Answer:
5/17 or 0.294...
Step-by-step explanation:
Used a Calculator....
Answer:
The height is 12 feet.
Step-by-step explanation:
The formula for area of a triangle is 1/2 ⋅ b (base) ⋅ h (height).
Now let's plug in the numbers.
According to the word problem, the base is 12 feet.
As of now, our equation is: 1/2 ⋅ 12 ⋅ h
The only number times 1/2 that would give you an answer of 72 is 144.
12⋅12 = 144.
This means the height is 12.
And, 1/2 ⋅ 12 ⋅ 12 ⋅ = 72.
Because the area of the triangle is 72, 72 is the number we are looking for.
Therefore, the height is 12.
I really hope this made sense, it was a bit rushed.
The tangent to
through (1, 1, 1) must be perpendicular to the normal vectors to the surfaces
and
at that point.
Let
. Then
is the level curve
. Recall that the gradient vector is perpendicular to level curves; we have

so that the gradient of
at (1, 1, 1) is

For the surface
, we have

so that
. We can obtain a vector normal to
by taking the cross product of the partial derivatives of
, and evaluating that product for
:


Now take the cross product of the two normal vectors to
and
:

The direction of vector (24, 8, -8) is the direction of the tangent line to
at (1, 1, 1). We can capture all points on the line containing this vector by scaling it by
. Then adding (1, 1, 1) shifts this line to the point of tangency on
. So the tangent line has equation

Draw a square and connect b to d
Answer:

Step-by-step explanation:
The formula of a volume of a cylinder:

<em>r</em><em> - radius</em>
<em>H</em><em> - height</em>
<em />
We have a diameter <em>d = 8 → d = 2r → 2r = 8 → r = 4</em>
and <em>H = 12.</em>
<em></em>
Substitute:
