1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Alenkinab [10]
2 years ago
8

What is the least common multiple of two numbers that have no common factors greater than 1

Mathematics
1 answer:
Maksim231197 [3]2 years ago
3 0
7 and 6 and the LCM would be 42
You might be interested in
Let f be defined by the function f(x) = 1/(x^2+9)
riadik2000 [5.3K]

(a)

\displaystyle\int_3^\infty \frac{\mathrm dx}{x^2+9}=\lim_{b\to\infty}\int_{x=3}^{x=b}\frac{\mathrm dx}{x^2+9}

Substitute <em>x</em> = 3 tan(<em>t</em> ) and d<em>x</em> = 3 sec²(<em>t </em>) d<em>t</em> :

\displaystyle\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\frac{3\sec^2(t)}{(3\tan(t))^2+9}\,\mathrm dt=\frac13\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\mathrm dt

=\displaystyle \frac13 \lim_{b\to\infty}\left(\arctan\left(\frac b3\right)-\arctan(1)\right)=\boxed{\dfrac\pi{12}}

(b) The series

\displaystyle \sum_{n=3}^\infty \frac1{n^2+9}

converges by comparison to the convergent <em>p</em>-series,

\displaystyle\sum_{n=3}^\infty\frac1{n^2}

(c) The series

\displaystyle \sum_{n=1}^\infty \frac{(-1)^n (n^2+9)}{e^n}

converges absolutely, since

\displaystyle \sum_{n=1}^\infty \left|\frac{(-1)^n (n^2+9)}{e^n}\right|=\sum_{n=1}^\infty \frac{n^2+9}{e^n} < \sum_{n=1}^\infty \frac{n^2}{e^n} < \sum_{n=1}^\infty \frac1{e^n}=\frac1{e-1}

That is, ∑ (-1)ⁿ (<em>n</em> ² + 9)/<em>e</em>ⁿ converges absolutely because ∑ |(-1)ⁿ (<em>n</em> ² + 9)/<em>e</em>ⁿ| = ∑ (<em>n</em> ² + 9)/<em>e</em>ⁿ in turn converges by comparison to a geometric series.

5 0
3 years ago
Antonio is a biologist studying life in a pond. He needs to know how deep the water is. He notices a water lily sticking straigh
quester [9]
For this problem we can represent the situation as a rectangle triangle.
 x: depth of water.
 40: Base. "Antonio pulls the lily to one side, keeping the stem straight, until the blossom touches the water at a spot"
 x + 8: Hypotenuse. "He notices water lily sticking straight up from the water, whose blossom is 8 cm above the water's surface." Antonio pulls the lily to one side, keeping the stem straight, until the blossom touches the water at a spot".
 By the Pythagorean theorem we have:
 x ^ 2 + 40 ^ 2 = (x + 8) ^ 2
 Clearing x:
 x ^ 2 + 1600 = x ^ 2 + 16x + 64
 x ^ 2 - x ^ 2 = 16x + 64 - 1600
 0 = 16x -1536
 1536 = 16x
 1536/16 = x
 x = 96
 answer:
 1) x ^ 2 + 40 ^ 2 = (x + 8) ^ 2
 2) the depth of the water is
 x = 96
6 0
3 years ago
The first transformation for this composition is [________], and the second transformation is a translation down and to the righ
Marysya12 [62]

Answer:

Step-by-step explanation:

B just took the until test

5 0
2 years ago
Read 2 more answers
Is ab perpendicular to cd ? Explain.
Afina-wow [57]
We know that
if two lines are perpendicular
then
the slopes 
m1*m2=-1

step 1
find the slope AB
A (0,2)
B (-3,-3)
m=(y2-y1)/(x2-x1)-----> m=(-3-2)/(-3-0)-----> m=-5/-3----> m1=5/3

step 2
find the slope CD
C (-4,1)
D (0,-2)
m=(y2-y1)/(x2-x1)-----> m=(-2-1)/(0+4)-----> m=--3/4----> m2=-3/4

step 3
multiply mi*m2
(5/3)*(-3/4)-----> -15/12
so
15/12 is not -1
therefore
 AB is not perpendicular to CD
4 0
3 years ago
Write the ratio as a percent.
natali 33 [55]

Answer:

62%

Step-by-step explanation:

This one's easy to solve as a percentage because the total number was 100 to begin with. Simply divide the number of employed students by the total amount of students, 62/100, which gets 0.62, or 62%.

5 0
2 years ago
Other questions:
  • Do mathematicians PARTY
    10·1 answer
  • Which sequence is ARITHMETIC?
    8·2 answers
  • Please Help! Find the slope of the line that passes through (71, -34) and (-11, -51).
    13·1 answer
  • Change 1/3 to sixths
    5·2 answers
  • Jose received a $100 gift card to his favorite coffee shop for his birthday. Every week he goes to the coffee shop and spends $5
    11·1 answer
  • HELP PLEASE<br><br><br><br> i cant tell wither its c or d cause im an idiot
    10·2 answers
  • Ji Sunn spent $24 at the local farmer’s market. She bought apples that cost $4 per pound and raspberries that cost $6 per pound.
    5·1 answer
  • Write an equation for the line that is perpendicular to Y=-3/7x+4 and passes through (-4,-5)
    5·1 answer
  • What is another way to wright the same equation, for example 1/4x-5
    15·1 answer
  • Need help 3x+10y=-10
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!