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iVinArrow [24]
2 years ago
14

For a ride on a rental scooter, Charlie paid a $3 fee to start the scooter plus 11 cents per minute of the ride. The total bill

for Charlie's ride was $13.56. For how many minutes did Charlie ride the scooter?
Mathematics
1 answer:
Sever21 [200]2 years ago
4 0
Answer: Charlie travelled for 96 minutes . <h2>Explanations : </h2>

Given

• A ride on a rental scooter cost $3 plus 11 cents per minute for a ride ,

,

• Total bill for Charlies ride = $13.56

,

• Let Charlies ride be equal to ,t minutes, long

,

• This is a linear function representing the total bill for Charlies ride as follows :

3\text{ + }0.11t=13.56\text{ }<h2>Therefore , solving for t , we get that t = </h2>\begin{gathered} 0.11t\text{ = 13.56 - 3 } \\ 0.11t\text{ = 10.56 } \\ \frac{0.11t}{0.11\text{ }}=\text{ }\frac{10.56}{0.11} \\ \therefore\text{ t = 96  minutes} \end{gathered}

• t = 96 minutes ,

• This means that Charlie travelled for, 96 minutes ,.

,

• With a total bill of $13.56 , Charlies ride was 96 minutes long.

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Evaluate : <br> \(\cos 12 \cos 24 \cos 36 \cos 48 \cos 72 \cos 84\)
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The answer in itself is 1/128 and here is the procedure to prove it:
cos(A)*cos(60+A)*cos(60-A) = cos(A)*(cos²60 - sin²A) 

<span>= cos(A)*{(1/4) - 1 + cos²A} = cos(A)*(cos²A - 3/4) </span>

<span>= (1/4){4cos^3(A) - 3cos(A)} = (1/4)*cos(3A) </span>

Now we group applying what we see above

<span>cos(12)*cos(48)*cos(72) = </span>
<span>=cos(12)*cos(60-12)*cos(60+12) = (1/4)cos(36) </span>

<span>Similarly, cos(24)*cos(36)*cos(84) = (1/4)cos(72) </span>

<span>Now the given expression is: </span>

<span>= (1/4)cos(36)*(1/4)*cos(72)*cos(60) = </span>

<span>= (1/16)*(1/2)*{(√5 + 1)/4}*{(√5 - 1)/4} [cos(60) = 1/2; </span>
<span>cos(36) = (√5 + 1)/4 and cos(72) = cos(90-18) = </span>
<span>= sin(18) = (√5 - 1)/4] </span>
<span>And we seimplify it and it goes: (1/512)*(5-1) = 1/128</span>
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