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:
C. 7790.83 cm^3
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3
We know the radius is 12.3
Using 3.14 for pi (This will give us an approximation, not an exact value)
V = 4/3(3.14) (12.3)^3
=7790.82984 cm^3
Answer:
6.34 × 10²
Step-by-step explanation:
Calculating scientific notation for a positive integer is simple, as it always follows this notation: a x 10b.
Step 1
To find a, take the number and move a decimal place to the right one position.
Original Number: 634
New Number: 6.34
Step 2
Now, to find b, count how many places to the right of the decimal.
New Number: 6 . 3 4
Decimal Count: 1 2
There are 2 places to the right of the decimal place.
Step 3
Building upon what we know above, we can now reconstruct the number into scientific notation.
Remember, the notation is: a x 10b
a = 6.34
b = 2
Now the whole thing:
6.34 x 10²
Step 4
Check your work:
10² = 100 x 6.34 = 634
3/1 is the slope of the line