Which of the following is the general solution of the differential equation dy/dx equals the quotient of 8 times x / y ?

a.)y^2 = x^2 + c

b.)x^2 - y^2 = c

c.)x^2 = 4x^2 + c

d.)y^2 = 8x^2 + c

i believe the answer is d

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)

the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!

need more detail

step-by-step explanation:

lele

provide more details to solve it

step-by-step explanation: