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: Consider three vectors: A = , B= , and C = Which of the following inequalities regarding the…

A: Given Data:  Vector A→=1i+2j-1k Vector B→=2i+3j+1k Vector C→=2i-2k

Q: Vector u = &lt;-7,3,-5&gt; and vector v = &lt;-1,1,0&gt;. Find v X u.

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

Q: The step function is defined as follows. 0(x) = {°³ 0 x < 0 1 x ≥ 0 Use integration by parts to show…

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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: 5. (a) Evaluate the line integral % 2 dic + dy+yz along the curve C(t) = [t², t³, t²], ɩ € [0, 1].

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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: Consider two vectors A = 3.56 i+ -3.07 k and B = 0.09j+ 1.82 k. Find the angle o between these two…

A: Given The two vectors are given as A→=3.56 i^+-3.07 k^ and B→=0.09 i^+1.82 k^ Angle between the two…

Q: (d) Find x₁ (t) and x₂(t) with the initial conditions of x₁ (0) = 0.2, x₁ (0) = x₂ (0) = x₂ (0) = 0.

A: Given that the x1 and x2 be the displacement of the masses m1 and m2 respectively. The kinetic…

Q: (a) L² (3x². 2 (3x² - 2x - 1) 8 (x - 3)dx (b) *(cos x) 8(x − n)dx 5 (c)( (cos x)8(x - 2π)dx

A: I have use the concept property of dirac delta function

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: Find the derivative of the function. y = e9x cos(x)

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Q: Which of the following statements is true Select one: O " "Sx, y)dxdy gives the area of the graph of…

A: Third option is true f(x, y, z) = f(y, x, z)

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: Express the position vector 7, velocity v, and acceleration ã in terms of the spherical coordinates…

A: Hey dear I have uploaded the solution in step 2 and 3

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: Konum (x) (cm) Zamanın karesi Ortalama hızlar (9 (s) Nokta Zaman (f) (s) (m/s) 1.5 3.5 5.8 8,5 11,5…

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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: The force acting on a particle is given by  F(r) = (A/r2)r̂,  where A is a positive constant. (a)…

A: A variable force F= (A/r2 ) where A is positive

Q: x² + 4x – 5 b Using Trigonometric Substitution dx = | f(e)dA · find the new limits of integration.…

A: Given that:- Basic mathematics equation is given in the question.

Q: The diagram below shows an infinitely long straight wire with a current I that is directed in the +x…

A: The diagram below shows an infinitely long straight wire with a current that is directed in the +x…

Q: Vector u = and vector v = . Find (vector u+v) X vector v.

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Q: B

A: We have to use vector addition here

Q: 8. Find the interval of convergen 7² 413 24 21 + 12 1 112 + -AL

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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: 4-7. Suppose that f(x)=1.5x² for –l-0.5) (b) P(0.5<X) (d) P(X<-2) (f) x such that P(x< X)=0.05.

A: Answer (d) :-

Q: For the vectors A→ and B→, find the magnitude and direction of the vector sum A→ +B→.

A: Step 1: Step 2: Step 3: Step 4:

Q: Which of the following is not true? ○ V1 (1) V2 (2) = V1 (2) ₂ (1) ○ V1 (1) V₂ (2) + ✨1 (2) ₂ (1) =…

A: If we take two Particles 1 and 2 and considering state ?1 and ?2 .

Q: Two vectors have the following magnitude, A = 12.2 m and B = 12.8 m. Their vector product is: AxB =…

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Q: Solve M„VN at (1,1-1) When M = (2yz)i – (x²y)j+(xz²)k and N = 2x?yz3

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Q: magnitude of A

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Q: find (a) 2u + v and (b) 5u - 2v.

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Q: Problem no 1: Find sum, difference and scalar and vetor product of vectors u = [-4,6], w = [0,4].…

A: Given vectors:u = [-4, 6] w = [0, 4]

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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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.