All categories

3 years ago

Write a rule for the nth term of the arithmetic sequence. d =1/2 , a6 =18.

Mathematics

1 answer:

Blizzard [7]3 years ago

4 0

Answer:

$a_{n}$ = $\frac{1}{2}$ n + 15

Step-by-step explanation:

The n th term of an arithmetic sequence is

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₆ = 18 and d = $\frac{1}{2}$ , then

a₁ + 5d = 18 , that is

a₁ + $\frac{5}{2}$ = 18 ( subtract $\frac{5}{2}$ from both sides )

a₁ = $\frac{31}{2}$

Thus

$a_{n}$ = $\frac{31}{2}$ + $\frac{1}{2}$ (n - 1) = $\frac{15}{2}$ + $\frac{1}{2}$ n - $\frac{1}{2}$ = $\frac{1}{2}$ n + 15

You might be interested in

Traci wants to buy rings that cost 50$ each. A jewler is offering a deal in which you buy 1 ring and get the 2nd for 25% off and

Rina8888 [55]

The first ring is $50, the second ring is 37.50 and the third ring is 25.00
The total of the rings before tax is 112.50 and $121.50 after tax

3 0

3 years ago

Você é um comandante de uma espaçonave. Sua missão é chegar até Alfa Centauro em cinco anos. A distância do Sol até Alfa Centaur

Deffense [45]

Answer:

The spaceship will get to Alpha Centaur in time

Step-by-step explanation:

<u><em>The complete question in English is</em></u>

You're the commander of a spaceship. Your mission is to reach Alpha Centaur in five years. The distance from the sun to Alpha Centaur is 2.5 x 10^13 miles. The distance from Earth to Sun is approximately 9.3 x 10^7

miles. Your spaceship can travel at the speed of light. You know that light can travel a distance of 5.88 x 10^12 miles in a year. Can you get to Alpha Centaur in time?

step 1

Find the time it takes for the spaceship to travel from Earth to the Sun

The distance from the Earth to Sun is equal to

$9.3*10^7\ miles$

The spaceship can travel at the speed of light

The light can travel a distance of $5.88*10^{12}\ miles$ in a year

using a proportion

$\frac{5.88*10^{12}\ miles}{1\ year}=\frac{9.3*10^7\ miles}{x}\\\\x=(9.3*10^7)/5.88*10^{12}\\\\x=1.58*10^{-5} \ years$

This time is very small in years

Convert to minutes

$1.58*10^{-5} \ years=1.58*10^{-5} (365)(24)(60)=8.3\ min$

step 2

Find the time it takes for the spaceship to travel from the Sun to Alpha Centaur

The distance from the the Sun to Alpha Centaur is equal to

$2.5*10^{13}\ miles$

The spaceship can travel at the speed of light

The light can travel a distance of $5.88*10^{12}\ miles$ in a year

using a proportion

$\frac{5.88*10^{12}\ miles}{1\ year}=\frac{2.5*10^{13}\ miles}{x}\\\\x=(2.5*10^{13})/5.88*10^{12}\\\\x=4.25\ years$

$4.25\ years< 5\ years$

therefore

The spaceship will get to Alpha Centaur in time

3 0

3 years ago

Write the expression using rational exponents. Then simplify and convert back to radical notation.

ioda

Answer:

The radical notation is $3x\sqrt[3]{y^2z}$

Step-by-step explanation:

Given

$\sqrt[3]{27 x^{3} y^{2} z}$

Step 1 of 1

Write the expression using rational exponents.

$\sqrt[n]{a^{m}}=\left(a^{m}\right)^{\frac{1}{n}}$

$=a^{\frac{m}{n}}:\left({27 x^{3} y^{2} z})^{\frac{1}{3}}$

$(a \cdot b)^{r}=a^{r} \cdot b^{r}:(27)^{\frac{1}{3}}\left(x^{3}\right)^{\frac{1}{3}} \cdot\left(y^{2}\right)^{\frac{1}{3}} \cdot(z)^{\frac{1}{3}}$

$=$(3^3)^{\frac{1}{3}}\left(x^{3}\right)^{\frac{1}{3}} \cdot\left(y^{2}\right)^{\frac{1}{3}} \cdot(z)^{\frac{1}{3}}$$

$=\left(3\right)\left(x}\right)} \cdot\left(y}\right)^{\frac{2}{3}} \cdot(z)^{\frac{1}{3}}$

$=3x \cdot(y)^{\frac{2}{3}} \cdot(z)^{\frac{1}{3}}$

Simplify $3 x \cdot(y)^{\frac{2}{3}} \cdot(z)^{\frac{1}{3}}$

$=3 x \sqrt[3]{y^{2} z}$

Learn more about radical notation, refer :

brainly.com/question/15678734

4 0

3 years ago

Pls help ??????????????

blagie [28]

The picture is cutted off

4 0

3 years ago

Read 2 more answers

Can i please have help with number 6

Allisa [31]

Length of the diameter = sqrt ( (-12- (-8)^2) +(2-0)^2) )
= sqrt (16 + 4) = sqrt20
so radius = sqrt 20 / 2 = sqrt5
so r^2 = 5

Center of the circle = coordinates of the midpoint of the diameter =

-8-12/2 , 2-0 / 2 = (-10, 1)

(x - a)^2 + (y - b)^2 = r^2 is general form of a circle so here the circle is:_

(x + 10)^2 + (y - 1)^2 = 5 Answer

Its B

7 0

3 years ago