How to write this in radical form

What is the value of the midpoint of AB on a

guapka [62]

Answer:

-14

Step-by-step explanation:

point AB = -23-5 /2 = -14

3 0

3 years ago

For the Sequence 2,6,10,14. Write the recursive rule, and a explicit rule

Evgen [1.6K]

Answer:

The recursive formula for given series is: $a_{n} = a_{n-1} + 4$

The explicit formula is given by: $a_{n} = 10 + 5(n-1)$

Step-by-step explanation:

Determining the Recursive Formula:

As the given sequence is: 2,6,10,14

The difference d can be computed by taking the difference between the consecutive terms of the mentioned sequence.

d = 6 -2 = 10 - 6 = 14 - 10 = 4

It is observed that the difference between the consecutive terms remains constant) with common difference d = 4
We know that if the difference between the consecutive terms remains constant), then the series is in arithmetic series. The recursive formula is: $a_{n} = a_{n-1} + d$

So, the recursive formula for given series is: $a_{n} = a_{n-1} + 4$

Determining the Explicit Rule or Formula:

An explicit formula defines the nth term of the sequence, where n being the term's location. In other words, a sequence can be defined as a formula in terms of n. So,

First determine the sequence whether the sequence is in arithmetic. As we know that 2,6,10,14 is in arithmetic.
Then find the common difference. Here, d = 6 -2 = 10 - 6 = 14 - 10 = 4
Establishing an explicit formula by analyzing the pattern. i.e. adding first term to the product of d (common difference) and one less than the term number

Hence, the explicit formula is given by:

$a_{n} = a_{1} + d (n-1)$

where,

aₙ is the nth term of the sequence

n is the term number

a₁ is the first term

d is the common difference

As the given sequence is: 2,6,10,14

a₁ = first term = 2

d = common difference = 6 - 2 = 4

Using explicit formula:

$a_{n} = a_{1} + d (n-1)$

$a_{n} = 10 + 5(n-1)$

$a_{n} = 10 + 5n-5$

$a_{n} = 5n+ 5$

Keywords: recursive formula, explicit formula, sequence

Learn more about recursive formula brainly.com/question/11673288

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4 0

4 years ago

To convert time in days it is necessary to multiply the time in years times 360 or 365.

solong [7]

To convert time in days it is necessary to multiply the time in years by 365

4 0

3 years ago

Read 2 more answers

HELP ASAP I’ll give brainzless

dem82 [27]

All of them.

1. If you multiply by 2, they will be equal.
2. If you multiply by 5000 they will be equal.
3. If you divide by 3 they will be equal.

3 0

3 years ago

Solve using law of sines or law of cosines!

malfutka [58]

Answer:

Part 5) The length of the ski lift is $1.15\ miles$

Part 6) The height of the tree is 18.12 m

Step-by-step explanation:

Part 5)

Let

A -----> Beginning of the ski lift

B -----> Top of the mountain

C -----> Base of mountain

we have

$b=0.75\ miles$

$A=20\°$

$C=180\°-50\°=130\°$ ----> by supplementary angles

Find the measure of angle B

Remember that the sum of the interior angles must be equal to 180 degrees

$B=180\°-A-C$

substitute

$B=180\°-20\°-130\°=30\°$

Applying the law of sines

$\frac{b}{sin(B)}=\frac{c}{sin(C)}$

substitute

$\frac{0.75}{sin(30\°)}=\frac{c}{sin(130\°)}$

$c=\frac{0.75}{sin(30\°)}(sin(130\°))$

$c=1.15\ miles$

Par 6)

see the attached figure with letters to better understand the problem

Applying the law of sines in the right triangle BDC

In the right triangle BDC 20 degrees is the complement of 70 degrees

$\frac{BC}{sin(70\°)}=\frac{x}{sin(20\°)}$

$BC=(sin(70\°))\frac{x}{sin(20\°)}$ -----> equation A

Applying the law of sines in the right triangle ABC

In the right triangle ABC 50 degrees is the complement of 40 degrees

$\frac{BC}{sin(40\°)}=\frac{x+15}{sin(50\°)}$

$BC=(sin(40\°))\frac{x+15}{sin(50\°)}$ -----> equation B

Equate equation A and equation B and solve for x

$(sin(70\°))\frac{x}{sin(20\°)}=(sin(40\°))\frac{x+15}{sin(50\°)}\\\\2.7475x=0.8391(x+15)\\\\2.7475x=0.8391x+12.5865\\\\2.7475x-0.8391x=12.5865\\\\x=6.60\ m$

Find the value of BC

$BC=(sin(70\°))\frac{6.6}{sin(20\°)}$

$BC=18.12\ m$

therefore

The height of the tree is 18.12 m

5 0

4 years ago