Constants Part A Consider the following function of variable r, for r 20: Find the value of the first derivative, dy/dr, atr4.25 Express your answer to 3 significant figures. y(r) = (r2-425r) expl-r). Submit Request Answer Part B Find the value of the second derivative, d ydr2 a4.25. Express your answer to 3 significant figures.

If ϕ = 90° − θ, what is the value of sin2 ϕ + sin2 θ?

Given ϕ=xy+yz+xzϕ=xy+yz+xz, find gradient ