All categories

2 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]2 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.

You might be interested in

A consensus forecast is the average of a large number of individual analysts' forecasts. Suppose the individual forecasts for a

stealth61 [152]

Answer:

a) 0.954

b) 0.937

c) 0.891

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 6 percent

Standard Deviation, σ = 1.3 percent

We are given that the distribution of particular interest rate is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) P(At least 3.8 percent.)

$P(x \geq 3.8)$

$P( x \geq 3.8) = P( z \geq \displaystyle\frac{3.8 - 6}{1.3}) = P(z > -1.69)$

$= 1 - P(z < -1.69)$

Calculation the value from standard normal z table, we have,

$P(x \geq 3.8) = 1 - 0.046 = 0.954 = 95.4\%$

b) P(At most 8 percent)

$P(x \leq 8) = P(z \leq \displaystyle\frac{8-6}{1.3}) = P(z \leq 1.53)$

Calculating the value from the standard normal table we have,

$P( x \leq 8) =0.937= 93.7\%$

c) P(Between 3.8 percent and 8 percent. )

$P(3.8 \leq x \leq 8) = P(-1.69 \leq z \leq 1.53)\\\\= P(z \leq 1.53) - P(z < -1.69)\\= 0.937 - 0.046 = 0.891 = 89.1\%$

$P(3.8 \leq x \leq 8) = 89.1\%$

3 0

2 years ago

What type of function can approach zero as x decreases without end?

Olin [163]

Answer: c. Exponential

7 0

2 years ago

Find dy/dx implicitly and find the largest interval of the form −a < y < a or 0 < y < a such that y is a differentia

mylen [45]

Answer:

dy/dx = -1/√(1 - x²)

For 0 < y < π

Step-by-step explanation:

Given the function cos y = x

-siny dy = dx

-siny dy/dx = 1

dy/dx = -1/siny (equation 1)

But cos²y + sin²y = 1

=> sin²y = 1 - cos²y

=> siny = √(1 - cos²y) (equation 2)

Again, we know that

cosy = x

=> cos²y = x² (equation 3)

Using (equation 3) in (equation 2), we have

siny = √(1 - x²) (equation 4)

Finally, using (equation 4) in (equation 1), we have

dy/dx = -1/√(1 - x²)

The largest interval is when

√(1 - x²) = 0

=> 1 - x² = 0

=> x² = 1

=> x = ±1

So, the interval is

-1 < x < 1

arccos(1) < y < arxcos(-1)

= 0 < y < π

6 0

2 years ago

You earn 13.76/hr part-time and work 10hrs/wk. your deductions are FICA(7.65%), federal tax withholding (9.8%) and state tax wit

PSYCHO15rus [73]

$137.60    (gross pay)
$10.53      (FICA)
$13.18      (Federal Tax)
$9.81        (State Tax)
---------------------------------
$103.78    (Net Pay)
$77.84      (Deposit)
---------------------------------
$25.94      (To You)
$38.92      (To Savings)

4 0

2 years ago

Read 2 more answers

A model that describes the population of a fishery in which harvesting takes place at a constant rate is given by dP dt = kP − h

Vadim26 [7]

It increases at T because the behavior increased its speed

8 0

2 years ago