If there is such a scalar function <em>f</em>, then



Integrate both sides of the first equation with respect to <em>x</em> :

Differentiate both sides with respect to <em>y</em> :


Integrate both sides with respect to <em>y</em> :

Plug this into the equation above with <em>f</em> , then differentiate both sides with respect to <em>z</em> :



Integrate both sides with respect to <em>z</em> :

So we end up with

We are given with a triangle and three medians. The intersection of the two medians is also given which is (4,5). What is asked is the intersection between another pair of medians. Since the medians of a triangle intersect at the centroid of a triangle, the intersection is also
<span>B. (4, 5)</span>
The information about the points being vertices that make up a line to represent the side of a hexagon is irrelevant, as we are only looking for the distance of a line based on their x and y coordinates.
Look at the point's x and y coordinates:
First point:
x = -5, y = 6
Second point:
x = 5, y = 6
You'll notice that the y-coordinate for both points is the same (6 = 6). This means that the segment created by the points will be horizontal, since there is only movement on the x-axis if you trace the segment from point to point.
To find the distance between the two points, we'll only need to subtract the first point's x-coordinate from the second:
5 - (-5) = 5 + 5 = 10
The answer will be the following statement:
Since the y-coordinates are the same, the segment is horizontal, and the distance between the points is 10 units.
It looks like you're given

Then by the additivity of definite integrals this is the same as

(presumably this is what the hint suggests to use)
Then by the fundamental theorem of calculus, we have

Answer:
x = 15°
Step-by-step explanation:
<u>We are given;</u>
sin(2x + 7) = cos(4x - 7)
We are required to solve for the value of x
- We need to know that for complementary angles;
Sin θ = Cos (90-θ) where, θ and 90-θ are complementary angles.
- Complementary angles are angles that add to 90°
- Therefore;
(2x +7) + (4x - 7) = 90
6x = 90
x = 15°
Therefore, the value of x is 15°