Write a recursive formula for each sequence given or described below.

Mathematics

1 answer:

valentinak56 [21]3 years ago

7 0

Answer:

$a_{n} =a_{n-1} +3000$ and a₁ =30000 for n = 2,3,4,5,6, ......

Step-by-step explanation:

Doug has joined a job with a starting salary of $30000 per year.

Hence, if a₁ is the salary of Doug in the first year, then

a₁ =30000

Now, each year Doug will receive a raise of $3000 in his salary.

Hence, in the 2nd year, his salary(a₂) will become ( a₁ +3000) per year.

Again, in the 3rd year, his salary(a₃) will become ( a₂ +3000) per year.

Therefor, in the similar manner the recursive formula for his salary in each year will be given as $a_{n} =a_{n-1} +3000$ and a₁ =30000 for n = 2,3,4,5,6, ...... {aₙ is the yearly salary of Doug in the nth year} (Answer)

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Justin cuts a 10-inch-long roll of cookie dough into 6 equal-length pieces. How many inches long is each piece of cookie dough?

mixas84 [53]

Answer: Each piece is 1 2/3 inch length.

Step-by-step explanation:

Total length of cookie dough =10-inch

Since it is being into divided into 6 equal-length pieces

We have that each piece will have=1 0-inch / 6 = 5/3 = 1 2/3 inch length.

6 0

3 years ago

The equation of a parabola is y=x^2-10x+27. Write the equation in vertex form

azamat

Answer:

$\large \boxed{y = (x - 5)^{2} + 2 }$

Step-by-step explanation:

y = x² - 10x + 27

y = ax² + bx + c

This is the general form of the equation for a parabola.

We must convert it to the vertex form

y = (x - h)² + k, where (h,k) are the coordinates of the vertex.

We can do this by completing the square.

$\begin{array}{rcll}y & = & x^{2} - 10x + 27 & \\y - 27 & = & x^{2} - 10x & \text{Subtracted 27 from each side}\\y - 27&= & x^{2} - 10x + 25 - 25 & \text{Added and subtracted (b/2)}^{2}\\y - 27&= & (x - 5)^{2} - 25 & \text{Wrote the first three terms as the square of a binomial}\\y& = & \mathbf{(x - 5)^{2} + 2} & \text{Added 27 to each side}\\\end{array}\\\text{The vertex form of the parabola is $\large \boxed{\mathbf{y = (x - 5)^{2} + 2 }}$}$ The figure below shows that your parabola has its vertex at (5,2).