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attashe74 [19]
2 years ago
9

Mai spends 7 and 3/5 hours in school each day. Her lunch period is 30 minutes long, and she spends a total of 42 minutes switchi

ng rooms between classes. The rest of her day is spent in 6 classes that are all the same length. How long is each class?
Mathematics
1 answer:
Sonja [21]2 years ago
8 0
First, we solve for the number of minutes in 7 and 3/5 hours by multiplying the number by 60 giving us,
                            (7 + 3/5) x (60) = 456 minutes
Spending 30 minutes for lunch will leave her with 426 minutes. Then, spending 42 minutes for switching of classes will finally give her 414 minutes. 

We then divide this value by 6 (for her 6 classes) giving us 69 minutes. Thus, each class is 69 minutes long. 
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Two sides of a triangle have lengths 12 m and 14 m. The angle between them is increasing at a rate of 2°/min. How fast is the le
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Answer:

1.692 m/min

Step-by-step explanation:

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We differentiate x with respect to \theta by applying chain rule.

\dfrac{dx}{d\theta} = \dfrac{336\sin\theta}{2\sqrt{340 - 336\cos\theta}} = \dfrac{168\sin\theta}{\sqrt{340 - 336\cos\theta}}

Rate of change of \theta is 2

\dfrac{\theta}{dt} = 2

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\dfrac{dx}{dt} = \dfrac{dx}{d\theta}\times\dfrac{d\theta}{dt}

\dfrac{dx}{dt} = \dfrac{168\sin\theta}{\sqrt{340 - 336\cos\theta}} \times2=\dfrac{336\sin\theta}{\sqrt{340 - 336\cos\theta}}

At 60°,

\dfrac{dx}{dt} = \dfrac{336\sin60}{\sqrt{340 - 336\cos60}} = 1.692 \text{ m/min}

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1 year ago
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