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Elenna [48]
3 years ago
10

Write a rule for the nth term of the sequence 37, 32, 27, 22, . . . .

Mathematics
1 answer:
Radda [10]3 years ago
5 0

Answer:

a(n) = 37 - 5(n -1)

Step-by-step explanation:

Notice that each new term is obtained by subtracting 5 from the previous term.  Thus, this is an arithmetic sequence with common difference -5 and first term 37.

The explicit formula for the nth term is a(n) = a(1) - 5(n - 1) =  37 - 5(n -1)

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A candle in the shape of a circular cone has a base of radius r and a height of h that is the same length as the radius. which e
ladessa [460]

Answer:

\frac{r(1-\sqrt{2})}{-3}

Step-by-step explanation:

Volume of cone = \frac{1}{3} \pi r^{2} h

Since we are given that a circular cone has a base of radius r and a height of h that is the same length as the radius

                          = \frac{1}{3} \pi r^{2} \times r

                          = \frac{1}{3} \pi r^{3}

Surface area of cone including 1 base = \pi r^{2} +\pi\times r \times \sqrt{r^2+h^2}

Since r = h

So, area = \pi r^{2} +\pi\times r \times \sqrt{r^2+r^2}

              = \pi r^{2} +\pi\times r \times \sqrt{2r^2}

              = \pi r^{2} +\pi\times r^2 \times \sqrt{2}

Ratio of volume of cone to its surface area including base :

\frac{\frac{1}{3} \pi r^{3}}{\pi r^{2} +\pi\times r^2 \times \sqrt{2}}

\frac{\frac{1}{3}r}{1+\sqrt{2}}

\frac{r}{3(1+\sqrt{2})}

Rationalizing

\frac{r}{3(1+\sqrt{2})} \times \frac{1-\sqrt{2}}{1-\sqrt{2}}

\frac{r(1-\sqrt{2})}{-3}

Hence the ratio the ratio of the volume of the candle to its surface area(including the base) is \frac{r(1-\sqrt{2})}{-3}

8 0
3 years ago
Read 2 more answers
How many gallons are in 48 pints?
vlabodo [156]

Answer:

6

Step-by-step explanation:

6 0
3 years ago
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Toni and Jade live on the same street as the Middle School. Toni lives 6.1
Nataly_w [17]

Answer:

Jade and Toni are 58.1 miles apart from each other.

Step-by-step explanation:

All you have to do is add the distances.

52 + 6.1 = 58.1

5 0
3 years ago
A business rents cars for $100 a day and vans for $200 a day. One day, it rented a total of 22 vehicles
ra1l [238]

Answer:

Vans - 7

Cars - 15

Step-by-step explanation:

$200 * 7 = $1400

$100 * 15 = $1500

$1400 + $1500 = $2900

8 0
2 years ago
What is the correct answer
krek1111 [17]

Answer:

3x - 9 - (6 / (x+4))

Step-by-step explanation:

               3x - 9

              |----------------------------------------

(x +4)       | (3x^2 + 3x - 42 )

                 3x^2 + 12x

           ------------------------------

                          -9x - 42

                          -9x - 36

-----------------------------------

                                 - 6

Answer: 3x - 9 - (6 / (x+4))

8 0
3 years ago
Read 2 more answers
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