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3 years ago

Find a formula for the general term of the sequence, assuming that the pattern of the first few terms continues. 2, 9, 16, 23

2 answers:

5 0

This is an arithmetic sequence which means all of these terms are all the same distance from one another.
an=a1+d(n-1)
an=2+7(n-1)
an=2+7n-7
Answer: an=7n-5

musickatia [10]3 years ago

3 0

It increases by 7 and it's arithmetic progression:
Where d = 7
a = 2

and the formula will be

$a_{n}$ = a + d (n-1) = 2 + 7*(n-1)

Where n starts from 1 and continues to the infinity

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Simplify csc(-x) /1+tan^2(x)

ruslelena [56]

$\frac{-x}{1+\tan^{2}(x)}=-\frac{\cos(x)^{2}}{\sin(x)}.$

5 0

3 years ago

Select all ratios that are equivalent to 4/8.

Elena-2011 [213]

Answer:

6/12

10/20

5/10

1/2

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

Given P = x^0.3 y^0.7 is the chicken lay eggs production function, where P is the number of eggs lay, x is the number of workers

lora16 [44]

Answer:

Part A)

$\displaystyle \frac{dy}{dx}=-\frac{3}{7}P^\frac{10}{7}x^{-\frac{10}{7}}$

Part B)

The daily operating cost decreases by about $143 per extra worker.

Step-by-step explanation:

We are given the equation:

$\displaystyle P=x^{\frac{3}{10}}y^{\frac{7}{10}}$

Where P is the number of eggs laid, x is the number of workers, and y is the daily operating budget (assuming in US dollars $).

We want to find dy/dx.

So, let’s find our equation in terms of x. We can raise both sides to 10/7. Hence:

$\displaystyle P^\frac{10}{7}=\Big(x^\frac{3}{10}y^\frac{7}{10}\Big)^\frac{10}{7}$

Simplify:

$\displaystyle P^\frac{10}{7}=x^\frac{3}{7}y$

Divide both sides by the x term to acquire:

$\displaystyle y=P^\frac{10}{7}x^{-\frac{3}{7}}$

Take the derivative of both sides with respect to x:

$\displaystyle \frac{dy}{dx}=\frac{d}{dx}\Big[P^\frac{10}{7}x^{-\frac{3}{7}}\Big]$

Apply power rule. Note that P is simply a constant. Hence:

$\displaystyle \frac{dy}{dx}=P^\frac{10}{7}(-\frac{3}{7})(x^{-\frac{10}{7}})$

Simplify. Hence, our derivative is:

$\displaystyle \frac{dy}{dx}=-\frac{3}{7}P^\frac{10}{7}x^{-\frac{10}{7}}$

Part B)

We want to evaluate the derivative when x is 30 and when y is $10,000.

First, we will need to find P. Our original equations tells us that:

$P=x^{0.3}y^{0.7}$

Hence, at x = 30 and at y = 10,000, P is:

$P=(30)^{0.3}(10000)^{0.7}$

Therefore, for our derivative, we will have:

$\displaystyle \frac{dy}{dx}=-\frac{3}{7}\Big(30^{0.3}(10000^{0.7})\Big)^\frac{10}{7}\Big(30^{-\frac{10}{7}}\Big)$

Use a calculator. So:

$\displaystyle \frac{dy}{dx}=-\frac{1000}{7}=-142.857142...\approx-143$

Our derivative is given by dy/dx. So, it represents the change in the daily operating cost over the change in the number of workers.

So, when there are 30 workers with a daily operating cost of $10,000 producing a total of about 1750 eggs, the daily operating cost decreases by about $143 per extra worker.

5 0

2 years ago

The Sunday Times had 14 sections with an average of 16 pages per section. How many pages were in the entire newspaper?

Gennadij [26K]

Answer:

224 pages total

Step-by-step explanation:

To find how many total pages, you have to multiply the number of sections by the number of pages in each section. 14 sections times 16 pages per section equals a total of 224 total pages.

7 0

3 years ago

Please check my answer : Find the equation of the line that has a slope of 8 and passes through the point (-3,4). I got y=8x-20

Paladinen [302]

The answer is y = -8x - 20. If you were to use y = 8x - 20 then you'd get 4 = -44, which, obviously, is not true. To fix it all you need to do is add a negative sign in front of the 8. y = -8x - 20.

7 0

3 years ago