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]
Express in simplest form: 12 (2 + ) − (4 + )
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.
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
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.
if
f(x)=5x+7
and
g(x)=-2x-4
find
f(g(x))=___x+___
Step-by-step explanation:
F(g(x)) = -10x-13
First blank: -10
Second blank: -13
Algebra 1 9th grade
-2x=-18/3
COMBINING LIKE TERMS: Challenge 7 – 3ab + 2a + 6ab + 5 – 4a + 3a – ab
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
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
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
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?
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
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
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?
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
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.
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
um ok.........................
are intersecting lines always coplanar
Answer:
yes
Step-by-step explanation:
1. Sum of two numbers = 15
Difference of the numbers = 3
Find the numbers.
What is their product?
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:
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?
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
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
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
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
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
Answer
14
you have to simplify
8+1/2(12)
14
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
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
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
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
Answer:
width is 9 length is 12 :)
Step-by-step explanation:
I'm doing this stuff rn