All categories

2 years ago

Graph the six terms of a finite sequence where a1 = −6.25 and r = 1.25.

Mathematics

1 answer:

Virty [35]2 years ago

3 0

Answer:

Step-by-step explanation:

As per the question statement, a₁ is -6.25 and common ratio (r) is 1.25.

Therefore, the six terms of finite sequence would be as per the following equation $f(n) = a1(r)^{n-1}$ . Thus, the series would be

a1 = -6.25
a2 = -6.25*r = -6.25*(1.25) = -7.8125
a3 = -6.25*r^2 = -6.25*(1.25)^2 = -9.765625
a4 = -6.25*r^3 = -6.25*(1.25)^3 = -12.20703125
a5 = -6.25*r^4 = -6.25*(1.25)^4 = -15.2587890625
a6 = -6.25*r^5 = -6.25*(1.25)^5 = -19.073486328125

So the points on the graph will be on following points,

(1, -6.25), (2, -7.8125), (3, -9.765625), (4, -12.20703125), (5, -15.2587890625), (6, -19.073486328125).

The graph would look like as attached.

You might be interested in

How do I find the percent of budget?

ch4aika [34]

Answer:

First, subtract the budgeted amount from the actual expense. If this expense was over budget, then the result will be positive.

Next, divide that number by the original budgeted amount and then multiply the result by 100 to get the percentage over budget. If your expenses were lower than your budgeted amount, then this number will be negative, describing the percentage under budget.

6 0

2 years ago

Find the general solution of the following ODE: y' + 1/t y = 3 cos(2t), t > 0.

Margarita [4]

Answer:

y = 3sin2t/2 - 3cos2t/4t + C/t

Step-by-step explanation:

The differential equation y' + 1/t y = 3 cos(2t) is a first order differential equation in the form y'+p(t)y = q(t) with integrating factor I = e^∫p(t)dt

Comparing the standard form with the given differential equation.

p(t) = 1/t and q(t) = 3cos(2t)

I = e^∫1/tdt

I = e^ln(t)

I = t

The general solution for first a first order DE is expressed as;

y×I = ∫q(t)Idt + C where I is the integrating factor and C is the constant of integration.

yt = ∫t(3cos2t)dt

yt = 3∫t(cos2t)dt ...... 1

Integrating ∫t(cos2t)dt using integration by part.

Let u = t, dv = cos2tdt

du/dt = 1; du = dt

v = ∫(cos2t)dt

v = sin2t/2

∫t(cos2t)dt = t(sin2t/2) + ∫(sin2t)/2dt

= tsin2t/2 - cos2t/4 ..... 2

Substituting equation 2 into 1

yt = 3(tsin2t/2 - cos2t/4) + C

Divide through by t

y = 3sin2t/2 - 3cos2t/4t + C/t

Hence the general solution to the ODE is y = 3sin2t/2 - 3cos2t/4t + C/t

3 0

3 years ago

Just help me out with this polynomial i need help <br> { -m^{2} + 6} + { -4m^{2} + 7m + 2} =

PolarNik [594]

Answer:

$-5m^2+7m+8$

Step-by-step explanation:

Here, we add up two polynomials shown.

The polynomials are:

$[-m^2 + 6]+[-4m^2 +7m + 2]$

In order to add up the 2 polynomials shown, we have to see the "like terms" and add them up.

We add up the " $m^2$ " terms and the constant (number) terms. There is one term with "m", so we leave it like that. Let's add up. Shown below:\

$[-m^2 + 6]+[-4m^2 +7m + 2]\\=-m^2-4m^2+6+2+7m\\=-5m^2+7m+8$

This is the sum of the 2 polynomials shown: $-5m^2+7m+8$

7 0

3 years ago

What is the volume of the cylinder below? A cylinder with a height of 12 millimeters and diameter of 18 millimeters. 108 pi mm3

Artemon [7]

Answer:

V =972 pi mm ^3

Step-by-step explanation:

The diameter is 18 so the radius is 1/2 of the diameter

18/2 = 9

r=9

The volume of a cylinder is

V = pi r^2 h

V = pi (9)^2 12

V =972 pi mm ^3

8 0

2 years ago

Read 2 more answers

After Friday's footbal game, Alana and her friends go out for ice cream. They share mega mountains sundae and finished the whole

Mrrafil [7]

What’s the question

6 0

2 years ago