Advanced Math

In some instances the Laplace transform can be used to solve linear differential equations with variable monomial coefficients. Use Theorem 7.4.1.

In some instances the Laplace transform can be used to solve linear differential equations with variable monomial coefficients. Use Theorem 7.4.1. THEOREM 7.4.1 Derivatives of TransformsIf F(s) = ℒ{f(t)} and n = 1, 2, 3, , thenℒ{tnf(t)} = (−1)n dn dsn F(s). Reduce the given differential equation to a linear first-order DE in the transformed function Y(s) …

In some instances the Laplace transform can be used to solve linear differential equations with variable monomial coefficients. Use Theorem 7.4.1. Read More »

In some instances the Laplace transform can be used to solve linear differential equations with variable monomial coefficients. Use Theorem 7.4.1.

In some instances the Laplace transform can be used to solve linear differential equations with variable monomial coefficients. Use Theorem 7.4.1. THEOREM 7.4.1 Derivatives of TransformsIf F(s) ={f(t)} and n = 1, 2, 3,, then{tnf(t)} = (−1)n dn dsn F(s). Reduce the given differential equation to a linear first-order DE in the transformed function Y(s) ={y(t)}. …

In some instances the Laplace transform can be used to solve linear differential equations with variable monomial coefficients. Use Theorem 7.4.1. Read More »

In some instances the Laplace transform can be used to solve linear differential equations with variable monomial coefficients. Use Theorem 7.4.1.

In some instances the Laplace transform can be used to solve linear differential equations with variable monomial coefficients. Use Theorem 7.4.1. THEOREM 7.4.1 Derivatives of TransformsIf F(s) ={f(t)} and n = 1, 2, 3,, then{tnf(t)} = (−1)n dn dsn F(s). Reduce the given differential equation to a linear first-order DE in the transformed function Y(s) ={y(t)}. …

In some instances the Laplace transform can be used to solve linear differential equations with variable monomial coefficients. Use Theorem 7.4.1. Read More »

Suppose that the sick leave taken by the typical worker per year has

Suppose that the sick leave taken by the typical worker per year has = 10, = 2, measured in days. A firm has n = 30 employees. Assuming independence, how many sick days should the firm budget if the financial officer wants the probability of exceeding the number of days budgeted to be less than …

Suppose that the sick leave taken by the typical worker per year has Read More »

Consider the curveCwith parametric equationsx(t)=cos(2t),y(t)=sin(t), where−2π​≤t≤2π​. a) Find a Cartesian equation forC. Then make a rough sketch of the curve. b) The curvatureκof a curveCat a given point is a measure of how quickly the curve changes direction at that point. For example, a straight line has curvatureκ=0at every point. At any point, the curvature can be calculated byκ(t)=(1+(dxdy​)2)23​∣∣​dx2d2y​∣∣​​.Show that the curvature of the curveCis:κ(t)=(1+16sin2t)23​4​.

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