Find a general term a, for the sequence whose first four terms are given.
1 /1,1/4,1/9,1/16

Answers

Answer 1

Answer:

  an = 1/n^2

Step-by-step explanation:

We notice that the denominators are the squares of successive integers. The general term will be ...

  [tex]\boxed{a_n=\dfrac{1}{n^2}}[/tex]


Related Questions

Express in simplest form: 12 (2 + ) − (4 + )

Answers

Answer:

20

Step-by-step explanation:

12 (2 + ) − (4 + )

24-4

=20

Answer:

20

Step-by-step explanation:

Find all points on the curve x=4cos(t),y=4sin(t) that have the slope of 12.

Answers

Answer:

[tex]\left (-\dfrac{4}{\sqrt{5}},\dfrac{8}{\sqrt{5}}\right )\text{ and }\left (\dfrac{4}{\sqrt{5}},-\dfrac{8}{\sqrt{5}}\right )[/tex].

Step-by-step explanation:

We need to find all the points on the curve x=4cos(t),y=4sin(t) that have the slope of 1/2.

[tex]x=4cos (t)[/tex]

[tex]\dfrac{dx}{dt}=-4sin (t)[/tex]

[tex]y=4sin (t)[/tex]

[tex]\dfrac{dy}{dt}=4cos (t)[/tex]

Now,

[tex]\dfrac{dy}{dx}=\dfrac{dy}{dt}\times \dfrac{dt}{dx}[/tex]

[tex]\dfrac{dy}{dx}=4cos (t)\times \dfrac{1}{-4sin (t)}[/tex]

[tex]\dfrac{dy}{dx}=-\cot t[/tex]

So, slope of the curve is [tex]-\cot t[/tex].

[tex]-\cot t=\dfrac{1}{2}[/tex]

[tex]-\tan t=2[/tex]

[tex]\tan t=-2[/tex]            ...(1)

Using [tex]\sec^2t=1+\tan^2t[/tex], we get

[tex]\sec^2t=1+(-2)^2[/tex]

[tex]\sec^2t=1+4[/tex]

[tex]\sec t=\pm \sqrt{5}[/tex]

[tex]\cos t=\pm \dfrac{1}{\sqrt{5}}[/tex]

Now,

[tex]\sin^2t=1-cos^2t[/tex]

[tex]\sin t=\pm \sqrt{1-\dfrac{1}{5}}[/tex]

[tex]\sin t=\pm \sqrt{\dfrac{4}{5}}[/tex]

[tex]\sin t=\pm \dfrac{2}{\sqrt{5}}[/tex]

It equation (1), tan(t) is negative. So, sin and cos have different signs.

If [tex]\sin t= \dfrac{2}{\sqrt{5}}[/tex], then [tex]\cos t=- \dfrac{1}{\sqrt{5}}[/tex].

[tex]x=4cos (t)=-\dfrac{4}{\sqrt{5}}[/tex]

[tex]y=4sin (t)=\dfrac{8}{\sqrt{5}}[/tex]

If [tex]\sin t=- \dfrac{2}{\sqrt{5}}[/tex], then [tex]\cos t= \dfrac{1}{\sqrt{5}}[/tex].

[tex]x=4cos (t)=\dfrac{4}{\sqrt{5}}[/tex]

[tex]y=4sin (t)=-\dfrac{8}{\sqrt{5}}[/tex]

Therefore, the two points are [tex]\left (-\dfrac{4}{\sqrt{5}},\dfrac{8}{\sqrt{5}}\right )\text{ and }\left (\dfrac{4}{\sqrt{5}},-\dfrac{8}{\sqrt{5}}\right )[/tex].

Please Help!! 10 Points!! Brainliest answer

Answers

Answer:

XW since it matches the same as IH  

Step-by-step explanation:

example if it asked another question saying what corresponds with XY. XY is on the last part of the statement so it would  correspond with IJ

URGENT PLS HELP

BD bisects ABC. Find each of the following
1. Find the measure of angle ABD if the measure of angle ABD = 6x + 4 and
the measure of angle DBC = 8x - 4
2. Find the measure of angle ABC if the measure of angle ABD = 5y - 3 and the
measure of angle DBC = 3y + 15.

