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
konstantin123 [22]
3 years ago
15

If the door to the library is at (2, 4), the door to the mall is at (8, 2), and one

Mathematics
1 answer:
guapka [62]3 years ago
5 0

Answer:

6 miles

Step-by-step explanation:

The distance formula is expressed as;

D = √(x2-x1)²+(y2-y1)²

D = √(2-4)²+(8-2)²

D = √(-2)²+(6)²

D = √4 + 36

AD = √40

AD = 6.32

Hence the approximate distance between the library  and the mall is 6 miles

You might be interested in
Consider the function ​f(x)equalscosine left parenthesis x squared right parenthesis. a. Differentiate the Taylor series about 0
dybincka [34]

I suppose you mean

f(x)=\cos(x^2)

Recall that

\cos x=\displaystyle\sum_{n=0}^\infty(-1)^n\frac{x^{2n}}{(2n)!}

which converges everywhere. Then by substitution,

\cos(x^2)=\displaystyle\sum_{n=0}^\infty(-1)^n\frac{(x^2)^{2n}}{(2n)!}=\sum_{n=0}^\infty(-1)^n\frac{x^{4n}}{(2n)!}

which also converges everywhere (and we can confirm this via the ratio test, for instance).

a. Differentiating the Taylor series gives

f'(x)=\displaystyle4\sum_{n=1}^\infty(-1)^n\frac{nx^{4n-1}}{(2n)!}

(starting at n=1 because the summand is 0 when n=0)

b. Naturally, the differentiated series represents

f'(x)=-2x\sin(x^2)

To see this, recalling the series for \sin x, we know

\sin(x^2)=\displaystyle\sum_{n=0}^\infty(-1)^{n-1}\frac{x^{4n+2}}{(2n+1)!}

Multiplying by -2x gives

-x\sin(x^2)=\displaystyle2x\sum_{n=0}^\infty(-1)^n\frac{x^{4n}}{(2n+1)!}

and from here,

-2x\sin(x^2)=\displaystyle 2x\sum_{n=0}^\infty(-1)^n\frac{2nx^{4n}}{(2n)(2n+1)!}

-2x\sin(x^2)=\displaystyle 4x\sum_{n=0}^\infty(-1)^n\frac{nx^{4n}}{(2n)!}=f'(x)

c. This series also converges everywhere. By the ratio test, the series converges if

\displaystyle\lim_{n\to\infty}\left|\frac{(-1)^{n+1}\frac{(n+1)x^{4(n+1)}}{(2(n+1))!}}{(-1)^n\frac{nx^{4n}}{(2n)!}}\right|=|x|\lim_{n\to\infty}\frac{\frac{n+1}{(2n+2)!}}{\frac n{(2n)!}}=|x|\lim_{n\to\infty}\frac{n+1}{n(2n+2)(2n+1)}

The limit is 0, so any choice of x satisfies the convergence condition.

3 0
3 years ago
Which of the following accurately shows the range of the function defined below?
il63 [147K]

Answer: The answer is (b) (2, ∞)

Step-by-step explanation:  We are given a function f(x) in the figure and we are to select out of the given options that accurately shows the range of the function defined.

\textup{For }x < 0, \textup{we have}~f(x)=3.

\textup{For }0\leq x

\textup{For }x\geq 2,\textup{ we have }f(x)=\dfrac{1}{2}x+5\geq 5.

Therefore, the range of the function f(x) will be greater then or equal to 2. So, the range will be [2, ∞).

Thus, the correct option is (b) (2, ∞).

7 0
3 years ago
Read 2 more answers
Ross had c number of coin collections with 15 coins in each collection. His aunt gave him 8 more coins. Write an expression that
Debora [2.8K]
 The answer is 15c+8. Hope that helps
5 0
3 years ago
Read 2 more answers
Find the sum of the following series.<br><br><br> PLEASE SOMEONE HELP!!!
Dmitry [639]

The given sum for n = 1 to n = 15 is equal to 255, so the correct option is B.

<h3>How to find the sum of the given series?</h3>

We want to find the sum of the series whose elements are of the form:

(2n + 1)

From n = 1 to n = 15.

Then our sum will be:

(2*1 + 1) + (2*2 + 1) + ... + (2*15 + 1).

3 + 5 + ... + 31

This is the sum of all odd numbers in the interval [3, 31]

Which gives:

S = 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 + 27 + 29 + 31 = 255

So the correct option is B.

If you want to learn more about sums:

brainly.com/question/24295771

#SPJ1

4 0
1 year ago
Are fractions with the same denominator?
Minchanka [31]

Answer:

To solve fractions, you MUST HAVE THE SAME DENOMINATORS WHEN DEALING WITH ADDITION AND SUBTRACTION.

Step-by-step explanation:

For example, 2/3 + 3/6

The denominators in this case have a common denominator which is 6.

All you have to do is multiply the 2/3 by 2 in the numerator and the denominator. Once you do, you'll get 4/6 which you could then add to 3/6 to get 7/6 which would equal 1 1/6 or 7/6 either is fine.

Hope this helps! :)

7 0
3 years ago
Read 2 more answers
Other questions:
  • What is the common difference for this arithmetic sequence?
    8·3 answers
  • A survey found that​ women's heights are normally distributed with mean 63.4 in and standard deviation 2.2 in. A branch of the m
    6·1 answer
  • Find the first, fourth, and eighth terms of the sequence.<br><br> A(n) = −2 ∙ 2x − 1
    9·1 answer
  • PLZZZZ HELP What is the slope of a line that is perpendicular to a line whose equation is 3y=−4x+2 ?
    9·1 answer
  • What is the greatest factor of 63 that is also a prime number?<br> 7<br> 9<br> 13<br> 21
    8·2 answers
  • Equation:
    8·1 answer
  • HELPPPP PLEASEEEEEEEREEREEEE
    9·1 answer
  • PLEASEEEEE HELP THIS IS DUE SOON
    5·2 answers
  • During a big race, Jeff races his car at a rate of 125 miles per hour for 3.2 hours. What is the distance of the race?
    13·2 answers
  • The numbers 1 through 15 are written on cards. One card is chosen at random. Event A is choosing a
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!