(1 point) An equation in the form y′+p(x)y=q(x)yn with n≠0,1 is called a Bernoulli equation and it can be solved using the substitution v=y1−n which transforms the Bernoulli equation into the following first order linear equation for v: v′+(1−n)p(x)v=(1−n)q(x)

Given the Bernoulli equation y′+76y=12e−7xy−5 we have n= -5 so v= y^6 .

We obtain the equation v′+ 49/6 v= 7/2e^(-7x) .

Solving the resulting first order linear equation for v we obtain the general solution (with arbitrary constant C) given by v=

Then transforming back into the variables x and y and using the initial condition y(0)=21/6 to find C= .

Finally we obtain the explicit solution of the initial value problem as y=

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.

c

step-by-step explanation:

there is vertical asymptote at x = 2 and x = 0

vertical asymptote occurs at the points where the denominator is 0. so we can say that

x = 2 occurs when there is a factor (x-2) in the denominator, and

x = 0 occurs when there is a factor "x" in the denominator

thus, the denominator of the equation would have "x * (x-2)", this is option c only. that's the correct answer.

a rotation about point l

step-by-step explanation:

quizlet

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.