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
adoni [48]
3 years ago
11

Can someone help me solve this?

Mathematics
1 answer:
serg [7]3 years ago
4 0

Answer:

(a) y = -3/5 x + 13/5

(b) y = 5/3 x + 1/3

Step-by-step explanation:

(a) The slope of the tangent line is dy/dx.  Use implicit differentiation:

x² + y² + 4x + 6y − 21 = 0

2x + 2y dy/dx + 4 + 6 dy/x = 0

2x + 4 + (2y + 6) dy/dx = 0

x + 2 + (y + 3) dy/dx = 0

(y + 3) dy/dx = -(x + 2)

dy/dx = -(x + 2) / (y + 3)

At the point (1, 2), the slope is:

dy/dx = -(1 + 2) / (2 + 3)

dy/dx = -3/5

Using point-slope form of a line:

y − 2 = -3/5 (x − 1)

Simplifying to slope-intercept form:

y − 2 = -3/5 x + 3/5

y = -3/5 x + 13/5

(b) The normal line is perpendicular to the tangent line, so its slope is 5/3.  It also passes through the point (1, 2), so point-slope form of the line is:

y − 2 = 5/3 (x − 1)

Simplifying to slope-intercept form:

y − 2 = 5/3 x − 5/3

y = 5/3 x + 1/3

You might be interested in
In how many ways can 7 people line if A needs to be first or last and B needs to be in the middle
12345 [234]

Answer:

<em>Assuming person A and person B are part of the 7 people</em>, there are 10 ways the 7 people can line up if A needs to be first or last and B needs to be in the middle.

Step-by-step explanation:

There are 2 places for A (first, last) and 5 places for B (anywhere but first or last). 2 x 5 = 10.

8 0
2 years ago
How do you simplify 4^-2h^-4j^3
notka56 [123]
    j^3
_______
4^2 h^4

when you have negatives, you want them to be positive. To do that you need to convert it into a fraction
7 0
3 years ago
Craig likes to collect records last year he had Tim records and his collection now he has 15 records what is the percent increas
Softa [21]

Answer:

50% I believe?

Step-by-step explanation:

7 0
2 years ago
The boxplot displays the scores from an economics chapter test. identify the second quartile.​
netineya [11]

Answer:

Step-by-step explanation:

The middle line is the median, then from left to right the lines are the first, second, third and fourth quartile.  

5 0
3 years ago
Read 2 more answers
Subtract the quotient of 18 and 3 from the sum of 22 and 9
netineya [11]
25 cuz 18/3=6 and 22+9=31. 31-6=25
7 0
3 years ago
Read 2 more answers
Other questions:
  • 5x7/10=. The product lies between. And.
    11·1 answer
  • ome pleated draperies must be twice as wide as the window they cover. How many square yards of material are needed to cover this
    15·1 answer
  • A recursive sequence requires you to use previous terms to find the next term. True False
    7·2 answers
  • A bakery has dozen whole-grain
    6·2 answers
  • Notah is studying ocean animals. He learns that the sixgill
    6·1 answer
  • Finde<br>3 rational number<br> 7 and 8<br>​
    10·2 answers
  • HELP PLEASE THANK U
    11·1 answer
  • PLZ I NEED HELP!!! THIS IS TIMED!!!! PLZ HELP ME!
    15·2 answers
  • Can somebody help me with my Geometry?​
    13·2 answers
  • Plssssss helpp :'Dd<br> If JL = 5x + 1 and MK = 8x - 32, find JL and NK.<br><br> JL =<br><br> NK =
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!