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galina1969 [7]
3 years ago
8

How many radians are contained in the angle AOT in the figure? Round your answer to three decimal places.

Mathematics
2 answers:
Ostrovityanka [42]3 years ago
4 0
1 radian = 57.3 degrees

60 <span>÷ 57.3 = 1.047
</span>

correct answer: C
Whitepunk [10]3 years ago
4 0

Answer:

Option C. 1.047 radians

Step-by-step explanation:

We have to find the measure of angle AOT in radians.

To convert measure of an angle from degree to radians we use the formula

\text{radians}=\frac{\pi(\text{degrees})}{180}

= \frac{\pi(60)}{180}=\frac{\pi }{3}

(Since measure of angle AOT is 60°)

= \frac{3.14}{3} (since π = 3.14)

= 1.047 radians

Therefore, option C. 1.047 radians is the correct option.

   

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How to Become a Millionaire Upon graduating from col- lege, Donna has no initial capital. However, during each year she makes de
lesantik [10]

Answer:

amount is 1000 × e^{0.08t}

$40762.20 balance of Donna's account will be 1 million dollars when she retires in 40 years

rate 14.97 %  when Donna's account will have a balance of 1 million dollars in 40 years when principal is $2500

Step-by-step explanation:

principal = $1000

rate = 8 % = 0.08

to find out

the future value, S(t)

principal when Donna's account will be 1 million dollars when she retires in 40 year

at what rate Donna's account will have a balance of 1 million dollars in 40 years

solution

we know compounded continuously formula i.e.

amount = principal × e^{rt}    ..................1

put the value principal and rate in equation 1 to find amount any time

amount = principal × e^{rt}

amount = 1000 × e^{0.08t}

in 2nd part we have time 40 year and amount 1 million so put rate amount and time in equation 1  to find principal

rt = 0.08 × 40 = 3.2

amount = principal × e^{rt}

1000000 = principal × e^{3.2}

principal = 1000000 / e^{3.2}

principal = 1000000 / 24.5325302

principal = 40762.20397

so $40762.20 balance of Donna's account will be 1 million dollars when she retires in 40 years

in 3rd part we have amount 1 million and principal $2500 and time 40 year put all these in equation 1 to find rate

amount = principal × e^{rt}

1000000 = 2500 × e^{40r}

take ln both side

ln e^{40r} =  ln (1000000 / 2500 )

40 r = ln 400

r = ln (400) / 40

r = 0.149787

so rate 14.97 %  when Donna's account will have a balance of 1 million dollars in 40 years when principal is $2500

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