Suppose the sequence {an} is arithmetic with a3 = 15, d = -3/2, and an=6
Find n.

Answer:

Yes, the limit does exist.

Step-by-step explanation:

By definition, a limit in the form:

[tex]\displaystyle \lim_{x\to a}f(x)[/tex]

Exists if and only if:

[tex]\displaystyle \lim_{x\to a^-}f(x)=\lim_{x\to a^+}f(x)[/tex]

We are given the limit:

[tex]\displaystyle \lim_{x\to 2}\frac{x^2+x-6}{x^2-4}[/tex]

So, in order to prove that this limit exists, we simply have to show that:

[tex]\displaystyle \lim_{x\to 2^-}\frac{x^2+x-6}{x^2-4}=\displaystyle \lim_{x\to 2^+}\frac{x^2+x-6}{x^2-4}[/tex]

Let's do the left-hand side first. We can factor the function:

[tex]=\displaystyle \lim_{x\to 2^-}\frac{(x+3)(x-2)}{(x+2)(x-2)}[/tex]

Simplify:

[tex]\displaystyle =\lim_{x\to 2^-}\frac{x+3}{x+2}[/tex]

By direct substitution:

[tex]\displaystyle =\frac{(2)+3}{(2)+2}=\frac{5}{4}[/tex]

Now, we can evaluate the right-hand side. Again, factor:

[tex]=\displaystyle \lim_{x\to 2^+}\frac{(x+3)(x-2)}{(x+2)(x-2)}[/tex]

Simplify:

[tex]\displaystyle =\lim_{x\to 2^+}\frac{x+3}{x+2}[/tex]

And by direct substitution:

[tex]\displaystyle =\frac{(2)+3}{(2)+2}=\frac{5}{4}[/tex]

Since both the left- and right-hand limits equal 5/4, our original limit does indeed exist.

Answer:

It should be C.

Step-by-step explanation:

I hope this helps

Answer:

9.17 feet

Step-by-step explanation:

Use the Pythogoras theorem, a^2 + b^2 = c^2

you are give c and b ( because one side is slanted, so c) so rearrange to get

c^2-b^2 = a^2

10^2 - 4^2 = 84

square root 84 to get

9.16515

Answer:

[tex]a \\ \frac{50}{0.25} = 200 \: \frac{km}{ {h}^{2} } \\ b \\ the \: area \: under \: graph = whole \: distance = \\ = 50 \times (2 + 1.5) \times 0.5 + \\ + 50 \times (0.5 + 1) \times 0.5 = 125km \\ c \\ \ \: average \: speed \: = \frac{125}{2} = 62.5 \frac{km}{h} [/tex]

9514 1404 393

Answer:

  (b)  9

Step-by-step explanation:

The product of segment lengths to the near and far intersection with the circle is the same for both secants.

  4(4+5) = 3(3+x) . . . . the above statement with numbers filled in

  36 = 9 +3x . . . . . . . simplify

  12 = 3 +x . . . . . . . . divide by 3

  9 = x . . . . . . . . . . . subtract 3

Answer:

x > 29

Step-by-step explanation:

Answer:

[tex]x > 29[/tex]

Step-by-step explanation:

Given: −x<−29

To find: Simplified

Solution: Simplification of an algebraic expression can be defined as the process of writing an expression in the most efficient and compact form without affecting the value of the original expression.

The process entails collecting like terms, which implies adding or subtracting terms in an expression.

Multiply both sides by -1 (reverse the inequality)

[tex](-x) (-1) > (-29) (-1)[/tex]

Simplify

[tex]x > 29[/tex]

Answer:

4496.8 pounds

multiply 642.4by7

Answer:

sorry I'm late but it's b I'm on unit test on edge

Answer: it is b

Step-by-step explanation:

Answer:

1536 in^2

Step-by-step explanation:

This is basically asking for the surface area so knowing that is a cube all the sides are equal so one side would be 16(16) which is 256 in ^2.  The knowing that there is 6 sides you would multiply it by 6 which is 256(6)= 1536^2

Answer:

the answer is A.

Step-by-step explanation:

Answer:

A=(-1,-1)

B=(0,2)

C=(2,0)

Step-by-step explanation:

Sorry for some reason it says C at the bottom and D in the graph...

