Find the maximum value of y = -2(x - 4)2 - 6.

y = -2(x-4)2-6

= -4(x-4) - 6

= -4x + 16 -6

y = 10- 4x

now if x is positive, x >= 0

then max value of y will be when x will nr minimum

so max y = 10- 4×0 = 10

so y = 10 at x =0 for x >=0

if x < 0 then

y will be increasing as x gets increase towards more negative. so max of y will be decided when x reaches to max negative.

they are simplified

step-by-step explanation:

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).