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3 years ago

Suppose the domain of g is ( negative infinity, infinity). Is the domain of f o g ( negative infinity, infinity)?

1 answer:

8 0

The domain and range of the composition of f of g is not necessarily equal to the domain and range of g since the function f . This will only be true if the domain and range of the function f is (negative infinity, infinity).

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Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in t

nataly862011 [7]

Let (x, y, z) be a point on the plane in the first octant. The box formed by this point has volume xyz, and you want to maximize this subject to the equation of the plane.

Use the method of Lagrange multipliers: the Lagrangian is

L(x, y, z) = xyz - λ (x + 2y + 3z - 6)

Find its critical points:

∂L/∂x = yz - λ = 0

∂L/∂y = xz - 2λ = 0

∂L/∂z = xy - 3λ = 0

∂L/∂λ = -(x + 2y + 3z - 6) = 0

Solving the first three equations for λ gives

λ = yz = xz/2 = xy/3

Solve these equations for y and z :

• yz = xz/2 => y = x/2 => 2y = x

• yz = xy/3 => z = x/3 => 3z = x

Substitute these solutions into the last equation and solve for x, then again for y and z :

x + 2y + 3z - 6 = 3x - 6 = 0 => 3x = 6 => x = 2, y = 1, z = 2/3

At this critical point, the maximum volume is

xyz = 2*1*2/3 = 4/3

4 0

3 years ago

What is a counter example in following sentence:

koban [17]

(1/2) ^2 = 1/2 * 1/2 = 1/4

1/4 < 1/2

4 0

2 years ago

Read 2 more answers

How many times as fast as a propeller plane at 266 mph is a jet at 625 mph?

ivann1987 [24]

2.3496240602

625÷266

5 0

3 years ago

Which expressions are equivalent to −tan⁡ θ?

zzz [600]

Answer:

−1/cotθ

1/cot(−θ)

tan(−θ)

Step-by-step explanation:

The tangent function is a the ratio for an angle defined as opposite / adjacent. A negative applied to −tan⁡ θ will give the opposite value. This is also true for the function when taken on a negative angle. tan(−θ) = −tan⁡ θ. This identity is also true for sin, sec, and cot. Recall that cotangent is the reciprocal of tangent and is defined as the ratio adjacent / opposite. Taking the reciprocal of cotangent will be the same as tangent. Using this information the following are equivalent:

1/cotθ

−1/cotθ ----> The reciprocal of Cot is Tan

1/cot(−θ) ----> The reciprocal of Cot is Tan and cot(−θ) = −cot⁡ θ.

−1/cot(−θ)

tan θ

tan(−θ)----> tan(−θ) = −tan⁡ θ

7 0

3 years ago

If Tan is 3/4 what is sin?

Pani-rosa [81]

Answer:

tanA=34⟹sinA=332+42−−−−−−√=35

Now, we have

sinAcosA=tanA

⟹3/5cosA=tanA

⟹cosA=13×54×3

⟹cosA=45

⟹cosAsinA=4×35×5=1225

Step-by-step explanation:

7 0

2 years ago