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oksian1 [2.3K]
3 years ago
7

. In April, it rained 1/4 of an inch on 15 different days. How many inches of rain fell

Mathematics
1 answer:
notka56 [123]3 years ago
5 0

Answer:

3.75, or \frac{15}{4} inches of rain during the 15 days of April.

Step-by-step explanation:

All you have to do is add \frac{1}{4} 15 times to get that number.

\frac{1}{4} +\frac{1}{4} +\frac{1}{4} +\frac{1}{4} +\frac{1}{4} +\frac{1}{4} +\frac{1}{4} +\frac{1}{4} +\frac{1}{4} +\frac{1}{4} +\frac{1}{4} +\frac{1}{4} +\frac{1}{4} +\frac{1}{4} = 3.75

You can also do 15 times \frac{1}{4}, which will result in the same thing.

#teamtrees #WAP (Water And Plant)

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A rectangular storage container with a lid is to have a volume of 2 m3. The length of its base is twice the width. Material for
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Dimensions are 2 m by 1 meter by 1 meter,

Minimum cost is $ 18.

Step-by-step explanation:

Let w be the width ( in meters ) of the container,

Since, the length is twice of the width,

So, length of the container = 2w,

Now, if h be the height of the container,

Volume = length × width × height

2 = 2w × w × h

1 = w² × h

\implies h=\frac{1}{w^2}

Since, the area of the base = l × w = 2w × w = 2w²,

Area of the lid = l × w = 2w²,

While the area of the sides = 2hw + 2hl

= 2h( w + l)

= 2\times \frac{1}{w^2}(w+2w)

=\frac{6w}{w^2}

=\frac{6}{w}  

Since, Material for the base costs $1 per m². Material for the sides and lid costs $2 per m²,

So, the total cost,

C(w) = 1\times 2w^2+2\times 2w^2 + 2\times \frac{6}{w}

=2w^2+4w^2+\frac{12}{w}

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Differentiating with respect to w,

C'(w) = 12w -\frac{12}{w^2}

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For maxima or minima,

C'(w) = 0

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For w = 1, C''(w) = positive,

Hence, for width 1 m the cost is minimum,

Therefore, the minimum cost is C(1) = 6(1)²+12 = $ 18,

And, the dimension for which the cost is minimum is,

2 m by 1 meter by 1 meter.

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