Find the radius of a circle with the given circumference.

Calculate the sum of the first 36 terms of the arithmetic sequence defined in which a36=14 and the common difference is d=1/8

user100 [1]

Answer:

425.25

Step-by-step explanation:

Since we are given 36th term as 14 and we know common difference is $\frac{1}{8}$ , it means that from the first term, we add $\frac{1}{8}$ to each and get 14 on the 36th term. To figure out the first term, thus, we have to subtract $\frac{1}{8}$ 35 times from 14. Let's do it to get first term:

$14-35(\frac{1}{8})=\frac{77}{8}=9.625$

The sum of arithmetic sequence formula is:

$S_{n}=\frac{n}{2}[2a+(n-1)d]$

Where,

$S_{n}$ is the sum of nth term (we want to figure this out for first 36 terms)
$a$ is the first term (we figured this out to be 9.625)
$n$ is the term number (36 for our case)
$d$ is the common difference (given as $\frac{1}{8}$ )

Substituting all the values, we get:

$S_{36}=\frac{36}{2}[2(9.625)+(36-1)(\frac{1}{8})]\\S_{36}=18[19.25+4.375]\\S_{36}=18[23.625]\\S_{36}=425.25$

First answer choice is right.

7 0

3 years ago

Read 2 more answers

Find the product of 3/5 x 7/4. Then, write another pair of factors with the same product

dezoksy [38]

Answer:

The product is 1.05

another pair of factors with the same product are 6/10 x 14/8

7 0

3 years ago

Read 2 more answers

Using Triangle Congruence Theorems

kodGreya [7K]

There are a total of five theorems congruent triangles. They are summarized as:

SAS
SSS
AAS
RHS and
ASA.

<h3>What are the definitions of the Theorems of Congruent Triangles?</h3>

SAS - Side Angle Side

According to the SAS rule, two triangles are said to be congruent if any two sides and any angle between the sides of one triangle are equal to the corresponding two sides and angle between the sides of the second triangle.

SSS - Side Side Side Rule

According to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are proportional to the size three sides of the second triangle.

AAS - Angle Angle Side Rule
Angle-Angle-Side is abbreviated as AAS. The triangles are said to be congruent when two angles and a non-included side of one triangle match the comparable angles and sides of another triangle.

ASA - Angle Side Angle rule

According to the ASA rule, two triangles are said to be congruent if any two angles and the side contained between the angles of one triangle are proportional to the size two angles and side included in between angles of the second triangle.

RHS - Right Angle- Hypotenuse side Rule

According to the RHS rule, two right triangles are said to be equivalent if their hypotenuses and one of their sides are identical to those of another right-angled triangle.

Learn more about theorems of congruent triangles at:
brainly.com/question/2102943
#SPJ1

4 0

2 years ago

What is the common ratio for the geometric sequence? 32, 8, 2, 12, ... Enter your answer in the box.

mamaluj [8]

Answer:

Given sequence is not a geometric progression and there will be no common ration for this sequence.

Step-by-step explanation:

Need to determine common ration for the following geometric sequence

32, 8, 2, 12, ...

In given geometric sequence

a1 = 32, a2=8, a3=2, a4=12 ……….

Common ratio = $\frac{a_2}{a_1} =\frac{a_3}{a_2} =\frac{a_4}{a_3}$

$\frac{a_2}{a_1}=\frac{8}{32}=\frac{1}{4}$

$\frac{a_3}{a_2} =\frac{2}{8}=\frac{1}{4}$

$\frac{a_4}{a_3}=\frac{12}{2}=6$

Since $\frac{a_2}{a_1}=\frac{a_3}{a_2}\neq\frac{a_4}{a_3}$ so we can say that given sequence is not a geometric progression and there will no no common ration for this sequence.

3 0

3 years ago

Convert 55° 16' 30" into radian measure.

Colt1911 [192]

Answer:

55° 16' 30" = 0.9648 radians .

Step-by-step explanation:

8 0

3 years ago