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Alpha Particle An alpha particle (the nucleus of a helium atom) has a mass of $6.64 \times 10^{-27} \mathrm{~kg}$ and a charge of $+2 e$. What are the magnitude and direction of the electric field that will balance the gravitational force on it?

Alpha Particle An alpha particle (the nucleus of a helium atom) has a mass of $6.64 \times 10^{-27} \mathrm{~kg}$ and a charge of $+2 e$. What are the magnitude and direction of the electric field that will balance the gravitational force on it?

Understanding Physics

How much will the temperature of a cup (180 g) of coffee at 95 ^ C be reduced when a 45 g silver spoon (specific heat $0.24 \mathrm{J} / \mathrm{g}^{\circ} \mathrm{C}$ ) at $25^{\circ} \mathrm{C}$ is placed in the coffee and the two are allowed to reach the same temperature? Assume that the coffee has the same density and specific heat as water.

How much will the temperature of a cup (180 g) of coffee at 95 ^ C be reduced when a 45 g silver spoon (specific heat $0.24 \mathrm{J} / \mathrm{g}^{\circ} \mathrm{C}$ ) at $25^{\circ} \mathrm{C}$ is placed in the coffee and the two are allowed to reach the same temperature? Assume that the coffee has the same density and specific heat as water.

Chemistry

Problem $22(b)$ is a special case of the general theorem that the inverse of a product of matrices is the product of the inverses in reverse order, that is, $(A B)^{-1}=B^{-1} A^{-1}$, Prove this theorem. Hint : This is easy!

Problem $22(b)$ is a special case of the general theorem that the inverse of a product of matrices is the product of the inverses in reverse order, that is, $(A B)^{-1}=B^{-1} A^{-1}$, Prove this theorem. Hint : This is easy!

Mathematical Methods in the Physical Sciences

LINEAR EQUATIONS; VECTORS, MATRICES, AND…

Matrix operations
Given the matrices $$ A=\left(\begin{array}{rrr} 1 & -1 & 1 \\ 4 & 0 & -1 \\ 4 & -2 & 0 \end{array}\right), \quad B=\left(\begin{array}{rrr} 1 & 0 & 1 \\ 2 & 1 & 1 \\ 2 & 1 & 2 \end{array}\right) $$ (a) Find $A^{-1}, B^{-1}, B^{-1} A B$, and $B^{-1} A^{-1} B$. (b) Show that the last two matrices are inverses, that is, that their product is the"unit matrix.

Given the matrices $$ A=\left(\begin{array}{rrr} 1 & -1 & 1 \\ 4 & 0 & -1 \\ 4 & -2 & 0 \end{array}\right), \quad B=\left(\begin{array}{rrr} 1 & 0 & 1 \\ 2 & 1 & 1 \\ 2 & 1 & 2 \end{array}\right) $$ (a) Find $A^{-1}, B^{-1}, B^{-1} A B$, and $B^{-1} A^{-1} B$. (b) Show that the last two matrices are inverses, that is, that their product is the"unit matrix.

Mathematical Methods in the Physical Sciences

LINEAR EQUATIONS; VECTORS, MATRICES, AND…

Matrix operations

Questions asked

ANSWERED

Supratim Pal verified

Numerade educator

1. What is the resulting DE when the arbitrary constant of y sin x - xy^2 = C is eliminated? A. (2xy - sin x) dy/dx - y^2 - y cos x = 0 B. (2xy + sin x) dy/dx + y^2 + y cos x = 0 C. (2xy - sin x) dy/dx + y^2 - y cos x = 0 D. (2xy + sin x) dy/dx - y^2 + y cos x = 0 2. Which of the following DE satisfies y = 1/(1+x^2)? A. (1 + x^2)y'' + 4xy' - 2y = 8x B. (1 + x^2)y'' + 4xy' - 2y = 0 C. (1 + x^2)y'' - 4xy' + 2y = 0 D. (1 + x^2)y'' + 4xy' + 2y = 0 3. Which of the following is an example of a PDE of degree 3, order 2, with independent variables s and r, and dependent variable v? A. (d^3 v / ds^2 dr)^2 = rsv B. (d^2 v / ds dr)^3 = rsv C. (d^3 s / dv^3)^2 = rsv D. (d^2 r / dv ds)^3 = rsv 4. To which DE does the function f(x) = (x^3 + C)e^(-3x) is a solution of? A. dy/dx + 3y = 3x^2 e^(-3x) B. dy/dx - 3y = 3x^2 e^(-3x) C. dy/dx + 3y = 3x^2 e^(3x) D. dy/dx - 3y = 3x^2 e^(3x)

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ANSWERED

Manisha Sarker verified

Numerade educator

Write, in parametric form, the equation of the straight line that is perpendicular to r = (2i + 4j) + (i - 2j)t and goes through (1, 0).

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ANSWERED

Anand Jangid verified

Numerade educator

A Carnot engine whose high-temperature reservoir is at 620 K takes in 550 J of heat at this temperature in each cycle and gives up 335 J to the low-temperature reservoir. a. How much mechanical work does the engine perform during each cycle? b. What is the temperature of the low-temperature reservoir? c. What is the thermal efficiency of the cycle?

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ANSWERED

Mukesh Devi verified

Numerade educator

Bud, a very large man of mass 130 kg, stands on a pogo stick. How much work is done as Bud compresses the spring of the pogo stick 0.50 m? (5 pts.)

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ANSWERED

Danielle Fairburn verified

Numerade educator

For the two vectors A and B in the given figure: a. Find the magnitude and direction of the vector product A x B; b. Find the magnitude and direction of B x A.

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ANSWERED

Nick Johnson verified

Numerade educator

For the two vectors in A and B in the given figure: a. Find the magnitude and direction of the vector product A x B; 10 pts. b. Find the magnitude and direction of B x A. 10 pts.

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ANSWERED

Sanchit Jain verified

Numerade educator

5. Given two vectors ( vec{A}=4.00 hat{imath}+7.00 hat{jmath} ) and ( vec{B}=5.00 hat{imath}-2.00 hat{jmath} ). 10pts. a. Find the magnitude of each vector. b. Write an expression for the vector difference ( vec{A}-vec{B} ) using unit vectors. c. Find the magnitude and direction of the vector difference ( vec{A}-vec{B} )

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