An object moves in the positive x-direction at a speed of 40 m/s. As it passes through the origin, it starts to experience a constant acceleration of 3.5 m/s2 in the negative x-direction. How much time elapses before the object returns to the origin

11,429 seconds.

Step-by-step explanation: Initially, the object is moving away from the origin in the positive x-direction but decelerating at constant rate until it reaches rest and then, the objects returns to the origin with a constant acceleration. By substituting the position equation of an object accelerating at constant rate, the following expression is found:

Which is a second-order polynomial. The time can be found easily by applying the General Second-Grade Equation, whose two roots are presented below:

The second roots contains the answer.

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

5x + 5

step-by-step explanation:

you should always add the diagrams and graphs we cannot see. this particular question is kind of borderline because we can make a graph for you.

(f + g)x = -x^2 +3x + 5 + x^2 + 2x

(f + g)x = 5x + 5

the graph of z = 5x + 5 is shown below. always use desmos when in doubt.