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Nata [24]
3 years ago
12

A colony of bees have produced about 4 oz of honey. Some time later they have about 7oz of honey. If the bees produce at a rate

of 1.5% per hour, how many hours did it take?
Mathematics
1 answer:
yanalaym [24]3 years ago
5 0

It took 50 hours to produce 3 oz of honey.

<u>Step-by-step explanation:</u>

Rate of production= 1.5% per hour

Initial amount of honey = 4 oz

Final amount of honey = 7 oz

Honey produced = 3 oz

Amount produced = (initial amount x rate x time) /100

3 = (4 x 1.5 x t) /100

300 = 6t

t = 300/6

t = 50 hours

It took 50 hours for the bees to produce 3 oz of honey.

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Answer:

Add 7 to both sides

Step-by-step explanation:

You would need to add 7 to both sides to cancel out the 7 on the right side of the equation to get x one step closer to being by itself.

Then you would get 4x = -8.

Next divide by 4 on both sides to get x by itself so do the inverse operation of what 4 was doing to x.

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2 years ago
The polar coordinates of a point are 3π 4 and 7.00 m. What are its Cartesian coordinates (in m)? (x, y) = 6.06,−3.5 m
Keith_Richards [23]

Answer:

a) \left(x,y\right)=\left(4.95,-4.95\right)

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Step-by-step explanation:

Polar coordinates are represented as: r\angle\theta, where 'r' is the length (or magnitude) of the line, and '\theta' is the angle measured from the positive x-axis.

in our case:

7\angle\dfrac{3\pi}{4}

to covert the polar to cartesian:

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y = r\sin{\theta}

we can plug in our values:

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y = 7\sin{\dfrac{3\pi}{4}} = 7\dfrac{\sqrt{2}}{2}

the Cartesian coordinates are:

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(b) to convert (x,y) = (6.06,-3.5)

we'll use the pythagoras theorem to find 'r'

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r^2 = (6.06)^2+(-3.5)^2

r = \sqrt{48.97} \approx 7

the angle can be found by:

\tan{\theta} = \dfrac{y}{x}

\tan{\theta} = \dfrac{3.5}{6.06}

\theta = \arctan{left(\dfrac{3.5}{6.06}\right)}

\theta = 0.5236 \text{radians}

to convert radians to degrees:

\theta = 0.5236 \times \dfrac{180}{\pi} \approx 30^\circ

writing in polar coordinates:

r\angle\theta = 7\angle30^\circ\,\,\text{OR}\,\,7\angle0.5236\,\text{radians}

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