Gabriel invested $4,500 at 4% interest, compounded quarterly (4 times a year). How much money would he have after 6 years?

The formula f(x + 1) = Two-thirds(f(x)) defines a geometric sequence where f(1) = 18. Which explicit formula can be used to mode

astraxan [27]

Answer:

The explicit formula is Tn = 18[(2/3)^(n-1)]

Where n is the term we are looking for

Step-by-step explanation:

Here, we want to get an explicit formula to model the equation

Now, F(2) = 2/3 * f1 = 2/3 * 18 = 12

F(3) = 2/3 * f(2) = 2/3 * 12 = 8

F(4) = 2/3 * F(3) = 2/3 * 8 = 16/3

F(5) = 2/3 * 16/3 = 32/9

Thus, seeing how the equations are progressing, we can definitely see a pattern.

That is Tn = (2/3)^(n-1)(18)

7 0

4 years ago

Help ASAP!!!

RideAnS [48]

Answer:

True

Step-by-step explanation:

4 0

3 years ago

Which definite integral approximation formula is this: the integral from a to b of f(x)dx ≈ (b-a)/n * [<img src="https://tex.z-d

Stella [2.4K]

The answer is most likely A.

The integration interval [a, b] is split up into n subintervals of equal length (so each subinterval has width (b - a)/n, same as the coefficient of the sum of y terms) and approximated by the area of n rectangles with base (b - a)/n and height y.

n subintervals require n + 1 points, with

x₀ = a

x₁ = a + (b - a)/n

x₂ = a + 2(b - a)/n

and so on up to the last point x = b. The right endpoints are x₁, x₂, … etc. and the height of each rectangle are the corresponding y 's at these endpoints. Then you get the formula as given in the photo.

• "Average rate of change" isn't really relevant here. The AROC of a function G(x) continuous* over an interval [a, b] is equal to the slope of the secant line through x = a and x = b, i.e. the value of the difference quotient

(G(b) - G(a) ) / (b - a)

If G(x) happens to be the antiderivative of a function g(x), then this is the same as the average value of g(x) on the same interval,

$g_{\rm ave}=\dfrac{G(b)-G(a)}{b-a}=\dfrac1{b-a}\displaystyle\int_a^b g(x)\,\mathrm dx$

(* I'm actually not totally sure that continuity is necessary for the AROC to exist; I've asked this question before without getting a particularly satisfying answer.)

• "Trapezoidal rule" doesn't apply here. Split up [a, b] into n subintervals of equal width (b - a)/n. Over the first subinterval, the area of a trapezoid with "bases" y₀ and y₁ and "height" (b - a)/n is

(y₀ + y₁) (b - a)/n

but y₀ is clearly missing in the sum, and also the next term in the sum would be

(y₁ + y₂) (b - a)/n

the sum of these two areas would reduce to

(b - a)/n = (y₀ + 2 y₁ + y₂)

which would mean all the terms in-between would need to be doubled as well to get

$\displaystyle\int_a^b f(x)\,\mathrm dx\approx\frac{b-a}n\left(y_0+2y_1+2y_2+\cdots+2y_{n-1}+y_n\right)$

7 0

3 years ago

Solve the following system of equations algebraically: 4x - 5y = 18 3x – 2y = 10

fiasKO [112]

Answer:

D

Step-by-step explanation:

Given the 2 equations

4x - 5y = 18 → (1)

3x - 2y = 10 → (2)

Multiplying (1) by 3 and (2) by - 4, then adding will eliminate the x- term

12x - 15y = 54 → (3)

- 12x + 8y = - 40 → (4)

Add (3) and (4) term by term to eliminate x, that is

- 7y = 14 ( divide both sides by - 7 )

y = - 2

Substitute y = - 2 into either of the 2 equations and solve for x

Substituting into (1)

4x - 5(- 2) = 18

4x + 10 = 18 ( subtract 10 from both sides )

4x = 8 ( divide both sides by 4 )

x = 2

solution is (2, - 2 ) → D

8 0

3 years ago

Solve the following equation for the variable x. ( 1/27 is a fraction )

igor_vitrenko [27]

The answer is,
$\frac{10935}{59048}$
Also equivalent to about, 0.185188.

5 0

3 years ago

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