complete the following steps to find an equation of the tangent plane to the surface at the point : step 1: determine the function that describes the surface in the form : step 2: find step 3: find step 4: find step 5: find step 6: find step 7: find the equation of the tangent plane at the given point is

Answers

Answer 1

Answer:

The point-normal form of a plane equation: (Fx(x0, y0, z0))(x - x0) + (Fy(x0, y0, z0))(y - y0) + (Fz(x0, y0, z0))(z - z0) = 0.

To find the equation of the tangent plane to a surface at a given point, follow these steps:

Step 1: Determine the function that describes the surface in the form F(x, y, z) = 0.

Step 2: Find the partial derivative of F with respect to x, denoted as Fx.

Step 3: Find the partial derivative of F with respect to y, denoted as Fy.

Step 4: Find the partial derivative of F with respect to z, denoted as Fz.

Step 5: Evaluate Fx, Fy, and Fz at the given point (x0, y0, z0).

Step 6: Use the gradient vector, which consists of the evaluated partial derivatives (Fx(x0, y0, z0), Fy(x0, y0, z0), Fz(x0, y0, z0)), as the normal vector to the tangent plane.

Step 7: Use the point-normal form of a plane equation: (Fx(x0, y0, z0))(x - x0) + (Fy(x0, y0, z0))(y - y0) + (Fz(x0, y0, z0))(z - z0) = 0. This is the equation of the tangent plane at the given point.

By following these steps, you will find the equation of the tangent plane to the surface at the specified point.

For more about plane equation:

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24x + 34p = p Solve for p
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Seven integers, x1, x2, x3, x4, x5, x6, and x7, are picked at random from the set of all integers between 10 and 110, inclusive. If each of these integers is divided by 7 and the 7 remainders are all added together, what would be the sum of the 7 remainders?

Select the postulate that is illustrated for the real numbers.
5•1=5

Answers

Answer:

Multiplication identity

Step-by-step explanation:

We are given that

$5\cdot 1=5$

We have to find which property of real number is used in given expression.

Multiplication identity: It is defined as the number by which multiply any number and get itself.

$a\cdot 1=1\cdot a=a$

Then, 1 is multiplication identity.

$5\cdot 1=5$

When we are multiplying 5 with 1 then we get 5.

Therefore, 1 is multiplication identity.

Hence, multiplication property of real numbers is used in given expression.

Multiplication Identity

What is the expression of 2+32times5

Answers

Answer:

2+32×5

If you want the answer:

2+160

162

Step-by-step explanation:

Answer:

2+5^32

Step-by-step explanation:

jenny`s mom says she has an hour before it's bedtime. Jenny's spends 3\5 of hour texting a friend and 3\8 of the remaining time brushing her teeth and putting on her pajamas. she spends the rest of the time reading her book. how long did jenny read?

Answers

15 minutes

Further explanation

Given:

Jenny has an hour before its bedtime.
Jenny spends $(3)/(5)$ of an hour texting a friend and $(3)/(8)$ of the remaining time brushing her teeth and putting on her pajamas.
She spends the rest of the time reading her book.

Question:

How long did Jenny read?

The Process:

Step-1: We need to calculate the time of texting a friend in minutes.

Recall that $\boxed{1 \ hour = 60 \ minutes}$

$\boxed{(3)/(5) \ hour = \ ? \ minutes}$

$\boxed{(3)/(5) \ hour = (3)/(5) * 60 \ minutes}$

We crossed out 5 and 60, i.e., $\boxed{60 / 5 = 12}$

$\boxed{(3)/(5) \ hour = 3 * 12 \ minutes}$

Therefore,

$\boxed{\boxed{ \ (3)/(5) \ hour = 36 \ minutes \ }}$

Step-2: Let us calculate the remaining time.

$\boxed{60 \ minutes - 36 \ minutes = 24 \ minutes }$

Step-3: Jenny spends $(3)/(8)$ of the remaining time brushing herteeth and putting on her pajamas.

$\boxed{(3)/(8) * 24 \ minutes}$

We crossed out 8 and 24, i.e., $\boxed{24 / 8 = 3}$

$\boxed{= 3 * 3 \ minutes}$

$\boxed{\boxed{ \ 9 \ minutes \ }}$

Step-4: Let us calculate how long Jenny read for the rest of time.

$\boxed{24 \ minutes - 9 \ minutes = 15 \ minutes }$

Thus, Jenny spent 15 minutes reading a book before its bedtime.

- - - - - - - - - -

Quick Steps:

Let us calculate how long Jenny read for the rest of time.

$\boxed{ \ = \bigg(1 - (3)/(8) \bigg) * \bigg(1 - (3)/(5) \bigg) * 60 \ minutes \ }$

$\boxed{ \ = (5)/(8) * (2)/(5) * 60 \ minutes \ }$

$\boxed{ \ = (10)/(40) * 60 \ minutes \ }$

$\boxed{ \ = (1)/(4) * 60 \ minutes \ }$

$\boxed{\boxed{ \ 15 \ minutes \ }}$

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Keywords: Jenny, has an hour, before its bedtime, spends 3/5 of an hour, texting a friend, 3/8 of the remaining time, brushing her teeth, putting on her pajamas, reading her book

First you'll need to get the same denominator. So instead of 3/5 and 3/8 you'll have 24/40 and 15/40. Now that we've changed the value of the denominator, the 40/40 will now represents the 1 hour that Jenny has before bedtime. So you add 24/40 and 15/40 and get 39/40. 39/40 stands for the time that Jenny has already spent brushing her teeth and texting her friend all together. Since the 1 hour is 40/40 subtract 39/40 from it to get 1/40. 1/40 is equal to the rest of the time Jenny spends reading or 1.5 minutes.

Which direction would the graph of y=-|x+2|+3 open?

Answers

Answer:

The absolute function opens in downward direction.

Step-by-step explanation:

we have to find the direction in which the graph of y=-|x+2|+3 open.

The general form of an absolute value function is f(x)=a|x-h|+k.

The absolute value function will always open to the negative direction when a is negative and positive direction i.e upward when a is positive.

Here, given absolute function is y=-|x+2|+3

which gives a=-1, negative

Hence, the absolute value function will always open to the negative direction. Because this is in the form y = -|x|, it opens down.

this is it, it will open down :)

A cup of brewed tea has 54 milligrams less caffeine than a cup of brewed coffee. If a cup of tea has 66 milligrams of caffeine, how much caffeine is in a cup of coffee? Write this problem in an equation.

Answers

Answer:

There is 120 milligrams of caffeine in a cup of coffee.

Step-by-step explanation:

A cup of brewed tea has 54 milligrams less caffeine than a cup of brewed coffee. A cup of tea has 66 milligrams of caffeine.

Let the amount of caffeine in a cup of coffee be = x

In the equation form, we can denote this as:

$66=x-54$

Solving for x

$x=66+54$

x = 120

Therefore, there is 120 milligrams of caffeine in a cup of coffee.

x-54= 66 x being the amount of caffeine in the cup of coffee.

The steps below show the incomplete solution to find the value of x for the equation 7x – 3x – 4 = –1 + 21:Step 1: 7x – 3x – 4 = –1 + 21

Step 2: 7x – 3x – 4 = 20

Step 3: 4x – 4 = 20Which of these is most likely the next step? (4 points)

4x = 24
4x = 16
4x = 5
4x = 80

Answers

Step 1 : 7x - 3x - 4 = -1 +21
Step 2 : 7x - 3x - 4 = 20
Step 3 : 4x - 4 = 20
Step 4 4x -4 +4 = 20 + 4
4x = 24

Answer 4x = 24

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