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serg [7]
3 years ago
11

Someone help with #1

Mathematics
2 answers:
Drupady [299]3 years ago
6 0
My answer was wrong, please delete this
snow_lady [41]3 years ago
4 0
Ok, first we set up 2 equations with the given info
let chips = c & pretzels = p

5c + 9p = 16.95
10c + 10p = 22.50

next we solve for a single variable in one of the equations (I chose the first one)
c =  \frac{16.95 - 9p}{5}

now plug it into our second equation
33.90 - 18p + 10p = 22.50
simplify
11.40 = 8p
divide
1.425 = p

next plug p back into our first equation
5c + 9(1.425) = 16.95
5c = 4.125
c = .825

Chips cost = $0.825
Pretzels cost = $1.425



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3 years ago
What is the approximate length of the apothem? 0. 4 cm 0. 8 cm 1. 5 cm 1. 9 cm.
arsen [322]

The length of apothem for a regular hexagon with radius of 18 cm and side of 18 cm is 15.6 cm

<h3>What is apothem?</h3>

The apothem of a regular polygon is a line segment from the center to the midpoint of one of its sides.

Let a represent the length of the apothem. Hence half of the side = 18/2 = 9 cm.

Using Pythagoras:

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1 year ago
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
Scilla [17]

Answer:

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,

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Now, if h be the height of the container,

Volume = length × width × height

2 = 2w × w × h

1 = w² × h

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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)

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=\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,

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

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

=6w^2+\frac{12}{w}

Differentiating with respect to w,

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

Again differentiating with respect to w,

C''(w) = 12 + \frac{24}{w^3}

For maxima or minima,

C'(w) = 0

\implies 12w -\frac{12}{w^2}=0

\implies 12w^3 - 12=0

w^3-1=0\implies w = 1

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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