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
goldfiish [28.3K]
3 years ago
7

Find an equation of the tangent to the curve at the given point by both eliminating the parameter and without eliminating the pa

rameter.x = 6 + ln(t), y = t2 + 6, (6, 7)
Mathematics
1 answer:
jek_recluse [69]3 years ago
4 0

Answer:2x-y=5

Step-by-step explanation:

Given

x=6+\ln t

y=t^{2}+6

\left ( a\right ) without eliminating parameter

\frac{\mathrm{d} x}{\mathrm{d} t}=\frac{1}{t}

\frac{\mathrm{d} y}{\mathrm{d} t}=2t

\frac{\mathrm{d} y}{\mathrm{d} x}=2t^2

at \left ( 6,7\right )

6=6+\ln\left ( t\right )

t=1

Equation of line is given by

2=\frac{y-7}{x-6}

2x-12=y-7

2x-y=5

\left ( b\right )by eliminating parameter

x-6=\ln \left ( t\right )

t=e^{x-6}

y=t^2 +6

y=e^{\left ( 2x-12\right )}+6

differentiating we get

\frac{\mathrm{d}y}{\mathrm{d} x}=2e^\left ( 2x-12\right )

at \left ( 6,7\right )

\frac{\mathrm{d}y}{\mathrm{d} x}=2

2\left ( x-6\right )=\left ( y-7\right )

2x-y=5

You might be interested in
Which image is graphed
BaLLatris [955]
The 1st one
y <x-1 and y>=-2x +4
4 0
3 years ago
A company has two manufacturing plants with daily production levels of 5x +14 items and 3x-7 ​items, respectively. The first pla
Llana [10]

Answer:

The first plant produces 2x + 21 more items daily than the second​ plant.

Step-by-step explanation:

The daily production of the two plants are:

Plant 1: 5x + 14

Plant 2: 3x - 7

Compute the number of items first plant produces more than the second​ plant as follows:

\text{Plant 1 - Plant 2}=5x+14-3x+7\\\\=2x+21

Thus, the first plant produces 2x + 21 more items daily than the second​ plant.

3 0
3 years ago
7. What is the equation of the line that passes through (-1, -4) and (0,5)?
Serga [27]

Answer:

A)y=9x+5

Step-by-step explanation:

If x=-1, y=-4,

  y=9*-1+5=(-9)+5=-4

If x=0, y=5,

  y=9*0+5=5

3 0
2 years ago
Write 85 expanded form
WARRIOR [948]
80 + 5 is 85 in extended form
3 0
3 years ago
Read 2 more answers
Based on the scatter plot, what type of association is shown between hours of sleep and test scores?
bonufazy [111]
This is easily (A) Positive Association
7 0
2 years ago
Other questions:
  • What is the slope of the line that has the equation 4x + 2y = 12?
    11·2 answers
  • A library buys 36 English books, 48 Science books and 72 Mathematics books. The thickness of each book is the same. Now, the lib
    14·2 answers
  • Which price choice is the lowest price per ounce? HELP! I HAVE 2 HRS TO GET CORRECT ANSWER!
    10·1 answer
  • Write as an improper fraction 7 2/5
    8·1 answer
  • An animal shelter has cats and dogs. The ratio of cats to dogs is 3 to 5. If there are 15 dogs, how many cats are there?
    10·2 answers
  • Solve for x. See attachment.....
    13·1 answer
  • What is a equivalent fraction for 3/9?
    6·1 answer
  • The linear equation that represents the values shown in the table below is <br><br><br> .
    11·2 answers
  • Solve 4X^2+7 = 8X +4 by using the quadratic formula
    10·1 answer
  • A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a radioactive substance. After 20 hours,
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!