H_o : \ \sigma^2 = 1.9$

The alternative hypothesis is $H_a : \ \sigma^2 \ne 1.9$

$X^2 = 13.74$

The decision rule is

Reject the null hypothesis

The conclusion is

There is no sufficient evidence to conclude that the variance of the immune response is equal to 1.9.

Step-by-step explanation:

From the question we are are told that

The variance is $\sigma ^2 = 1.9$

The sample size is n = 30

The sample variance is $s^2 = 0.9$

The level of significance is $\alpha = 0.05$

The null hypothesis is $H_o : \ \sigma^2 = 1.9$

The alternative hypothesis is $H_a : \ \sigma^2 \ne 1.9$

Generally the test statistics is mathematically represented as

$X^2 = \frac{ (n- 1 ) * s^2 }{ \sigma^2 }$

=> $X^2 = \frac{ (30 - 1 ) * 0.9 }{1.9 }$

=> $X^2 = 13.74$

Generally from the degree of freedom is mathematically represented as

$df = n- 1$

=> $df = 30 - 1$

=> $df = 29$

Generally from the chi distribution table the critical value of $\frac{\alpha}{2} \ and \ 1 - \frac{ \alpha }{2}$ at a degree of freedom of $df = 29$ is

$X^2 _{ \frac{\alpha }{2} , df } = X^2 _{ \frac{0.05 }{2} , 29 } = 45.7$

=> $X^2 _{ 1 - \frac{\alpha }{2} , df } = X^2 _{1 - \frac{0.05 }{2} , 29 } = 16.0 5$

Gnerally from the values obtained we see that

$X^2 < X^2 _{ 1 - \frac{\alpha }{2} , df }$ hence

The decision rule is

Reject the null hypothesis

The conclusion is

There is no sufficient evidence to conclude that the variance of the immune response is equal to 1.9.

6 0

3 years ago

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valentina_108 [34]

Answer:

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3 years ago

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astraxan [27]

Answer:

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Step-by-step explanation:

7 0

3 years ago