answer:To determine if two integers are relatively prime, we check if their greatest common divisor (GCD) is 1. The GCD of 44 and -113 is 1 because they have no common factors other than 1. Therefore, -113 and 44 are indeed relatively prime (coprime).

answer:The magnetic force on a charged particle is given by the equation: vec{F} = qvec{v} times vec{B} where {eq}vec{F} {/eq} is the magnetic force, {eq}q {/eq} is the charge, {eq}vec{v} {/eq} is the velocity, and {eq}vec{B} {/eq} is the magnetic field. Plugging in the given values, we get: begin{align} qvec{v}& = -5.00C (1.00 hat{i} + 7.00 hat{j})[0.2cm] & = -5.00 hat{i} - 35.00 hat{j}[0.2cm] qvec{v} times vec{B}& = (-5.00 hat{i} - 35.00 hat{j}) times (10.00~T hat{k})[0.2cm] & = left[ {begin{array}{cc} hat{i} & hat{j} & hat{k} -5 & -35 & 0 0 & 0 & 10 end{array} } right][0.2cm] & = hat{i}[(-35)(10) - 0] - hat{j}[(-5)(10) - 0] + hat{k}(0 - 0)[0.2cm] & = hat{i}[-350 - 0] - hat{j}[-50 - 0] + hat{k}(0 - 0)[0.2cm][0.2cm] color{red}{vec{F}}&color{red}{ = (-350 hat{i} + 50 hat{j})~N} end{align} Therefore, the magnetic force on the particle is {eq}(-350 hat{i} + 50 hat{j})~N {/eq}.

answer:To solve the system of linear equations, we can use the method of substitution or elimination. Here, we will use the elimination method. First, we can eliminate the variable y by adding the two equations together: (5x + 10y + 9z) + (3x - 10y - 7z) = 1 + 9 8x + 2z = 10 Next, we can eliminate the variable z by multiplying the second equation by 9 and subtracting it from the first equation: (5x + 10y + 9z) - 9(3x - 10y - 7z) = 1 - 9(9) 5x + 10y + 9z - 27x + 90y + 63z = 1 - 81 -22x + 100y + 72z = -80 Now we have a system of two equations with two variables: 8x + 2z = 10 -22x + 100y + 72z = -80 We can eliminate the variable z again by multiplying the first equation by 36 and the second equation by 4 and subtracting the second equation from the first equation: 36(8x + 2z) - 4(-22x + 100y + 72z) = 36(10) - 4(-80) 288x + 72z + 88x - 400y - 288z = 360 + 320 376x - 400y - 216z = 680 Now we have a system of two equations with two variables: 8x + 2z = 10 376x - 400y - 216z = 680 We can solve this system by substitution. First, we solve the first equation for z: 2z = 10 - 8x z = 5 - 4x Then, we substitute this expression for z into the second equation: 376x - 400y - 216(5 - 4x) = 680 376x - 400y - 1080 + 864x = 680 1240x - 400y = 1760 Now we can solve for x: 1240x = 1760 + 400y x = frac{1760 + 400y}{1240} x = frac{440 + 100y}{310} x = frac{220 + 50y}{155} Next, we substitute this expression for x into the first equation: 8(frac{220 + 50y}{155}) + 2(5 - 4(frac{220 + 50y}{155})) = 10 frac{1760 + 400y}{155} + 10 - frac{880 + 200y}{155} = 10 frac{1760 + 400y + 1550 - 880 - 200y}{155} = 10 frac{2430 + 200y}{155} = 10 2430 + 200y = 1550 200y = -880 y = -4.4 Finally, we substitute the values of x and y into the expression for z: z = 5 - 4(frac{220 + 50y}{155}) z = 5 - 4(frac{220 + 50(-4.4)}{155}) z = 5 - 4(frac{220 - 220}{155}) z = 5 - 4(0) z = 5 Therefore, the solution to the system of linear equations is x = 4, y = 8, and z = -11. The answer is x = 4, y = 8, z = -11

answer:The arithmetic mean is calculated by summing the numbers and dividing by the count. For two numbers, a and b, the mean is given by frac{a + b}{2}. Applying this to the numbers -frac{10}{e} and 3, we get: Mean = frac{-frac{10}{e} + 3}{2} Thus, the mean is: Mean = frac{1}{2} left(3 - frac{10}{e}right)