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
sergiy2304 [10]
3 years ago
11

Find an equation of the tangent plane to the given surface at the specified point. z = ln(x − 8y), (9, 1, 0)

Mathematics
1 answer:
Archy [21]3 years ago
4 0

Answer:

x - 8y - z = 1

Step-by-step explanation:

Data provided according to the question is as follows

f(x,y) = z = ln(x - 8y)

Now the equation for the tangent plane to the surface

For z = f (x,y) at the point P (x_0,y_0,z_0) is

z - z_0 = f_x(x_0,y_0)(x-x_0) + f_y(x_0,y_0)(y-y_0)\\

Now the partial derivatives of f are

f_x(x,y) = \frac{1}{x-8y} \\\\f_y(x,y) = \frac{8}{x-8y} \\\\P(x_0,y_0,z_0) = (9,1,0)\\\\f_z(9,1,0) = (\frac{1}{x-8y})_^{(9,1,0)}

\\\\=\frac{1}{9-8}

= 1

Now

f_y(9,1,0)=(\frac{8}{x-8y})_{(9,1,0)}\\\\ = -\frac{8}{9 - 8}

= -8

So, the tangent equation is

z - 0 = 1\times (x - 9) -8\times (y - 1)

Now after solving this, the following equation arise

z = x - 9 - 8y + 8

z = x - 8y - 1

Therefore

x - 8y - z = 1

You might be interested in
A building contractor examined 6 floor joists in a home and found that they had the following widths:
miss Akunina [59]

Answer:

Step-by-step explanation:8 inches

89 is the answe 89

8 0
2 years ago
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Juli2301 [7.4K]

Answer:

4/8

Step-by-step explanation:

8 is how many cookies in total and 4 is how many that needs to be distributed.

7 0
2 years ago
What is 1/5 of 1/2 of 1/4 of 152?
Alona [7]
1/5 of 152 is 30.4
1/2 of 152 is 76
1/4 of 152 is 38

hope this helped :)



4 0
3 years ago
Read 2 more answers
Jake is using a horse trailer to take his horses to his new ranch. 1 Horse= 1,200 lb Trailer= 2,700 lb Jake's truck can tow a ma
Kitty [74]

Answer:

Jack can take only 1 horse on his trailer to be towed by the truck without going over the maximum weight the truck.

Step-by-step explanation:

Given:

Weight of 1 horse = 1,200 lb

Weight of trailer = 2,700 lb

Jacks'truck can tow a maximum of 5000 pounds.

To find the maximum number of horses Jack can take in his trailer without going over the maximum weight his truck can tow.

Solution:

Let the maximum number of horses that Jack can take be = x

Using unitary method to find weight of x horses.

If 1 horse weights = 1,200 lb

Then x horses will weight in lbs = 1,200\times x = 1,200x

Total weight of horses and trailer in lbs = 1200x+2700

Since the maximum weight the truck can tow = 5,000 lb, so the inequality can be given as:

1200x+2700\leq5000

Subtracting both sides by 2700.

1200x+2700-2700\leq5000-2700

1200x\leq2300

Dividing both sides by 1200.

\frac{1200x}{1200}\leq\frac{2300}{1200}

x\leq1.91

From the inequality solution for x, we can conclude that Jack can take only 1 horse on his trailer to be towed by the truck without going over the maximum weight the truck.

3 0
3 years ago
Zen deposited some money in a savings account. The graph below shows the value of Zen's investment y, in dollars, after x months
kifflom [539]

The y-intercept of 1000 in the graph is at the point where x is equal to 0.

At x=0, it means no month have passed. It is the initial point where Zen deposited the money.

What is the amount (y axis)? 1000!

So y represents the initial deposit of Zen, which is 1000.


ANSWER: Answer choice D (Amount of money Zen deposited in the savings account)

6 0
3 years ago
Read 2 more answers
Other questions:
  • Solve 55/z + 1/5 = 7/z
    5·1 answer
  • The radius of a pizza dish is 12 inches. which expression would best describe the circumference of the pizza dish?
    10·1 answer
  • Which of the expressions are equivalent to the one below? theirs multiple answers
    5·1 answer
  • When a certain valve is open, 281 gallons go through it in one hour. The number of gallons that would go through in 94 hours is
    5·2 answers
  • Which of the following is the solution to the compound inequality below? 5/2+x_>1/3 or x+2 < -29/6 A.x_>-2/3or x <-2
    6·1 answer
  • Which pair of inequalities is equivalent to 0 Choose the correct answer below.
    7·2 answers
  • Plz help me plz plz plz its math
    7·1 answer
  • Pls answer i’m begging
    13·2 answers
  • Brainliest reward need brief working out
    15·1 answer
  • The weight of a boy was 15kg last year. If his weight increases by 3kg this year, find the percentage increase in his weight.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!