All categories

2 years ago

What is the third term of the sequence described by the following explicit formula? an = 9 + (n - 1)8

Mathematics

1 answer:

worty [1.4K]2 years ago

6 0

Answer: Solve for a: a = $\frac{8n+1}{n}$

Solve for n: $n=\frac{1}{a-8}$

Step-by-step explanation:

solve for n: Move all terms to the left side and set them equal to zero. Then set each factor equal to zero.

solve for a: Divide each term in an = 9 + (n−1) ⋅ 8 by n and simplify.

You might be interested in

Determine the general solution of: sin 3x - sin x = cos2x

SpyIntel [72]

Sin³ x-sin x=cos ² x

we know that:
sin²x + cos²x=1 ⇒cos²x=1-sin²x
Therefore:

sin³x-sin x=1-sin²x
sin³x+sin²x-sin x-1=0

sin³x=z

z³+z²-z-1=0

we divide by Ruffini method:
1   1 -1 -1
1 1 2 1 z=1
-------------------------------------
1   2 1 0
-1   -1 -1 z=-1
--------------------------------------
1 1 0 z=-1

Therefore; the solutions are z=-1 and z=1

The solutions are:
if z=-1, then
sin x=-1   ⇒x= arcsin -1=π+2kπ (180º+360ºK) K∈Z

if z=1, then
sin x=1   ⇒ x=arcsin 1=π/2 + 2kπ (90º+360ºK) k∈Z

π/2 + 2kπ U   π+2Kπ=π/2+kπ k∈Z ≈(90º+180ºK)

Answer: π/2 + Kπ or 90º+180ºK K∈Z
Z=...-3,-2,-1,0,1,2,3,4....

6 0

3 years ago

Where are the black dots located?!!

Ludmilka [50]

-2, 2 and for the other 4,5

3 0

3 years ago

Read 2 more answers

A vertex of square is at(1,1) and its two parallel sides are y=x and y=x+1. find the equation of the remaining sides.Show your w

belka [17]

Answer:

$\displaystyle y = - x + 2$

$y = - x +1$

Step-by-step explanation:

we are given a vertex of a square i.e (1,1)

and the equations of the two parallel sides

notice that, the given vertex coordinates satisfy one of the parallel side i.e y=x which means that (1,1) points lie on one of Parallel sides

remember that,

every angles of a square is 90°

therefore,

we need to figure out the remaining Perpendicular line of the given Parallel sides so

let's figure out the perpendicular line of y=x line

recall that,

Parallel lines have the same slope thus

$\displaystyle m_{ \rm perpedicular} = - 1$

since we are given a vertex the equation of the perpendicular line should be

$\displaystyle y - 1 = - 1(x - 1)$

distribute:

$\displaystyle y - 1 = - x + 1$

add 1 to both sides:

$\displaystyle y = - x + 2$

to figure out the second perpendicular line we can consider the coordinates (0.5,0.5) of y=x equation

so the slope of the perpendicular line is -1

and the equation:

$y - 0.5 = - 1(x - 0.5)$

distribute:

$y - 0.5 = - x +0 .5$

add 0.5 to both sides:

$y = - x +1$

and we are done!

4 0

3 years ago

Convert the decimal 0.984 to a fraction. 984/100 984/1000 984/99 984/999

Ivan

The second one (984/1000)

8 0

3 years ago

Read 2 more answers

A geologist have two rocks on a scale that weighs 2 1/2 lbs together rock a was 1/7 of a the total weight how much did rock a we

katen-ka-za [31]

Simply get the product of 2 and 1/2 by 1/7.

firstly, let's convert the mixed fraction to "improper" and then multiply.

$\bf \stackrel{mixed}{2\frac{1}{2}}\implies \cfrac{2\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{5}{2}}\qquad \qquad \cfrac{5}{2}\cdot \cfrac{1}{7}\implies \stackrel{\textit{rock A weight}}{\cfrac{5}{14}}$

4 0

4 years ago