mixed number: 4 1/15

Exact: 61/15

## Related Questions

The base of an aquarium with given volume V is made of slate and the sides are made of glass. If slate costs five times as much (per unit area) as glass, find the dimensions of the aquarium that minimize the cost of the materials. (Let x, y, and z be the dimensions of the aquarium. Enter your answer in terms of V.)

The dimensions of the aquarium that minimize the cost of the materials:

Step-by-step explanation:

Let x, y and z be the dimensions of aquarium .

Surface area of an aquarium = xy+2yz+2xz

Volume of aquarium V=  ----A

We are given that slate costs five times as much (per unit area) as glass

So, Cost function : C=5xy+2yz+2xz

Now we will use langrage multiplier to find the dimensions of the aquarium that minimize the cost of the materials.

So,

----1

-----2

----3

Multiply 1 ,2 and 3 by x,y and z respectively.

----4

-----5

----6

Now equate 4 and 5

5xy+2xz=5xy+2yz

x=y

Substitute y=x in 5 and 6 and equate them

Substitute the values in A

Hence,

The dimensions of the aquarium that minimize the cost of the materials:

Jenny drove 715 miles in 11 hours.At the same rate, how long would it take her to drive 325 miles?

5 hours

715/11 = 65
325/65 = 5

80

Step-by-step explanation:

80

angle a = angle s

amr and msr are similar triangles

Simple question!

Step-by-step explanation:

I'm never challenged in school, could you send me your hw each day?

Email ivaliu2008+outlook.com

Thanks!

100 gallons per 5 hours

Step-by-step explanation:

100 gallons/5hours = 20 gallons/hour

Determine whether the geometric series is convergent or divergent. 6 + 5 + 25/6 + 125/36 + ... If it is convergent, find its sum. (If the quantity diverges, enter DIVERGES.)

The -th term in the series is 6 multiplied by the -th power of 5/6:

and so on.

Consider the -th partial sum,

Multiplying both sides by 5/6 gives

and substracting this from gives

As , it's clear that the sum converges to 36.

The geometric series in the question is convergent with a common ratio of 5/6. Using the formula for the sum of an infinite geometric series, the sum of the series is found to be 36.

### Explanation:

In mathematics, specifically in series, determining whether a geometric series is convergent or divergent is centered around the common ratio value. In terms of this particular series: 6 + 5 + 25/6 + 125/36 + ..., the common ratio is 5/6. Given this common ratio, it's clear that it falls between -1 and 1. Hence, this geometric series is convergent.

Once we establish it is a convergent series, we can calculate its sum using the formula for the sum of an infinite geometric series: S = a / (1 - r), where 'a' is the first term and 'r' is the common ratio. Inserting the respective values a = 6 and r = 5/6, we get: S = 6 / (1 - 5/6) = 36. Hence, the sum of this infinite geometric series is 36.

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19 + 11 - 12² ÷ 3 (12 - 9) · 11)) - 7 =Use PEMDAS for this.

Also it's a made up question

PEMDAS = Parentheses, Exponents, Multiplication, Division, Addition, Subtraction

First, subtract the numbers in the parentheses, then multiply by 11.

(12 - 9) = (3)

3 x 11 = 33

19 + 11 - 12^2 ÷ 3(33) - 7

Now, just multiply 33 by 3, and then square 12 (12 x 12).

19 + 11 - 144 ÷ 99 - 7

Now, you can divide 144 by 99, this is an infinite number, so..

144 ÷ 99 = 1.455

19 + 11 - 1.455 - 7