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3 years ago

Write a recursive rule for an= Зn — 6.

Mathematics

1 answer:

mart [117]3 years ago

8 0

Answer:

Explicit formula: a(n)=3n-6

Recursive formula: a(n)=-3+(n-1)3 <--

Step-by-step explanation:

a(n)=3n-6 where a(1)=3(1)-6=-3 and d=3

<u>Plug values into recursive formula:</u>

a(n)=a1+(n-1)d

a(n)=-3+(n-1)3

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Suppose we want to express the point (2,3) in R2 as the solution space of a linear system of equations. (a) What is the smallest

kow [346]

Answer:

Step-by-step explanation:

Smallest number of equations required are:

$N=2(forR^2)$

Let equations are

$2x+3y=13\\7x+y=17$

Yes we can add one more equation

We can add infinite such equations so that solution remains same.

General form of such equations are called inconsistent equations

6 0

4 years ago

Find the solution of the differential equation that satisfies the given initial condition. y' tan x = 3a + y, y(π/3) = 3a, 0 &lt

Paladinen [302]

Answer:

$y(x)=4a\sqrt{3}* sin(x)-3a$

Step-by-step explanation:

We have a separable equation, first let's rewrite the equation as:

$\frac{dy(x)}{dx} =\frac{3a+y}{tan(x)}$

But:

$\frac{1}{tan(x)} =cot(x)$

So:

$\frac{dy(x)}{dx} =cot(x)*(3a+y)$

Multiplying both sides by dx and dividing both sides by 3a+y:

$\frac{dy}{3a+y} =cot(x)dx$

Integrating both sides:

$\int\ \frac{dy}{3a+y} =\int\cot(x) \, dx$

Evaluating the integrals:

$log(3a+y)=log(sin(x))+C_1$

Where C1 is an arbitrary constant.

Solving for y:

$y(x)=-3a+e^{C_1} sin(x)$

$e^{C_1} =constant$

So:

$y(x)=C_1*sin(x)-3a$

Finally, let's evaluate the initial condition in order to find C1:

$y(\frac{\pi}{3} )=3a=C_1*sin(\frac{\pi}{3})-3a\\ 3a=C_1*\frac{\sqrt{3} }{2} -3a$

Solving for C1:

$C_1=4a\sqrt{3}$

Therefore:

$y(x)=4a\sqrt{3}* sin(x)-3a$

3 0

4 years ago

write the equation of the line perpendicular to 3x + y = 4, containing the point (-6, -1). Write in slope intercept form.

Advocard [28]

First thing you need to do is find the slope. The slope must be opposite in sign and flipped.

4 0

3 years ago

Read 2 more answers

What do the arrows and coefficients in equations communicate.

jok3333 [9.3K]

Step-by-step explanation:

arrows mean

an example:

6>5

what ever the arrows pointing at is smaller than the othernumber

8 0

3 years ago

A rectangular bathroom floor is covered with square tiles that are 1 1/2 feet by 1 1/2 feet. The length of the bathroom floor is

kenny6666 [7]

Answer:

The number of square tiles required to cover the bathroom floor is approximately 31.

Step-by-step explanation:

The dimensions of the rectangular floor of the bathroom are:

Length = 10.5 ft.

Breadth = 6.5 ft.

The dimensions of the square tiles are:

Side = 1.5 ft.

The area of the rectangular floor of the bathroom is:

$Area\ of Bathroom\ floor=Length\times Breadth\\=10.5\times6.5\\=68.25$

The area of 1 square tile:

$Area\ of\ 1\ square\ tile=(SIde)^{2}\\=(1.5)^{2}\\=2.25$

The number of tiles required to cover the bathroom floor is:

$Number\ of\ tiles=\frac{Area\ of\ bathroom\ floor}{Area\ of\ 1\ square\ tile} \\=\frac{68.25}{2.25}\\ =30.3333\\\approx31$

Thus, the number of square tiles required to cover the bathroom floor is approximately 31.

6 0

3 years ago