Answers


Align the horizontal edge of the protractor with the base of the triangle. Place the center point of the protractor on the vertex of the angle. Follow the side of the triangle until it reaches the angle measurement mark. Note the measurement.

if
f(x)=5x+7
and
g(x)=-2x-4
find
f(g(x))=___x+___​

Answers

Step-by-step explanation:

F(g(x)) = -10x-13

First blank: -10

Second blank: -13

Algebra 1 9th grade
-2x=-18/3​

Answers

You would just decide both sides by 2.

-x = -9/3 ⇨ -3
Since both numbers are negative, the product becomes a positive.
x=3

Hope this helped!

COMBINING LIKE TERMS: Challenge 7 – 3ab + 2a + 6ab + 5 – 4a + 3a – ab​

Answers

Answer:

Hope this helps;))

Step-by-step explanation:

-3ab+6ab=3ab

2a-4a+3a=1a

7+5=12

12+3ab+1a

Answer:

-2+2ab-a

Step-by-step explanation:

Never combine unlike terms

Ex. Never combine a and ab

By following those rules, you will get -2+2ab-a as your answer.

Whats value of x is in the solution set of 2(3x-1)>4x-6 A.-10 B.-5 C.-3 D-1

Answers

Answer:

B. -5

Step-by-step explanation:

3x-1 > 4x-6

   +1

3x>4x-5

     -4x

-x>-5

/-1   /-1

x>-5

a flag pole that is 10 m talk casts a shadow that is 6 m long. what is the distance from the top of the pole to the end of the shadow

Answers

Answer:

11.66 meters

Step-by-step explanation:

First draw a diagram. See attachment.

We notice that if we draw everything out, we get a right triangle.

The flag pole and its shadow are the two legs, with lengths 10 and 6 meters. We want to find the distance from the top of the pole to the end of the shadow, so we need to use the Pythagorean Theorem, which states that for a right triangle with legs a and b and hypotenuse c:

a² + b² = c²

Here, a = 10 and b = 6, and we want to find c:

a² + b² = c²

10² + 6² = c²

100 + 36 = c²

136 = c²

c = √136 = 2√34 ≈ 11.66 meters

~ an aesthetics lover

Answer:

11.7

Step-by-step explanation:

Tier: Homework 1
Solve 2(4y - 5) = 14 983

Answers

Answer:

y = 1874.25

Step-by-step explanation:

2(4y - 5) = 14 983

2*4y + 2*-5 = 14983

8y - 10 = 14983

8y = 14983 + 10

8y = 14993

y = 14993/8

y = 1874.25

Answer:

Step-by-step explanation:

2(4y - 5) = 14

8y - 10 = 14

8y = 24

y = 3

Which of these would not produce a representative sample that determines the favorite sport of the students at the local high school?

Answers

Answer:

The answer is ask ten students wearing football jersey each day for a week

Step-by-step explanation:

Answer:

it its the pizza one because people could be bias and that would not give a very acturate answer

Step-by-step explanation:

27x^0y^-2 for x=4 and y=3

Answers

Answer:

A3=44 56-7

Step-by-step explanation:

Find the length of DE if D is between points C and E, CD = 6.5 cm and CE = 13.8 cm

Answers

Answer:

DE= 7.3

Step-by-step explanation:

you subtract the length if CE - CD to get DE

13.8 - 6.5 = 7.3


Under the Declaration of Independence ordinary citizens have the right to do what and why?

Answers

Answer:

yes, ordinary netizens have a right to do what they want or what opinion they want to say. Declaration of Indepence is not just for powerful people but also for ordinary netizens in order for them to spek the truth

Convert 6 7/20
into a decimal

Answers

Hey there!

ANSWER: [tex]0.35[/tex]EXPLANATION:

[tex]6 \frac{7}{20}[/tex] as a decimal

The percentage for 6 7/20 is 35%. So if that was the percent, then the decimal would be 0.35.

[tex]0.35(ANSWER)[/tex]

Hope this helps!

[tex]\text {-TestedHyperr}[/tex]

Find the value of x of this triangle.​

Answers

Answer:

12x

Step-by-step explanation:

Answer: x = 35°

Step-by-step explanation:

A triangle adds up to 180°. Therefore, the equation to find the value of x is 110+2x = 180.Subtract 110 on both sides. 2x = 70Divide by 2 on both sides. x = 35°

alessialol I will add you back on snap and um I forgot y password to my other acc. so ya and whats the google classroom code?

sorry people but if you will just leave me alone bc im mad at some people

Answers

um ok.........................

are intersecting lines always coplanar

Answers

Answer:

yes

Step-by-step explanation:

1. Sum of two numbers = 15
Difference of the numbers = 3
Find the numbers.
What is their product?

Answers

The answer is 45 because you multiply 9 and 6
The numbers are 9 and 6 as 9+6=15 and 9-6=3, the product would be 9*6=54.

