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1 year ago

Find the area and perimeter

Mathematics

1 answer:

mihalych1998 [28]1 year ago

6 0

Answer:

Area=2232 square ft

Perimeter=206 ft

Step-by-step explanation:

given

the diagram is a rectangle

length=72 ft

width=31 ft

we know that

formula of the area of rectangle= length × width

Area=72×31 square ft

Area=2232 square ft

Now calculate the perimeter

perimeter of rectangle=2(length+width)

perimeter=2(72+31)

perimeter=2(103)

perimeter=206 ft

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Which of the following series are convergent?

Westkost [7]

Answer:

All of them

Step-by-step explanation:

According to the ratio test, for a series ∑aₙ:

If lim(n→∞) |aₙ₊₁ / aₙ| < 1, then ∑aₙ converges.

If lim(n→∞) |aₙ₊₁ / aₙ| > 1, then ∑aₙ diverges.

(I) aₙ = 10 / n!

lim(n→∞) |(10 / (n+1)!) / (10 / n!)|

lim(n→∞) |(10 / (n+1)!) × (n! / 10)|

lim(n→∞) |n! / (n+1)!|

lim(n→∞) |1 / (n+1)|

0 < 1

This series converges.

(II) aₙ = n / 2ⁿ

lim(n→∞) |((n+1) / 2ⁿ⁺¹) / (n / 2ⁿ)|

lim(n→∞) |((n+1) / 2ⁿ⁺¹) × (2ⁿ / n)|

lim(n→∞) |(n+1) / (2n)|

1/2 < 1

This series converges.

(III) aₙ = 1 / (2n)!

lim(n→∞) |(1 / (2(n+1))!) / (1 / (2n)!)|

lim(n→∞) |(1 / (2n+2)!) × (2n)! / 1|

lim(n→∞) |(2n)! / (2n+2)!|

lim(n→∞) |1 / ((2n+2)(2n+1))|

0 < 1

This series converges.

3 0

3 years ago

There is a total of $39.55. There are 3 times as many dimes as nickels, how many of each coin type was collected ?

katovenus [111]

Number of dimes collected is 339 and number of nickels collected is 113

Solution:

Given that There is a total of $39.55

There are 3 times as many dimes as nickels

To find: Number of dimes and nickels collected

Let "d" be the number of dimes collected

Let "n" be the number of nickels collected

We know that,

1 dime = $ 0.10

1 nickel = $ 0.05

From given information,

There are 3 times as many dimes as nickels

So, we get

Number of dimes = 3(number of nickels)

d = 3n

Given that there is total of $ 39.55

number of dimes collected x value of 1 dime + number of nickels collected x value of 1 nickel = $ 39.55

$3n \times 0.10 + n \times 0.05 = 39.55\\\\0.3n + 0.05n = 39.55\\\\0.35n = 39.55\\\\n = \frac{39.55}{0.35}\\\\n = 113$

Substitute n = 113 in d = 3n

$d = 3(113) = 339$

Summarizing the results:

number of dimes collected = 339

number of nickels collected = 113

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3 years ago

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leonid [27]

1 + 3i, - sqrt 10 would be the other two answers

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Nicole bought a mattress priced at $938. Shipping and handling cost an additional 27% of the price. What was the total cost of t

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3 years ago