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4 years ago

7

A new freezer costs $500 plus $0.20 a day to operate. An old freezer costs $20 plus $0.50 a day to operate. After how many days

is the cost of operating each freezer the same?

1 answer:

Aleks [24]4 years ago

8 0

The answer is 1600 days!!!!

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The distance along a circle between two<br>points on the circle

GarryVolchara [31]

Answer:Diameter

Step-by-step explanation:The diameter is how far away one point on a circle is from another point straight across on a circle.

8 0

3 years ago

Read 2 more answers

The first, third and thirteenth terms of an arithmetic sequence are the first 3 terms of a geometric sequence. If the first term

Salsk061 [2.6K]

Answer:

The first three terms of the geometry sequence would be $1$ , $5$ , and $25$ .

The sum of the first seven terms of the geometric sequence would be $127$ .

Step-by-step explanation:

<h3>1.</h3>

Let $d$ denote the common difference of the arithmetic sequence.

Let $a_1$ denote the first term of the arithmetic sequence. The expression for the $n$ th term of this sequence (where $n\!$ is a positive whole number) would be $(a_1 + (n - 1)\, d)$ .

The question states that the first term of this arithmetic sequence is $a_1 = 1$ . Hence:

The third term of this arithmetic sequence would be $a_1 + (3 - 1)\, d = 1 + 2\, d$ .
The thirteenth term of would be $a_1 + (13 - 1)\, d = 1 + 12\, d$ .

The common ratio of a geometric sequence is ratio between consecutive terms of that sequence. Let $r$ denote the ratio of the geometric sequence in this question.

Ratio between the second term and the first term of the geometric sequence:

$\displaystyle r = \frac{1 + 2\, d}{1} = 1 + 2\, d$ .

Ratio between the third term and the second term of the geometric sequence:

$\displaystyle r = \frac{1 + 12\, d}{1 + 2\, d}$ .

Both $(1 + 2\, d)$ and $\left(\displaystyle \frac{1 + 12\, d}{1 + 2\, d}\right)$ are expressions for $r$ , the common ratio of this geometric sequence. Hence, equate these two expressions and solve for $d$ , the common difference of this arithmetic sequence.

$\displaystyle 1 + 2\, d = \frac{1 + 12\, d}{1 + 2\, d}$ .

$(1 + 2\, d)^{2} = 1 + 12\, d$ .

$d = 2$ .

Hence, the first term, the third term, and the thirteenth term of the arithmetic sequence would be $1$ , $(1 + (3 - 1) \times 2) = 5$ , and $(1 + (13 - 1) \times 2) = 25$ , respectively.

These three terms ( $1$ , $5$ , and $25$ , respectively) would correspond to the first three terms of the geometric sequence. Hence, the common ratio of this geometric sequence would be $r = 25 /5 = 5$ .

<h3>2.</h3>

Let $a_1$ and $r$ denote the first term and the common ratio of a geometric sequence. The sum of the first $n$ terms would be:

$\displaystyle \frac{a_1 \, \left(1 - r^{n}\right)}{1 - r}$ .

For the geometric sequence in this question, $a_1 = 1$ and $r = 25 / 5 = 5$ .

Hence, the sum of the first $n = 7$ terms of this geometric sequence would be:

$\begin{aligned} & \frac{a_1 \, \left(1 - r^{n}\right)}{1 - r}\\ &= \frac{1 \times \left(1 - 2^{7}\right)}{1 - 2} \\ &= \frac{(1 - 128)}{(-1)} = 127 \end{aligned}$ .

7 0

3 years ago

The base of a circular fence with radius 10 m is given by x = 10 cost, y = 10 sin t. the height of the fence at position (x, y)

antiseptic1488 [7]

The parametric equations for x and y describe a circle of radius 10 m, so the length of the base of the fence is the length of the circumference of a circle of radius 10 m. The formula for that circumference (C) is ...

... C = 2πr

... C = 2π·(10 m) = 20π m

The height as a function of angle (t) is found by substituting for x and y.

... h(t) = h(x(t), y(t)) = 4 + 0.01·((10cos(t))²-)10sin(t))²) = 4+cos(2t)

The average value of this over the range 0 ≤ t ≤ 2π is 4, since the cosine function has two full cycles in that range, and its average value over a cycle is zero.

Thus, the area of one side of the fence is that of a rectangle 20π m long and 4 m wide. That will be

... (20π m)·(4 m) = 80π m²

The amount of paint required to cover both sides of the fence is

... 2×(80π m²)×(1 L)/(10 m²) = 16π L ≈ 50.3 L

_____

You can work out the integral for area as a function of t. When you do, you will find it gives this same result.

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3 years ago

The number of typographical errors in a document follows a Poisson distribution with a mean of 3 errors per page. Let X represen

n200080 [17]

Answer:

probability of x is 0.22 correct to two decimal places

Step-by-step explanation:

step 1. use the poisson formula given as

p(x) = (λˣe∧-λ) ÷x! where λ is the mean and it called lambda,λ = 3, e is mathematical constant and it approximately = 2.7183, x is the chosen value which is equal to 2, Λ is raise to power, ! is factorial sign

p(x=2) =( 3² x 2.7183⁻³) ÷ 2! = 0.22

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3 years ago

Find the real solutions of the following equation.<br> If K= x + 1/x-1 <br> and k^2- k=20, find x.

ser-zykov [4K]

X
=
k
2
+
1
2
First one……..

4 0

3 years ago