Find the equations of the tangents to the given curve that pass through the point (18, 12).

x = 9t2 + 9
y = 6t3 + 6

y = (tangent at smaller t)
y = at larger t)

Step-by-step explanation:

The tangent of a curve is given by the following first degree function:

In which is a function in which the curve pass through and m is the slope, given by the following formula:

In this problem, we have that:

.

So:

And

So:

.

Which means that

The curve passes through (18,12). This means that .

So the equation is:

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt

the graph in the attached figure

step-by-step explanation:

we have

using a graphing tool

the graph in the attached figure

the roots are ( x-intercepts) x=-0.5,x=1,x=3

the y-intercept is the point (0,3)