Construct the ∆ABC :AB=5cm A=45° B=60°

Write the next three terms of the arithmetic sequence.

JulijaS [17]

The next three terms are: 1/6 , 0 and -1/6

Step-by-step explanation:

Given sequence is:

$\frac{5}{6} , \frac{2}{3} ,\frac{1}{2}, \frac{1}{3} ...$

First of all, we have to find the common difference

$here\\a_1 = \frac{5}{6}\\a_2 = \frac{2}{3}\\a_3 = \frac{1}{2}\\a_4 = \frac{1}{3}\\d = a_2-a_1 = \frac{2}{3} -\frac{5}{6} = \frac{4-5}{6} = -\frac{1}{6}\\d = a_3 - a_2 = \frac{1}{2} - \frac{2}{3} = \frac{3-4}{6} = =\frac{1}{6}$

The common difference is -1/6

We can simply add -1/6 to the previous term to find the next terms so,

Adding -1/6 to 1/3

$\frac{1}{3} - \frac{1}{6} = \frac{2-1}{6} = \frac{1}{6}\\\frac{1}{6} - \frac{1}{6} = 0\\0-\frac{1}{6} = -\frac{1}{6}$

Hence,

The next three terms are: 1/6 , 0 and -1/6

Keywords: Arithmetic sequence, common difference

Learn more about arithmetic sequence at:

#LearnwithBrainly

4 0

3 years ago

A movie theater has a seating capacity of 387. The theater charges $5.00 for children, $7.00 for students, and $12.00 of

Rainbow [258]

Answer:

The attendance was 198 children, 90 students and 99 adults.

Step-by-step explanation:

We define:

c: children attendance

s: students attendance

a: adult attendance

The equation that describes the total ticket sales is:

$5c+7s+12a=2808$

We also know that the children attendance doubles the adult attendance:

$c=2a$

The third equation is the seating capacity, which we assume is full:

$c+s+a=387$

We start by replacing variables in two of the equations:

$c=2a\\\\s=387-c-a=387-2a-a=387-3a$

Then, we solve the remaining equation for a:

$5c+7s+12a=2808\\\\5(2a)+7(387-3a)+12a=2808\\\\10a+(2709-21a)+12a=2808\\\\10a+12a-21a=2808-2709\\\\a=99$

Then, we solve for the other two equations:

$c=2a=2*99=198\\\\s=387-3a=387-3*99=387-297=90$

The attendance was 198 children, 90 students and 99 adults.

8 0

3 years ago

Simplify the expressions by distributing the negatives and combining like terms

Illusion [34]

Answer:

-2 times 6d=-12d

-2 times -11= 22

Answer: -12d+22

Step-by-step explanation:

5 0

2 years ago

The sphere is _____ cubic centimeters bigger than the cube. (Round to the nearest cubic centimeter.)

Misha Larkins [42]

ANSWER

The sphere is 10762 cubic centimeters bigger than the cube.

EXPLANATION

We want to find the difference in the volumes of the sphere and the cube.

To do this, we have to find the volumes of the sphere and cube and subtract that of the cube from the sphere.

The volume of a sphere is given as:

$V=\frac{4}{3}\pi r^3$

where r = radius

The radius of the sphere is 15 centimeters. Therefore, the volume of the sphere is:

$\begin{gathered} V=\frac{4}{3}\cdot\pi\cdot15^3 \\ V\approx14137\operatorname{cm}^3 \end{gathered}$

The volume of a cube is given as:

$V=s^3$

where s = length of the side

The length of the side of the cube is 15 centimeters. Therefore, the volume of the cube is:

$\begin{gathered} V=15^3 \\ V=3375\operatorname{cm}^3 \end{gathered}$

Therefore, the difference in the volumes of the sphere and cube is:

$\begin{gathered} V_d=V_s-V_c \\ V_d=14137-3375 \\ V_d=10762\operatorname{cm}^3 \end{gathered}$

Therefore, the sphere is 10762 cubic centimeters bigger than the cube.

6 0

9 months ago

472,558 to the nearest hundred thousand

Marrrta [24]

473,000 u round up to the next thousand

4 0

3 years ago

Read 2 more answers

Construct the ∆ABC :AB=5cm A=45° B=60°​

Construct the ∆ABC :AB=5cm A=45° B=60°