A curve is given the equation xy=25 and the equation of a line y=mx+b. i. Express m in terms of b given that the line and the curve have one and only one point of intersection.
ii. If the line intersects the curve in two distinct points, find the set of values of b, given m=-5

Below in bold.

Step-by-step explanation:

i, This is a rectangular hyperbola with symmetry about the line y = -x

   If it touches the graph at one point only then

y = 25/x

y = mx + b so

25/x = mx + b

mx^2 + bx + 25 = 0

Using the quadratic formula:

x = (-b + sqrt(b^2 - 25*4*m)) / 2m

Now there's only one value of x so

b^2 - 25*4*m = 0

b^2 = 100m

m = b^2/100.

m = +/-b/10.

ii  In this case b^2 > 100m

If m = |-5|

b^2 > 500

b > +/-√500

So b > √500 or b < -√500.

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.

damm bro the struggle

step-by-step explanation: