Answer:
x = 10 - 10sqrt(3)/3
Approximately 4.2265 cm
Volume = 1539.6 cm³
Step-by-step explanation:
Let the height be x
V = (20 - 2x)(40 - 2x)x
V = (800 - 80x - 40x + 4x²)x
V = 4x³ - 120x² + 800x
dV/dx= 12x² - 240x + 800 = 0
3x² - 60x + 200 = 0
x = [60 +/- sqrt(60² - 4(3)(200))]/6
x = [30 +/- 10sqrt(3)]/3
x = 10 +/- 10sqrt(3)/3
Approximately,
15.7735 and 4.2265
d²V/dx² = 24x - 240
For max, d²V/dx² < 0
So, x = 4.2265
V = (20 - 2x)(40 - 2x)x
Plug in x = 10 - 10sqrt(3)/3
V = 1539.600718
Answer:
<h2>y = 32 (Verified Answer) ✅</h2>
Step-by-step explanation:
We will use a proportion to solve this.

Now, we cross multiply.
2y = 16 x 4
2y = 64
Now, we must divide by 2 to get the correct value for y
y = 64/2
y = 32
Now, we can use the same proportion to check our answer.
2(32) = 16 x 4
64 = 64 ✅
Answer:
-6, -3
3, 8
Step-by-step explanation:
In order to find the number that are solutions to the compound inequalities, you first solve fr x on each inequality.
First inequality:
interval = (-∞ , -3]
Second inequality:
interval = (2 , ∞)
The interval solution is (-∞ , -3] U (2 , ∞)
The number that are included in the previous interval are:
-6, -3
or
3, 8
To answer the question above, investigate the placement of the blocks on the scale. Since the figure is not given above, general rules should be followed.
To balance the scale, add 4 blocks on the side which contains only 5 blocks or take away 4 blocks from the side containing 9 blocks.
Answer:
Not similar because of different interior angles
Step-by-step explanation:
<u>For triangle XYZ:</u>
- We should find the missing angle
- The missing angle will be labelled z
- All triangle interior angles add up to 180
z + 55 + 84 = 180
z + 139 = 180
z = 180 - 139
z = 41
<u>For triangle PQR:</u>
- The missing angle will be labelled q
q + 55 + 38 = 180
q + 93 = 180
q = 180 - 93
q = 87
Since the interior angles of the 2 triangles aren't equal, they are not similar