Answer:
x = 32
Step-by-step explanation:
Each angle of the equilateral triangle is 60°.
(2x -4)° = 60°
x -2 = 30 . . . . . . divide by 2°
x = 32
__
5y° = 60°
y = 12 . . . . . . . . . divide by 5°
Answer:
24 and 48
Step-by-step explanation:
If she had 24 of each, she would have 3 packs of cups, and 4 packs of plates.
If she had 48 of each, she would have 6 packs of cups, and 8 packs of plates.
The dimensions of a cylinder which has this maximum volume are equal to 1.83 units and 3 units.
<u>Given the following data:</u>
- Height of cylinder, h = 5.5 units.
- Radius of cylinder, r = 4.5 units.
<h3>How to calculate the volume of this cylinder?</h3>
Mathematically, the volume of a cylinder can be calculated by using this formula:
V = πr²h
Next, we would convert the above multi-variable function into a single-variable function by applying the properties of 2 similar triangles:
H/H - h = R/r
H - h = r(H/R)
h = H/R(R - r)
V = πHr²/R(R - r)
In order to maximize the volume of this cylinder, we would determine the critical points of the function by differentiating wrt r:
dV/dr = πH/R(2rR - 2r² - r²)
(2rR - 3r²) = 0
r = 2R/3
r = (2 × 4.5)/3
Maximum radius, r = 3 units.
For the max. height, we have:
h = H/R(R - r)
h = H/R(R - 2R/3)
h = H/3
h = 5.5/3
Maximum height, h = 1.83 units.
Read more on cylinder here: brainly.com/question/315709
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Synthetic division with complex numbers<span> is very similar to regular </span>synthetic division<span>. For example, if you were dividing a polynomial by x + 2, you would </span>use<span>the value of x = 2 in </span>synthetic division<span>.</span>