For 0 < t < 2, v(t) = t + 1. For 2 < t < 4, v(t) = -t/2 +4, sketch a graph of x(t) assuming x(0) = -1

Q: A graph of x vs. t4, with x on the vertical axis and t4 on the horizontal axis, is linear. Its slope…

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Q: A sphere of radius r has surface area A = 4πr2 and volumeV = (4/3)πr3. If the radius of sphere 2 is…

A: a)The ratio of the areas, A2/A1

Q: The vectors A and B are given by A = 2î + 3j and B = -i + 29.  (A) Determine the scalar product…

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Q: Find the following quantities for A⃗ and B⃗ A⃗ = −12mˆi + 4.0mˆj + 1.5mˆk B⃗ = 2.8Nˆi − 21Nˆk (a) A⃗…

A: Given, A = −12mˆi + 4.0mˆj + 1.5mˆk B = 2.8Nˆi − 21Nˆk

Q: Given  vector M= 4 î + 4 ĵ − 5  and vector N= 5 î − 4 ĵ − 3k̂ , calculate the vector product, vector…

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Q: Part (a) What is the length of the vector A? |A| = sin() cotan() atan() cosh() Hints: 0% deduction…

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Q: Use backward-difference formula to evaluate the first derivative of y = x2 + 4x – 5 at x=0 using a…

A: Given equationTo Find,First derivative of the function using the backward-difference formula Formula…

Q: Vectors A and B lie in an xy plane. A has magnitude 7.6 and angle 116° relative to +x direction: B…

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Q: A vector a of magnitude 17 units and another vector b of magnitude 5.5 units differ in directions by…

A: Given: Magnitude of a vector a is |a| =17 units Magnitude of second vector b is |b| =5.5 units and…

Q: Vector A has a magnitude of 4.0 at 530 counterclockwise from + x-axis and Vector B has a magnitude…

A: Given value--- A = 4 unit  , 53 degree . B = 5 unit , 130 degree. We have to find--- A ● B

Q: Let vector a= &lt;0,-4,5&gt; and vector b= &lt;1,0,5&gt;. Find a X b

A: The objective of the question is to find the cross product of two vectors a and b. The cross product…

Q: If the vector Kâ- +Lây+ M â, shows the maximum increase rate and direction of the scalar V at point…

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Q: (H.W) We consider the vector: A = 31 + j + 2k %3D (a) Find the length of A Ans. 14 (b) Find the…

A: Here we are using the general formulas of vector analysis

Q: 2 • Find the angle between each of the following pairs of vectors: (a) Ả = -2.00î + 6.00ĵ and B =…

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Q: Given vectors T = 2a, 2a, 6a, + 3a, and S = a + 2a, + a., find: (a) the scalar projec- tion of T on…

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Q: Two vectors are given by d = 7.0f + 2.6 and b = 5.41 +9.7). Find (a) d x b (b) d b d + b) %3D and…

A: Given:a→ = 7.0 i^ +2.6 j^ b→ = 5.4 i^ + 9.7 j^

Q: Given the following information, find the unit vector of Force A Force A = 200 N Θ = 30o (on x-y…

A: Given: Vector A : 200 N Angles θ=30∘ ( on x-y plane) ϕ=50∘ ( on x-z plane)

Q: or the two vectors: (vectors)G= 2ˆi-3ˆj+1ˆk and (vector)H= 2ˆi+1ˆj-1ˆk what is (vector)G· (vector)H?…

A: Given data The vector G is given as  G→=2i^-3j^+k^. The vector H is given as  H→=2i^+j^-k^. The dot…

Q: Consider the following vectors: A = 4.6i + 1.4j+ 3.4k B = -6.5i + 7.lj + 10.2k Part (a) What is the…

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Q: = Given the following vectors: A 15.0 m at 40.0° counterclockwise from the +y-axis, B=20.0 m at…

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Q: The vector product of two vectors A and B is a vector and so has both a magnitude and direction: 1.…

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Q: Express this product in units of km3 in standard scientific notation and with the appropriate number…

A: given that (4.2 km) × (4.0 m) × (13.24 × 10−3 mm)

Q: B

A: We have to use vector addition here

Q: Given the pair of vectors, A = (9.0oî – 2.00ĵ ) and B = (-2.00î + 7.0oj ), use the definition of a…

A: A→ = (9i^ - 2j^) B→ = (-2i^ + 7j^)

Q: Select each of the following vectors that is a unit vector: 0 (1/√√3, 1/√√3, 1/√3) (1, 2, 3) □ (1,…

A: Given data: The given vectors are:  (a) 13,13,13(b) 1,2,3(c) (1,1,1)(d) (1,0,0) ms(e) 12,12,0(f)…

Q: Q1 (30 pts): Find the solution of the equation 4x(1 - u)dx + (x² + 4)du = 0 subject to the initial…

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Q: magnitude of A

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Q: (a) Sketch the two vectors in the xy-plane, and label the angles. (b) Compute A· B . (c) Using the…

A: a) The given vectors are, Analyze the following figure representing the given vector.

Q: Vector A = 7.2 i + 2.6 j. Vector B = 7.5 i + 7.4 j. The magnitude of the cross product i.e. |AxB|…

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Q: The force F has a magnitude of 590 N. Express F as a vector in terms of the unit vectors i and j.…

A: Given: The magnitude of the force is 590 N. The angle made by force F with the x-axis in the clock…

Q: A vector a of magnitude 14 units and another vector b of magnitude 4.2 units differ in directions by…

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Q: = 2. At any point of the curve x Tangent vector 3 cos t, y = 3 sin (ii) Unit tangent vector

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Q: Let a=i-2j-2k and b=6i +31 + 2k; Find? (a) a + b and ab (b)-2a+ (c) The magnitude of a and b (d)āx b…

A: Given:-  a→= i^-2j^-2k^b→= 6i^+3j^+2k^ Find:-  a) a→+b→  and a→-b→ b) -2a→+b→3 c) The magnitude of…

Q: Find the unit vector ˆeD in the direction of vector D~ = 1/2 ˆı +ˆj + 2/3 ˆk .   (a) 1/√ 61 3ˆı +…

A: The vector D can be given as, D→=12i^+j^+23k^

Q: Given vector A =   and vector B = , what is the component magnitude of vector B in the direction of…

A: Given data: Vector A = 2i + j -17k Vector B = 11i +j -11k

Q: The vector -5.2 A→ has a magnitude of 37 mm and points in the positive x direction. Find the x…

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Q: For the given vectors V₁ and V₂, determine V₁ + V₂, V1 + V2, V1-V2, V₁ X V2, V₂ X V₁, and V₁ V₂.…

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Q: Vector C can be written (-3i+1j) cm O (-4i+2j) cm O (i-3j) cm (2i+-4j) cm y (cm) 2 1 x (cm)

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Half Life

The concept of Half Life has numerous practical applications some of them includes figuring out the effective drug dosage to finding out when a radioactive becomes safe to use. If you look for a career in Nuclear Physics you will need this concept.