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3 years ago

F(n) = -11 + 22(n = 1) Complete the recursive formula of f(n). f(1) = f(n) = f(n - 1)+

Mathematics

1 answer:

Maslowich3 years ago

7 0

Answer:

$f(n)=f(n-1)+22$ .

Step-by-step explanation:

Note: In the given function it should be (n-1) instead of (n=1).

Consider the given function is

$f(n)=-11+22(n-1)$

It is the explicit form of an A.P.

For $n=1$ ,

$f(1)=-11+22(1-1)=-11+0=-11$

For $n=2$ ,

$f(2)=-11+22(2-1)=-11+22=11$

Common difference is

$d=a_2-a_1=11-(-11)=11+11=22$

The recursive formula of an A.P. is

$f(n)=f(n-1)+d$

Substitute $d=22$ in the above formula.

$f(n)=f(n-1)+(22)$

$f(n)=f(n-1)+22$

Therefore, required recursive formula is $f(n)=f(n-1)+22$ .

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Let h(x)=20e^kx where k ɛ R (Picture attached. Thank you so much!)

zloy xaker [14]

Answer:

$k=0$

$\displaystyle \begin{aligned} 2k + 1& = 2\ln 20 + 1 \\ &\approx 2.3863\end{aligned}$

$\displaystyle \begin{aligned} k - 3&= \ln \frac{1}{2} - 3 \\ &\approx-3.6931 \end{aligned}$

Step-by-step explanation:

We are given the function:

$\displaystyle h(x) = 20e^{kx} \text{ where } k \in \mathbb{R}$

Given that h(1) = 20, we want to find k.

h(1) = 20 means that h(x) = 20 when x = 1. Substitute:

$\displaystyle (20) = 20e^{k(1)}$

Simplify:

$1= e^k$

Anything raised to zero (except for zero) is one. Therefore:

$k=0$

Given that h(1) = 40, we want to find 2k + 1.

Likewise, this means that h(x) = 40 when x = 1. Substitute:

$\displaystyle (40) = 20e^{k(1)}$

Simplify:

$\displaystyle 2 = e^{k}$

We can take the natural log of both sides:

$\displaystyle \ln 2 = \underbrace{k\ln e}_{\ln a^b = b\ln a}$

By definition, ln(e) = 1. Hence:

$\displaystyle k = \ln 2$

Therefore:

$2k+1 = 2\ln 2+ 1 \approx 2.3863$

Given that h(1) = 10, we want to find k - 3.

Again, this meas that h(x) = 10 when x = 1. Substitute:

$\displaystyle (10) = 20e^{k(1)}$

Simplfy:

$\displaystyle \frac{1}{2} = e^k$

Take the natural log of both sides:

$\displaystyle \ln \frac{1}{2} = k\ln e$

Therefore:

$\displaystyle k = \ln \frac{1}{2}$

Therefore:

$\displaystyle k - 3 = \ln\frac{1}{2} - 3\approx-3.6931$

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3 years ago

If you go out to eat with 3 friends and your meal was $72.50, there is 6.75% sales tax

netineya [11]

After the tax and the tip are counted, we conclude that each friend must pay $30.

<h3>How much should each person pay?</h3>

We know that the meal cost is $72.50.

Now, there is a 6.75% sales tax and a 15% tip on the waiter (we assume that the tip is based on the total meal cost, after the tax is applied).

Then the total meal cost is:

C = $72.50*( 1 + 6.75%/100%) = $72.50*(1 + 0.0675) = $77.39

Now we also need to add the tip, which is a 15% of that, so the total cost with the tip included is:

C' = $77.39*(1 + 15%/100%) = $88.998 = $90

(Where we rounded up).

Then, if there are 3 friends, each one must pay:

$90/3 = $30

Each friend must pay $30.

If you want to learn more about taxes:

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