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3 years ago

The radius of a semicircle is 1 kilometer. what is the semicircle's perimeter? use 3.14 for pie.

Mathematics

1 answer:

Aleksandr-060686 [28]3 years ago

5 0

Answer:

5.14 km

Step-by-step explanation:

A semicircle is 1/2 of a circle so the perimeter is just 1/2 of the circumference

C = 2 * pi r for a circle so for a semicircle

1/2* 2* pi *r

pi*r

3.14 * 1

3.14

If we want to include the piece that closes the semicircle, we need to add the diameter

d = 2r = 2(1) = 2

2+3.14 = 5.14

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An automobile travels past the farmhouse at a speed of v = 45 km/h. How fast is the distance between the automobile and the farm

yulyashka [42]

Answer:

$\frac{ds}{dt} = 39.586 km/h$

Step-by-step explanation:

let distance between farmhouse and road is 2 km

From diagram given

p is the distance between road and past the intersection of highway

By using Pythagoras theorem

$s^2 = 2^2 +p^2$

differentiate wrt t

we get

$\frac{d}{dt} s^2 = \frac{d}{dt} (4 + p^2)$

$2s \frac{ds}{dt} =2p \frac{dp}{dt}$

$\frac{ds}{dt} = \frac{p}{s}\frac{dp}{dt}$

$\frac{ds}{dt} = \frac{p}{\sqrt{p^2 +4}} \frac{dp}{dt}$

putting p = 3.7 km

$\frac{ds}{dt} = \frac{3.7}{\sqrt{3.7^2 +4}} 45$

$\frac{ds}{dt} = 39.586 km/h$

3 0

4 years ago

Y = -7/6x + 10<br> slope =<br> y-intercept =

arsen [322]

Answer:

the answer is actualy 12

Step-by-step explanation:

4 0

3 years ago

Approximately 40% of the calls to an airline reservation phone line result in a reservation being made. (round to three decimal

IRISSAK [1]

Answer:

The probability that none of the 10 calls result in a reservation is 0.60%. In turn, the probability that at least one call results in a reservation being made is 99.40%.

Step-by-step explanation:

Since approximately 40% of the calls to an airline reservation phone line result in a reservation being made, supposing an operator handles 10 calls, to determine what is the probability that none of the 10 calls result in a reservation, and what is the probability that at least one call results in a reservation being made, the following calculations must be performed:

0.6 ^ 10 = X

0.006 = X

0.006 x 100 = 0.60%

Therefore, the probability that none of the 10 calls result in a reservation is 0.60%.

100 - 0.60 = 99.40

In turn, the probability that at least one call results in a reservation being made is 99.40%.

3 0

3 years ago

-7 over 8 ÷ 7 over -4

Vlad1618 [11]

Answer:

1/2

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

For each of the following situations, explain why the combinations rule or the permutations rule should be used. (a) Determine t

Vesnalui [34]

Answer:

See explanation

Step-by-step explanation:

(a) Total number of distinct objects = 12

Number of object that should be selected = 5.

Number of different groups of 5 items that can be selected from 12 distinct items

$=C^{12}_5=\dfrac{12!}{5!(12-5)!}=\dfrac{12!}{5!\cdot 7!}=\dfrac{7!\cdot 8\cdot 9\cdot 10\cdot 11\cdot 12}{2\cdot 3\cdot 4\cdot 5\cdot 7!}=8\cdot 9\cdot 11=792$

You should use the combinations rule, since the number of arrangements within each group is of interest (the order of elements within each group is not your business).

(b) Total number of distinct objects = 12

Number of object that should be selected = 5.

Number of different arrangements of 5 items that can be selected from 12 distinct items

$=P^{12}_5=\dfrac{12!}{(12-5)!}=\dfrac{12!}{7!}=\dfrac{7!\cdot 8\cdot 9\cdot 10\cdot 11\cdot 12}{7!}=8\cdot 9\cdot 10\cdot 11\cdot 12=95,040$

You should use the permutations rule, since the number of arrangements within each group is of interest (the order of elements within each group has value for you because arrangements 1,2,3,4,5 and 5,4,3,2,1 are different arrangements).

7 0

3 years ago