Consider the system of differential equations with initial values: 2 y = y + sint; = x + 2 cost; (0) = 0 y(0) = 0 solve this system with the following indicating methods: a: by the method of laplace transforms. b: simplify it by differentiating one of the equation and then substitute to the other equation to form a 2nd order linear differential equation with constant coefficients. find this 2nd order ode with the corresponding initial values. (make sure you write down two initial conditions.) c: solve the 2nd order ode in part b with method of undetermined coefficients. (for the purpose of reviewing for the final exam)

step-by-step explanation:

what does 'mandy have ben 780 bottle caps. ' mean?

no oblique asymptote

step-by-step explanation:

to find the oblique asymptote of f(x)

here numerator has degree 1 and denomintor degree 2

degree of numerator < degree of denominator

hence there is no oblique asymptote

when the degree of the denominator > that of the numerator, we saw that the value in the denominator got so much bigger, so quickly,   giving us a horizontal asymptote of the x-axis. or we can write

f(x) = a polynomial of x + a proper fraction.

in this case only we have oblique asymptotes but not when numerator has less degree.

the homeowners insurance cost for a 115,000 wood frame house is 80,500.

step-by-step explanation:

it is given that the coverage rate for wood frame house is 0.7.

the value of wood frame house is 115,000.

.

homeowners insurance cost for a 115,000 wood frame house is

therefore the homeowners insurance cost for a 115,000 wood frame house is 80,500.

let x and 400 - x be the two numbers.  

==> 0.80x + 0.85(400 - x) = 400 - 68 from the statement of the problem.  

< ==> 0.80x + 0.85(400 - x) = 400 - 68  

==> 340 - 0.05x = 332  

< ==> -0.05x = -8 ==> x = 160, the first number ==> 400 - x = 240, the second number.