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3 years ago

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

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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You want to go to the skate park, and you have two options:

Tcecarenko [31]

Answer:

See Explanation

Step-by-step explanation:

<u>Define the variables</u>

Let the entry fee be c and the hourly rate be m

Let the number of hours be x and the total amount be y

<u>Work to solve</u>

For Sami's skate

$c = 6$ and $m = 2$

For Brad's skate

$c =10$ and $m = 1$

<u>The equations</u>

The equation is derived using: $y = mx + c$

For Sami's skate

$y = 2x + 6$

For Brad's skate

$y = x + 10$

<u>When the cost are the same</u>

To do this, we equate both expressions

i.e.

$y = y$

$2x + 6 = x + 10$

$2x -x = 10 - 6$

$x = 4$

i.e. the cost are the same at the 4th hour

<u>What is the cost</u>

Substitute 4 for x in any of the equations

$y = x + 10$

$y = 4 + 10$

$y = 14$

<em>The cost is $14.00</em>

3 0

2 years ago

In a right –angled triangle, the length of hypotenuse and shorter sides are 13 cm and 5 cm respectively. Work out the other side

stellarik [79]

Answer: The other side is 12 cm.

Step-by-step explanation:

$a^{2} + b^{2} = c^{2}$
$a^{2} + (5)^{2} = (13)^{2}$
$a^{2} + 25 = 169$
$a^{2} = 144$
$a = \sqrt{144}$
$a = 12$

7 0

3 years ago

The U.S. Energy Information Administration (US EIA) reported that the average price for a gallon of regular gasoline is $3.94 (U

tekilochka [14]

Answer:

a) 25

b) 49

c) 97

Step-by-step explanation:

The sample size is calculated using the formula, n = $(\frac{\sigma\times z}{\textup{Margin of error}})^2$

Now,

for 95% confidence level value of z-factor = 1.96

Given:

Mean = $3.94

standard deviation = $0.25

thus,

a) for margin of error = $0.10

n = $(\frac{\sigma\times z}{\textup{Margin of error}})^2$

or

n = $(\frac{0.25\times1.96}{\textup{0.10}})^2$

or

n = 4.9²

or

n = 24.01 ≈ 25 (Rounded off to next integer)

b) for margin of error = $0.07

n = $(\frac{\sigma\times z}{\textup{Margin of error}})^2$

or

n = $(\frac{0.25\times1.96}{\textup{0.07}})^2$

or

n = 7²

or

n = 49

c) for margin of error = $0.05

n = $(\frac{\sigma\times z}{\textup{Margin of error}})^2$

or

n = $(\frac{0.25\times1.96}{\textup{0.05}})^2$

or

n = 9.8²

or

n = 96.04 ≈ 97 (Rounded off to next integer)

6 0

3 years ago

You're planning to buy a boat, a motor, and some miscellaneous boating equipment. The boat costs $325, the motor costs $225, and

arlik [135]

325 + 225 + 79 = 629
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= A. $191

7 0

3 years ago

The radius of a circle measures 12 centimeters what is the area

Andrej [43]

Answer:

$144\pi$

Step-by-step explanation:

$\pi(r^{2} )$

$\pi(12^{2} )$

$144\pi$

7 0

2 years ago