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3 years ago

the larger of two numbers is eight more than the smaller number. their sum is twenty-two. find the number

Mathematics

1 answer:

lakkis [162]3 years ago

4 0

The bigger number is 15 and the smaller number 7. 15 is 8 more than 7. The sum of 15 and 7 is 22.

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A geometric sequence is defined by the equation an = (3)3 − n.

Delvig [45]

PART A

The geometric sequence is defined by the equation

$a_{n}=3^{3-n}$

To find the first three terms, we put n=1,2,3

When n=1,

$a_{1}=3^{3-1}$

$a_{1}=3^{2}$

$a_{1}=9$
When n=2,

$a_{2}=3^{3-2}$
$a_{2}=3^{1}$

$a_{2}=3$

When n=3

$a_{3}=3^{3-3}$

$a_{3}=3^{0}$
$a_{1}=1$
The first three terms are,

$9,3,1$

PART B

The common ratio can be found using any two consecutive terms.

The common ratio is given by,
$r= \frac{a_{2}}{a_{1}}$
$r = \frac{3}{9}$

$r = \frac{1}{3}$

PART C

To find
$a_{11}$

We substitute n=11 into the equation of the geometric sequence.

$a_{11} = {3}^{3 - 11}$

This implies that,

$a_{11} = {3}^{ - 8}$

$a_{11} = \frac{1}{ {3}^{8} }$

$a_{11}=\frac{1}{6561}$

4 0

3 years ago

25 points! pls show work if can!!!!!!!!

Nataliya [291]

Answer: 8.4

Step-by-step explanation:

15-6.6

3 0

3 years ago

Read 2 more answers

What does 25 over 144 + 1 equal

Brut [27]

Answer:

26/144

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Write -3r+3u in polar form PLEASE HELP

tamaranim1 [39]

We have that
 -3r+3u

Step 1
Use the distance formula to find the radius
r = √(x^2 + y^2)
(x,y)----------> (-3,3)
r= √(-3^2 + 3^2)=√18=3√2

Step 2
Use the tangent to find the angle
θ = arctan(y/x)
θ = arcTan(3/-3)= -45°-------> II Quadrant
then
θ=180-45=135°

Step 3
write in polar form
(x,y)------------> (r, θ)
so
(-3,3)----------> (3√2, 135°)

the answer is (3√2, 135°)

6 0

3 years ago

Jackson Middle School has 3 students in choir for every 1 student in band. If there are 52 students in band, how many students a

Monica [59]

Answer:

A. 156 students are in choir

Step-by-step explanation:

It states that for every 3 students in choir equals 1 student in band which give you the equation 1x3. So if band has 52 students then your new equation is 52x3 which is 156! Hope this helps!:)

6 0

3 years ago