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
zloy xaker [14]
3 years ago
13

T what point does the curve have maximum curvature? Y = 7ex (x, y) = what happens to the curvature as x → ∞? Κ(x) approaches as

x → ∞.
Mathematics
1 answer:
Nookie1986 [14]3 years ago
5 0

Formula for curvature for a well behaved curve y=f(x) is


K(x)= \frac{|{y}''|}{[1+{y}'^2]^\frac{3}{2}}


The given curve is y=7e^{x}


{y}''=7e^{x}\\ {y}'=7e^{x}


k(x)=\frac{7e^{x}}{[{1+(7e^{x})^2}]^\frac{3}{2}}


{k(x)}'=\frac{7(e^x)(1+49e^{2x})(49e^{2x}-\frac{1}{2})}{[1+49e^{2x}]^{3}}

For Maxima or Minima

{k(x)}'=0

7(e^x)(1+49e^{2x})(98e^{2x}-1)=0

→e^{x}=0∨ 1+49e^{2x}=0∨98e^{2x}-1=0

e^{x}=0  ,  ∧ 1+49e^{2x}=0   [not possible ∵there exists no value of x satisfying these equation]

→98e^{2x}-1=0

Solving this we get

x= -\frac{1}{2}\ln{98}

As you will evaluate {k(x})}''<0 at x=-\frac{1}{2}\ln98

So this is the point of Maxima. we get y=7×1/√98=1/√2

(x,y)=[-\frac{1}{2}\ln98,1/√2]

k(x)=\lim_{x\to\infty } \frac{7e^{x}}{[{1+(7e^{x})^2}]^\frac{3}{2}}

k(x)=\frac{7}{\infty}

k(x)=0







You might be interested in
12. On a table there were 16 dimes and quarters. The value of the coins was
7nadin3 [17]
6 quarters and 10 dimes
6 0
3 years ago
Write the equivalent fractions of 11/12
skelet666 [1.2K]

Answer:

11/2, 22/4, 33/6, 44/8, 55/10, 66/12, 77/14, 88/16, 99/18, 110/20, 121/22, 132/24, 143/26, 154/28, 165/30, 176/32, 187/34, 198/36, 209/38, 220/40, and so on ...

8 0
3 years ago
9.<br><br><br>How many times greater is the 6 in 6,275 than the 6 in 62.75?​
joja [24]

Answer:100

Step-by-step explanation:

3 0
2 years ago
7TH GRADE MATH NEED ASAPP
Illusion [34]
I believe it is A because 3p has to be equal to or greater than 45
4 0
3 years ago
Read 2 more answers
Show Your Knowledge
crimeas [40]

9514 1404 393

Answer:

  • 15 nickels
  • 3 dimes

Step-by-step explanation:

Let d represent the number of dimes Molly has. Then she has 18-d nickels, and the total value (in cents) of her coins is ...

  5(18 -d) +10d = 105

  5d +90 = 105 . . . . . . simplify

  5d = 15 . . . . . . . . . . . subtract 90

  d = 3 . . . . . . . . divide by 5; number of dimes

  18-d = 15 . . . . . number of nickels

Molly has 3 dimes and 15 nickels.

8 0
3 years ago
Read 2 more answers
Other questions:
  • 3. The picture below shows a relationship between the number of circles and triangles.
    5·1 answer
  • COMPLETE<br> the equation x2 - 9 = 0 has<br> real solution(s).
    12·1 answer
  • If b=3-2s and A= -2s^2+2s+3 find an expression that equals 2b+2A in standard form
    10·1 answer
  • I have no idea what I’m doing
    14·2 answers
  • Who else does this?<br><br> 2.0 × 657586877674437546= ___?
    5·2 answers
  • Amelia is getting ready to go on a family vacation. They are driving the whole way, so she wants to have her favorite TV shows d
    6·2 answers
  • What is the slope of the line represented by the equation ?
    7·1 answer
  • Using pennies, nickels, dimes or quarters, determine which kind of coin is in each circle. First clue: The total value of the fo
    7·1 answer
  • Find the equation of a line parallel to y=4x−4 that contains the point (−2,0). Write the equation in slope-intercept form.
    9·1 answer
  • 1 3/5 gallons of gasoline were used to drive 25 1/2 miles. How many miles per gallons did the car get?​
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!