So the product is 54 and the two numbers we had to find are 9 and 6.


William just accepted a job at a new company where he will make an annual salary of
$60000. William was told that for each year he stays with the company, he will be
given a salary raise of $5000. How much would William make as a salary after 5
years working for the company? What would be his salary after t years?
Salary after 5 years:
Salary after t years:

Answers

Answer:

Salary after 5 years: 60000+(5000)5= 85000

Salary after T years: 6000+(5000)t

Step-by-step explanation:

The way that you would find the amount of money needed after 5 years is by multiplying the 5000, since that is William's raise per year, and then adding 60000, which is the original salary.

In order to find William's salary after t years, since you do not have a number, but have t, you would want to multiply 5000, which is the yearly raise, and t, hich can be any amount of years. After that, you would want to add William's original income to find an answer.

whats the final answer?

Answers

Step-by-step explanation:

Tanø=opp/adj

Tan30=x/7. (× b.s 7)

x=7Tan30

x= 4.04

P + 4 Solve for p
--------- = 5
6

Answers

Answer:

p = 26

Step-by-step explanation:

(p+4)/6 = 5

Multiply each side by 6

(p+4)/6 *6 = 5*6

p+4 = 30

Subtract 4 from each side

p+4-4 = 30-4

p = 26

solve for x. ax-bx=k​

Answers

Answer:

x= k/a-b

Step-by-step explanation:

Move all terms to the left side and set equal to zero as well as each factor.

Hope this helps.

The value of x is k/ (a-b).

What is Algebra?

algebra is the branch of mathematics that helps in the representation of problems or situations in the form of mathematical expressions. it involves variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression.

Given:

ax-bx=k​

x(a-b)=k

x= k/ (a-b)

Hence, the value  x is k/(a-b)

Learn more about algebra here:

https://brainly.com/question/24875240

#SPJ2

#2 - Simplify the expression. Type your answer with all lowercase letters and no spaces. * 3h - e + 2h - 5e

Answers

Answer:

5h-6e

Step-by-step explanation:

3h - e + 2h - 5e =

= 3h + 2h - e - 5e

= 5h-6e

Answer:

5h - 4e

Step-by-step explanation:

Add 3h and 2h to get 5h then subtract e from 5e which equals 4e

Hope this helps!

order fruits from least to greatest according to the unit prices 0.84, 2.25, 1.17

Answers

Answer:

0.84, 1.17, 2.25

Step-by-step explanation:

Answer:

.84, 1.17, 2.25

Step-by-step explanation:

You can answer this on your own by finding which numbers are farther away from zero. So the farther you get from zero, the more you have.

8+1/2(12)=x

Solve please

Answers

Answer

14

you have to simplify

8+1/2(12)

14

8+1=9/2(12)=24
9/24 =0.375

60% of a class studied for the quiz. 70% of the class passed the quiz. If 12 people did not study for the quiz, how many students passed the quiz

Answers

Answer:

21

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

Round the following numbers to 2 decimal places 3526.48502 12.6433 0.2099

Answers

Step-by-step explanation:

3526.49 12.64 0.21

I hope this helps

Answer:

3526.49

12.64

.21

Step-by-step explanation:

1. On the left of the decimal place, take the third number and if it is = to or higher than 5, round the second number up by 1.

3526.485 becomes 3526.49

2. If it is lower than 5, then just leave the second number alone.

12.6433 becomes 12.64

3. If it is a decimal place number, just take the third number and if it is higher than 5, increase the second number.

.2099 becomes .21

You are working hard at the local grocery store each weekend. You have decided to put your money in a compound interest bearing account earning 4% per year. How many years would you estimate that it would take for you to double your money

Answers

Answer:

The answer would be 18 years

Step-by-step explanation:

hope this helps:)

the length of a rectangle is 3 inches m ore that its width. if the perimeter is 42 inches, what are the dimensions of the rectangle

Answers

Answer:

width is 9 length is 12 :)

Step-by-step explanation:

I'm doing this stuff rn

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