If

represent a family of surfaces for different values of the constant

. The gradient of the function

defined as

is a vector normal to the surface

.
Given <span>the paraboloid

.
We can rewrite it as a scalar value function f as follows:

The normal to the </span><span>paraboloid at any point is given by:

Also, the normal to the given plane

is given by:

Equating the two normal vectors, we have:
</span>

Since, -1 = 2 is not possible, therefore
there exist no such point <span>
on the paraboloid
such that the tangent plane is parallel to the plane 3x + 2y + 7z = 2</span>
.
Answer:
4 2/7 - 6/7 = 24/
7
= 3 3/
7
Step-by-step explanation:
Conversion a mixed number 4 2/
7
to a improper fraction: 4 2/7 = 4 2/
7
= 4 · 7 + 2/
7
= 28 + 2/
7
= 30/
7
To find a new numerator:
a) Multiply the whole number 4 by the denominator 7. Whole number 4 equally 4 * 7/
7
= 28/
7
b) Add the answer from previous step 28 to the numerator 2. New numerator is 28 + 2 = 30
c) Write a previous answer (new numerator 30) over the denominator 7.
Four and two sevenths is thirty sevenths
Subtract: 30/
7
- 6/
7
= 30 - 6/
7
= 24/
7
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(7, 7) = 7. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 7 × 7 = 49. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - thirty sevenths minus six sevenths = twenty-four sevenths.
Answer:
200 days
Step-by-step explanation:
600/3 = 200
3x 200 = 600
Answer:
48.
or 
51.
or 
54.
or 
57.
or 
Step-by-step explanation:
48. 
-There are two equations:
Equation 1:

or
Equation 2:

Solving equation 1:




(Inequality sign changed, because of dividing by a negative number)
-Solving equation 2:




(Inequality sign changed, because of dividing by a negative number)
-Answers:
or 
51. 
-There are two equations:
Equation 1:

or
Equation 2:

-Solving equation 1:



-Solving equation 2:



Answers:
or 
54. 
-There are two equations:
Equation 1:

or
Equation 2:

-Solving equation 1:





-Solving equation 2:





-Answers:
or 
57. 
-There are two equations:
Equation 1:

or
Equation 2:

-Solving equation 1:





Solving equation 2:





Answers:
or 
And we are finished.
<u />
Answer:
<h2>The answer is option C</h2>
Step-by-step explanation:

To find h(-67) , substitute the value of x that's - 67 into h(x). That is for every x in h(x) , replace it with - 67
We have

We have the final answer as
<h3>h( - 67) = 3158</h3>
Hope this helps you