But hope this helps :)

Step-by-step explanation:

p^2+2p=63

p^2+2p+1^2=63+1^2

p^2+2p+1=64

(p+1)^2=64

p+1=8

p=8-1

p=7

Answer:

0.18

Rounded

0.2

Step-by-step explanation:

Answer:

x = 16

Step-by-step explanation:

Based in the tangent-secant theorem, we have the following equation showing the relationship between the secant and the tangent:

(2 + x)*2 = 6²

4 + 2x = 36

Subtract 4 from both sides

2x = 36 - 4

2x = 32

Divide both sides

2x/2 = 32/2

x = 16

Answer:

Step-by-step explanation:

Answer:

$13.97

Step-by-step explanation:

First, find how much the cost was for the two coffees:

2.38 + 3.65

= 6.03

Find how much change he got by subtracting this from 20:

20 - 6.03

= 13.97

So, he got $13.97 in change

Answer:

At first the total money spent by Mr. Newcomb = $ 2.38 + $3.65

=> 6.03

Now

According to the question

Change she get = 20 - 6.03

= 13.97

Answer:

answer is 13 inch.,

Step-by-step explanation:

BCD is  equilateral triangle so all side is equal.

and ABD is right angled  triangle so. use pythagoras  theorem.

BD = 13 inch then DC also 13 inch

Answer:

Its D

Step-by-step explanation:

Ed2021

Answer

x greater-than-or-equal-to 0

Step-by-step explanation:

yes

Answer:

120

Step-by-step explanation:

Since you have to find volume you have to multiply all the numbers.

So, 4*5*6 = 120

Answer:

120cm2

Step-by-step explanation:

Volume= length times width times the height. So.. 6×5×4= 120cm2 (btw the 2 means squared)

Answer:

i really dont know

Step-by-step explanation:

i really dont know

Answer:

27

Step-by-step explanation:

162 divide by 3 = 54 divided by 2 =27 I think this is the answer

Answer:

hope it helps.

Step-by-step explanation:

50 + x =120

x = 120 -50

x = 70

Answer:

38.7°

Step-by-step explanation:

Let the angle we're looking for be called x.

Consider ΔADF (which consists of sides AD, FD and FA, and which contains the angle x.

tan(angle)=opposite/adjacent

tan(x)=FD/FA

x=tan⁻¹(12/15)=38.6598082541°≈38.7°

Therefore, the length of the angle be [tex]x=38.65[/tex] degree.

What is the trigonometry?

Trigonometry states that the trigo mean 'triangle', and metry means métron is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Here given that,

Let the length of the angle be [tex]x[/tex].

Consider Δ[tex]ADF[/tex]

which consists of sides [tex]AD, FD[/tex] and [tex]FA[/tex], and which contains the angle [tex]x[/tex].

So,

tan(x)=Perpendicular / Base

i.e.,

[tex]tan(x)=\frac{FD}{FA}\\\\tan(x)=\frac{FD}{FA}\\\\x=tan^{-1}(\frac{12}{15})\\\\x=38.65[/tex]

Hence, the length of the angle be [tex]x=38.65[/tex] degree.

To know more about the trigonometry

https://brainly.com/question/27269972

#SPJ2

Answer:

I could be wrong but it's 2/7 (i think)

Step-by-step explanation:

I hope this helps :)

Answer:Maria rate = 1/13 job/hr

-----

Felipe rate = 1/16 job/hr

----

Together rate = 1/x job/h

Step-by-step explanation: rate + rate = Together rate

1/13 + 1/16 = 1/x

----

16x + 13x = 13*16

------

29x = 13*16

x = 7.17 hrs = 7 hr 10 min 12 seconds (time to do the job together)

-------------

Cheers,

Rubberduck100000.

Answer:

The volume of hemisphere = 2/3 pie r ^3

or, 18 pie = 2/3 pie r ^ 3

or, 27 = r ^ 3

or, r = 3 inches #

hope this helps

All the best!!

Answer:

Pay attention in class

WRITE DOWN FORMULAS

contribute in class

Try to memorize formulas

Try your best!

Try writing down problems cause if you understand how to write a problem on what your learning you have a good chance at getting the answer correct Also if you have any questions on the math your doing right now I could maybe try to help best of luck!