Consider the homogeneous second-order linear differential equation y′′+4y′−12y=0. Which of the following pairs gives two solutions to this equation? A. y1=e2x, y2=e−6x B. y1=e3x, y2=e1x C. y1=e2x, y2=e−2x D. y1=e−12x, y2=xe−12x E. y1=cos(−12x),y2=sin(−12x) F. y1=e−4x, y2=e−12x Then for these solutions find a particular solution of the form y=c1y1+c2y2 that satisfies the initial conditions y(0)=−5,y′(0)=0. y = y1 + y2.

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.

3

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!

what i would say the best answer is a. 40.5

d.) yes, because the volume of the cone is greater than the volume of the sphere

step-by-step explanation: