Surface area is just the area of all these 4 triangles plus the rectangle.
First we can find the area of the rectangle.
Half of the length is 28 cm, so the full length must be 28 * 2 = 56 cm.
The base for the left and right triangles are 27. The heights would be the net length minus half the length of the rectangle:
Calculate the area:
We have two of these triangles.
Now do the other two pair of triangles. The bases for them are 28 + 28 = 56 cm. The heights would be the net width minus the width of the rectangle:
Now find the area:
We have two of these triangles.
Add all the areas together:
1) The function is
3(x + 2)³ - 32) The
end behaviour is the
limits when x approaches +/- infinity.3) Since the polynomial is of
odd degree you can predict that
the ends head off in opposite direction. The limits confirm that.
4) The limit when x approaches negative infinity is negative infinity, then
the left end of the function heads off downward (toward - ∞).
5) The limit when x approaches positive infinity is positivie infinity, then
the right end of the function heads off upward (toward + ∞).
6) To graph the function it is important to determine:
- x-intercepts
- y-intercepts
- critical points: local maxima, local minima, and inflection points.
7)
x-intercepts ⇒ y = 0⇒ <span>
3(x + 2)³ - 3 = 0 ⇒ (x + 2)³ - 1 = 0
</span>
<span>⇒ (x + 2)³ = -1 ⇒ x + 2 = 1 ⇒
x = - 1</span>
8)
y-intercepts ⇒ x = 0y = <span>3(x + 2)³ - 3 =
3(0 + 2)³ - 3 = 0 - 3×8 - 3 = 24 - 3 =
21</span><span>
</span><span>
</span><span>9)
Critical points ⇒ first derivative = 0</span><span>
</span><span>
</span><span>i) dy / dx = 9(x + 2)² = 0
</span><span>
</span><span>
</span><span>⇒ x + 2 = 0 ⇒
x = - 2</span><span>
</span><span>
</span><span>ii)
second derivative: to determine where x = - 2 is a local maximum, a local minimum, or an inflection point.
</span><span>
</span><span>
</span><span>
y'' = 18 (x + 2); x = - 2 ⇒ y'' = 0 ⇒ inflection point.</span><span>
</span><span>
</span><span>Then the function does not have local minimum nor maximum, but an
inflection point at x = -2.</span><span>
</span><span>
</span><span>Using all that information you can
graph the function, and I
attache the figure with the graph.
</span>
Answer:
1. 360
2. Yes because in a regular hexagon all angles are congruent so the exterior angles are as well
3. (i) 60 (ii) 120
4.
(i) 1. 360 2. Yes because in a regular octagon all angles are congruent so the exterior angles are as well 3. (i) 45 (ii) 135
(ii) 1. 360 2. Yes because in a regular 20-gon all angles are congruent so the exterior angles are as well 3. (i) 18 (ii) 162
Step-by-step explanation:
Works for each polygon
1. First take the number of sides and subtract it by 2 then multibly that by 180
6-2=4x180=720
Then divide by the number of angles and subrtact that number by 180 to find the measure of one exterior angle
720/6=120
180-120=60
Then multiply by the number of exterior angles
60x6=360
2. Regular polygons always have equal angles so the exterior angles are as well
3. Put in your numbers from earlier
(i) 60 (ii)120
Hope this helps! :)
P.S. Feel free to mark brainliest :)
