Answer:
3.25
Step-by-step explanation:
–2x + 4y = –7 . . . . . (1)
y = -1/2x + 5 . . . . . . (2)
Putting (2) into (1), we have:
-2x + 4(-1/2x + 5) = -7
-2x - 2x + 5 = -7
-4x = -7 - 5 = -12
x = -12/-4 = 3
y = -1/2(3) + 5 = -3/2 + 5 = 7/2
Hence, the system has one solution.
Answer:
Step-by-step explanation:
<u>According to the triangle inequality theorem, any side length is less than the sum of the other two:</u>
- x < 2x + 1 + x + 4 ⇒ x < 3x + 5 ⇒ 2x > - 5 ⇒ x > - 2.5
- 2x + 1 < x + x + 4 ⇒ 2x + 1 < 2x + 4 ⇒ 1 < 4, any value of x
- x + 4 < x + 2x + 1 ⇒ x + 4 < 3x + 1 ⇒ 2x > 3 ⇒ x > 3/2
<u>Common solution of the three inequalities above is:</u>
Correct choice is C
Answer:
-7
Step-by-step explanation:
−10−(−3)
=−10−(−3)
=−10+3
=−7
The volume of the cylinder is:
V = pi * r ^ 2 * h = 64
The surface area is:
A = 2 * pi * r ^ 2 + 2 * pi * r * h
We write the area as a function of r:
A (r) = 2 * pi * r ^ 2 + 2 * pi * r * (64 / (pi * r ^ 2))
Rewriting:
A (r) = 2 * pi * r ^ 2 + 2 * (64 / r)
A (r) = 2 * pi * r ^ 2 + 128 / r
Deriving:
A '(r) = 4 * pi * r - 128 / r ^ 2
We equal zero and clear r:
0 = 4 * pi * r - 128 / r ^ 2
128 / r ^ 2 = 4 * pi * r
r ^ 3 = 128 / (4 * pi)
r = (128 / (4 * pi)) ^ (1/3)
r = 2.17 cm
The height is:
h = 64 / (pi * r ^ 2)
h = 64 / (pi * (2.17) ^ 2)
h = 4.33 cm
Answer:
The dimensions giving the minimum surface area are:
r = 2.17 cm
h = 4.33 cm
