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3 years ago

Write a recursive formula for the sequence -1,-2,-3,-4...

Mathematics

1 answer:

myrzilka [38]3 years ago

7 0

Answer:

f(1) = -1

f(n) = f(n-1) -1

Step-by-step explanation:

The first term is -1. Each term is 1 less than the previous. These equations say that.

f(1) = -1

f(n) = f(n-1) -1

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ICE Princess25 [194]

Answer

2 + 2 = 21

Step-by-step explanation:

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The diagram shows a triangle.The sizes of the angles, in degrees, arex 30Work out the value ofx.Diagram NOTaccurately drawn

Korvikt [17]

X=25 degrees

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3 years ago

The equation V = 16300 (0.94)^t represents the value (in dollars) of a car t years after its purchase. Use this equation to comp

Dafna1 [17]

Solution:

Given:

$V=16300(0.94)^t$

The value of a car after t - years will depreciate.

Hence, the equation given represents the value after depreciation over t-years.

To get the rate, we compare the equation with the depreciation formula.

$\begin{gathered} A=P(1-r)^t \\ \text{where;} \\ P\text{ is the original value} \\ r\text{ is the rate} \\ t\text{ is the time } \end{gathered}$

Hence,

$\begin{gathered} V=16300(0.94)^t \\ A=P(1-r)^t \\ \\ \text{Comparing both equations,} \\ P=16300 \\ 1-r=0.94 \\ 1-0.94=r \\ r=0.06 \\ To\text{ percentage,} \\ r=0.06\times100=6\text{ \%} \\ \\ \text{Hence, } \\ P\text{ is the purchase price} \\ r\text{ is the rate} \end{gathered}$

Therefore, the value of this car is decreasing at a rate of 6%. The purchase price of the car was $16,300.

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1 year ago

Let Ebe the set of all even positive integers in the universe Zof integers, and XE : Z R be the characteristic function of E.

AnnZ [28]

Answer:

$\mathbf{X_E (2) = 1}$

$\mathbf{X_E (-2) = 0 }$

$\mathbf{\{ x \in Z: X_E(x) = 1\} = E}$

Step-by-step explanation:

Let E be the set of all even positive integers in the universe Z of integers,

i.e

E = {2,4,6,8,10 ....∞}

$X_E : Z \to R$ be the characteristic function of E.

∴

$X_E(x) = \left \{ {{1 \ if \ x \ \ is \ an \ element \ of \ E} \atop {0 \ if \ x \ \ is \ not \ an \ element \ of \ E}} \right.$

For XE(2)

$\mathbf{X_E (2) = 1}$ since x is an element of E (i.e the set of all even numbers)

For XE(-2)

$\mathbf{X_E (-2) = 0 }$ since - 2 is less than 0 , and -2 is not an element of E

For { x ∈ Z: XE(x) = 1}

This can be read as:

x which is and element of Z such that X is also an element of x which is equal to 1.

∴

$\{ x \in Z: X_E(x) = 1\} = \{ x \in Z | x \in E\} \\ \\ \mathbf{\{ x \in Z: X_E(x) = 1\} = E}$

E = {2,4,6,8,10 ....∞}

5 0

3 years ago