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2 years ago

A recursive function is shown below:

1 answer:

Ber [7]2 years ago

8 0

$f(1)=\fbox2\ and\ f(n)=f(n-1)-5\\\underline{f(2)}=f(2-1)-5=f(1)-5=2-5=\fbox{-3}\\\underline{\underline{f(3)}}=f(3-1)-5=\underline{f(2)}-5=-3-5=\boxed{-8}\\f(4)=f(4-1)-5=\underline{\underline{f(3)}}-5=-8-5=\boxed{-13}\\\vdots\\Answer:\boxed{\boxed{2;-3;-8;-13;-18;...}\leftarrow answer}$

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At the ice cream parlor there are thirty flavors, but for the last week they have only had 25 flavors.

myrzilka [38]

Answer: Percent change = 20%

===========================================================

Work Shown:

A = old value = 25 (last week's number)

B = new value = 30 (current week's number)

C = percent change

C = [ (B-A)/A ] * 100%

C = [ (30-25)/25 ] * 100%

C = [ 5/25 ] * 100%

C = 0.20* 100%

C = 20%

The percent change is 20%

The positive value of C indicates we have a percent increase.

8 0

2 years ago

How do I differentiate this?

disa [49]

Answer:

$\frac{8}{\left(-x+2\right)^2}$ & $x = 1, x = 3$

Step-by-step explanation:

I'm sure you are familiar with the product rule,

If y = u*v => dy/dx = u * dv/dx + v * dy/dx <----- product rule

In this case:

$u=3x+2,\:v=\left(2-x\right)^{-1},\\=>\frac{d}{dx}\left(3x+2\right)\left(2-x\right)^{-1}+\frac{d}{dx}\left(\left(2-x\right)^{-1}\right)\left(3x+2\right)$

Now remember the sum rule:

$\frac{d}{dx}\left(3x+2\right) = \frac{d}{dx}\left(3x\right)+\frac{d}{dx}\left(2\right),\\\frac{d}{dx}\left(3x\right) = 3,\\\frac{d}{dx}\left(2\right) = 0\\\frac{d}{dx}\left(3x+2\right) = 3$

For this second bit we apply the chain rule:

$\frac{d}{dx}\left(\left(2-x\right)^{-1}\right) = -\frac{1}{\left(2-x\right)^2}\frac{d}{dx}\left(2-x\right),\\\frac{d}{dx}\left(2-x\right) = -1,\\\\=> -\frac{1}{\left(2-x\right)^2}\left(-1\right)\\=> \frac{1}{\left(2-x\right)^2}$

If we substitute these values back into the expression... $\frac{d}{dx}\left(3x+2\right)\left(2-x\right)^{-1}+\frac{d}{dx}\left(\left(2-x\right)^{-1}\right)\left(3x+2\right)$

...we get the following:

$3\left(2-x\right)^{-1}+\frac{1}{\left(2-x\right)^2}\left(3x+2\right)$

The rest is just pure simplification:

$3\left(2-x\right)^{-1}+\frac{1}{\left(2-x\right)^2}\left(3x+2\right)\\= \frac{3}{-x+2}+\frac{3x+2}{\left(-x+2\right)^2}\\= \frac{3\left(-x+2\right)}{\left(-x+2\right)^2}+\frac{3x+2}{\left(-x+2\right)^2}\\\\= \frac{3\left(-x+2\right)+3x+2}{\left(-x+2\right)^2}\\\\= \frac{8}{\left(-x+2\right)^2}$

Now let's equate this to equal 8 for the second bit and solve for x:

$\frac{8}{\left(-x+2\right)^2}=8,\\\frac{8}{\left(-x+2\right)^2}\left(-x+2\right)^2=8\left(-x+2\right)^2,\\8=8\left(-x+2\right)^2,\\\left(-x+2\right)^2=1,\\x = 1, x = 3$

4 0

2 years ago

Evaluate the determinant for the following matrix: 1 4 4 5 2 2 1 5 5

Elina [12.6K]

A Laplace expansion along the first row gives

$\begin{vmatrix}1&4&4\\5&2&1\\1&5&5\end{vmatrix}=1\begin{vmatrix}2&1\\5&5\end{vmatrix}-4\begin{vmatrix}5&1\\1&5\end{vmatrix}+4\begin{vmatrix}5&2\\1&5\end{vmatrix}$
$=1(10-5)-4(25-1)+4(25-2)$
$=1$

7 0

3 years ago

Write an expression for "8 times z."

garri49 [273]

Answer: 8z 8(z)

Explanation: well 8 times z is simply 8(z)I don’t really think there is another way

5 0

2 years ago

Will give brainlest answer pls help!

mojhsa [17]

You can use 2 step equations to solve real-world problems by assessing the situation, trial and error, As in for example;
if you cannot open a twist off bottle cap by turning it to the right. You have two options twisted to the left to loosen or turn it to the right and not open it”

“ Lefty Lucy righty tightly”

Or if you are married and your husband cheats on you you can do one or two of the following stay or a go

For example stay and be an idiot or go and love yourself and take everything he has

8 0

3 years ago