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erastova [34]
3 years ago
14

The length of a kitchen wall is 24 2/3 feet long. A border will be placed along the wall of the kitchen. If the border strips ar

e 1 3/4 feet long, how many strips of border are needed?

Mathematics
1 answer:
krek1111 [17]3 years ago
5 0

Total length of the kitchen wall = 24 2/3 feet.

Let us convert 24 2/3 feet into improper fracion.

24 2/3 = (24*3+2)/3 = 74/3 feet.

Length of each strip = 1 3/4 feet.

Let us convert 1/3/4 feet in improper fracion.

1 3/4 feet = (1*4+3)/4 = 7/4 feet.

Total number of strips required = (Total length of the kitchen wall) ÷ (Length of each strip)

= 74/3 feet ÷ 7/4 feet.

Let us convert division sign into multiplication, we get

74/3 × 4/7.

Multiplying across, we get

296/21.

On dividing 296 by 21, we get 14.09 approximately.

14.09 represents more than 14.

So, we can round it to the next whole number, that is 15.

Therefore, 15 strips of border are needed.

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3 years ago
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Vsevolod [243]

At the start, the tank contains

(0.25 lb/gal) * (100 gal) = 25 lb

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Sugar is added to the tank at a rate of <em>P</em> lb/min, and removed at a rate of

\left(1\frac{\rm gal}{\rm min}\right)\left(\dfrac{S(t)}{100}\dfrac{\rm lb}{\rm gal}\right)=\dfrac{S(t)}{100}\dfrac{\rm lb}{\rm min}

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\dfrac{\mathrm dS}{\mathrm dt}=P-\dfrac S{100}

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\dfrac{\mathrm dS}{P-\frac S{100}}=\mathrm dt

\displaystyle\int\dfrac{\mathrm dS}{P-\frac S{100}}=\int\mathrm dt

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\ln\left|P-\dfrac S{100}\right|=-100t-100C=C-100t

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S(t)=100P-100Ce^{-100t}=100P-Ce^{-100t}

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S(995)=100P-(100P-25)e^{-99,500}=2.5\implies\boxed{P\approx0.025}

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