A point in geometry is a location.
It has no size, width, length or depth. A point is shown by a dot. A line is defined as a line of points that extends infinitely in two directions.
The first thing we must do in this case is find the derivatives:
y = a sin (x) + b cos (x)
y '= a cos (x) - b sin (x)
y '' = -a sin (x) - b cos (x)
Substituting the values:
(-a sin (x) - b cos (x)) + (a cos (x) - b sin (x)) - 7 (a sin (x) + b cos (x)) = sin (x)
We rewrite:
(-a sin (x) - b cos (x)) + (a cos (x) - b sin (x)) - 7 (a sin (x) + b cos (x)) = sin (x)
sin (x) * (- a-b-7a) + cos (x) * (- b + a-7b) = sin (x)
sin (x) * (- b-8a) + cos (x) * (a-8b) = sin (x)
From here we get the system:
-b-8a = 1
a-8b = 0
Whose solution is:
a = -8 / 65
b = -1 / 65
Answer:
constants a and b are:
a = -8 / 65
b = -1 / 65
<span>96 degrees
Looking at the diagram, you have a regular pentagon on top and a regular hexagon on the bottom. Towards the right of those figures, a side is extended to create an irregularly shaped quadrilateral. And you want to fine the value of the congruent angle to the furthermost interior angle. So let's start.
Each interior angle of the pentagon has a value of 108. The supplementary angle will be 180 - 108 = 72. So one of the interior angles of the quadrilateral will be 72.
From the hexagon, each interior angle is 120 degrees. So the supplementary angle will be 180-120 = 60 degrees. That's another interior angle of the quadrilateral.
The 3rd interior angle of the quadrilateral will be 360-108-120 = 132 degrees. So we now have 3 of the interior angles which are 72, 60, and 132. Since all the interior angles will add up to 360, the 4th angle will be 360 - 72 - 60 - 132 = 96 degrees.
And since x is the opposite (or congruent) angle to this 4th interior angle, it too has the value of 96 degrees.</span>
We find the length of AD using the similarity of right triangle property. See image attached.
AD² = BD × CD
AD² = 9 × 36
AD² = 324
AD² = 18²
AD = 18
The length of AD is 18 units
Answer:
218.25 seconds
Step-by-step explanation:
54.73
54.56
54.32
54.54
+_____
218.15
