Question

1. Let Q1 = x, where (x, y) satisfies that (1)x + (−3)y = −22 (−1)x + (7)y = 54 . Let Q = ln(3+|Q1|). Then T = 5 sin2 (100Q) satisfies:— (A) 0 ≤ T < 1. — (B) 1 ≤ T < 2. — (C) 2 ≤ T < 3. — (D) 3 ≤ T < 4. — (E) 4 ≤ T ≤ 5.

2. Let (Q1, Q2) = (x, y), where (x, y) solves x = (7)x + (−2)y + (−14) y = (−6)y + (−3)x + (26) . Let Q = ln(3 + |Q1| + 2|Q2|). Then T = 5 sin2 (100Q) satisfies:— (A) 0 ≤ T < 1. — (B) 1 ≤ T < 2. — (C) 2 ≤ T < 3. — (D) 3 ≤ T < 4. — (E) 4 ≤ T ≤ 5

3.Let Q1, Q2 be constants so that x = Q1a + Q2 solves the system (−10)x + (9)y = a (−1)x + (−9)y = −8 . Let Q = ln(3 + |Q1| + 2|Q2|). Then T = 5 sin2 (100Q) satisfies:— (A) 0 ≤ T < 1. — (B) 1 ≤ T < 2. — (C) 2 ≤ T < 3. — (D) 3 ≤ T < 4. — (E) 4 ≤ T ≤ 5.

Answer #1

Doubt in this then comment below.. i will explain you.

By rules and regulations we are allow to do only one problem at a time...i solve 2 problems..

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2. Let Q1 = y(2), Q2 = y(3), where y = y(x) solves y' + 2xy =
2x^3 , y(0) = 1. Let Q = ln(3 + |Q1| + 2|Q2|). Then T = 5 sin^2
(100Q) satisfies:— (A) 0 ≤ T < 1. — (B) 1 ≤ T < 2. — (C) 2 ≤
T < 3. — (D) 3 ≤ T < 4. — (E) 4 ≤ T ≤ 5.

Let Q1 be a constant so that Q1 = L(−3, 2), where z = L(x, y) is
the equation of the tangent plane to the surface z = ln(5x − 7y) at
the point (x0, y0) = (2, 1). Let Q = ln(3 + |Q1|). Then T = 5 sin2
(100Q)
satisfies:— (A) 0 ≤ T < 1. — (B) 1 ≤ T < 2. — (C) 2 ≤ T
< 3. — (D) 3 ≤ T < 4. —...

Let Q1 be a constant so that Q1 = L(20, 12), where z = L(x, y)
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8y) at the point (x0, y0) = (7, 11). Let Q = ln(3 + |Q1|). Then T =
5 sin2 (100Q)
satisfies:— (A) 0 ≤ T < 1. — (B) 1 ≤ T < 2. — (C) 2 ≤ T
< 3. — (D) 3 ≤ T < 4. —...

Let Q1 be a constant so that Q1 = L(5, 17), where z = L(x, y) is
the equation of the tangent plane to the surface z = x 6 + (y − x)
4 at the point (x0, y0) = (3, 4). Let Q = ln(3 + |Q1|). Then T = 5
sin2 (100Q)
satisfies:— (A) 0 ≤ T < 1. — (B) 1 ≤ T < 2. — (C) 2 ≤ T
< 3. — (D) 3 ≤...

Let Q1, Q2, Q3 be constants so that (Q1, Q2) is the critical
point of the function f(x, y) = xy + y − x, and Q3 = 1 if f has a
local minimum at (Q1, Q2), Q3 = 2 if f has a local maximum at (Q1,
Q2), Q3 = 3 if f has a saddle point at (Q1, Q2), and Q3 = 4
otherwise. Let Q = ln(3 + |Q1| + 2|Q2| + 3|Q3|). Then T =...

Let Q1, Q2, Q3 be constants so that (Q1, Q2) is the critical
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has a local minimum at (Q1, Q2), Q3 = 2 if f has a local maximum at
(Q1, Q2), Q3 = 3 if f has a saddle point at (Q1, Q2), and Q3 = 4
otherwise. Let Q = ln(3 + |Q1| + 2|Q2| + 3|Q3|). Then...

let Q1= y(2) and Q2= y(3) where y=y(x) solves...
(dy/dx) + (2/x)y
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Let Q1, Q2, Q3, Q4 be constants so that y =Q1+Q2x+Q3x^2+Q4x^3
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Please show all steps!
Thank you!

Let F ( x , y ) = 〈 e^x + y^2 − 3 , − e ^(− y) + 2 x y + 4 y 〉.
a) Determine if F ( x , y ) is a conservative vector field and, if
so, find a potential function for it. b) Calculate ∫ C F ⋅ d r
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