Answer:
wenus.
Step-by-step explanation:
4 inches. hduruuruthtututuu4u4
First find the secant line. The slope of the secant line through
(when
) and
(when
) is the average rate of change of
over the interval
![[-1,2]](https://tex.z-dn.net/?f=%5B-1%2C2%5D)
:
The tangent line to
will have a slope determined by the derivative:
Both the secant and tangent will have the same slope when
, or when
.
Answer:
See below.
Step-by-step explanation:
A good idea would be to write if as:
-x^4 + 0x^3 + 0x^2 + 0x + 1, then you can perform long division.
Answer:
h ≈ 7.816 cm
r ≈ 5.527 cm
Step-by-step explanation:
The volume of a cone is:
V = ⅓ π r² h
The lateral surface area of a cone is:
A = π r √(r² + h²)
1/4 of a liter is 250 cm³.
250 = ⅓ π r² h
h = 750 / (π r²)
Square both sides of the area equation:
A² = π² r² (r² + h²)
Substitute for h:
A² = π² r² (r² + (750 / (π r²))²)
A² = π² r² (r² + 750² / (π² r⁴))
A² = π² (r⁴ + 750² / (π² r²))
Take derivative of both sides with respect to r:
2A dA/dr = π² (4r³ − 2 × 750² / (π² r³))
Set dA/dr to 0 and solve for r.
0 = π² (4r³ − 2 × 750² / (π² r³))
0 = 4r³ − 2 × 750² / (π² r³)
4r³ = 2 × 750² / (π² r³)
r⁶ = 750² / (2π²)
r³ = 750 / (π√2)
r³ = 375√2 / π
r = ∛(375√2 / π)
r ≈ 5.527
Now solve for h.
h = 750 / (π r²)
h = 750 / (π (375√2 / π)^⅔)
h = 750 ∛(375√2 / π) / (π (375√2 / π))
h = 2 ∛(375√2 / π) / √2
h = √2 ∛(375√2 / π)
h ≈ 7.816
Notice that at the minimum area, h = r√2.
Answer:
110/289 feet
Step-by-step explanation:
Step one:
given data
Area of the floor= 55/14 square feet.
The length of the floor= 8 1/2 feet-----convert to simple fraction= 17/2 feet
Step two:
The expression for the area of the room is
Area= L*W
55/14= 17/2*W
55/14=17W/2
cross multiply
17W*14=55*2
289W=110
divide both sides by 289
W= 110/289 feet
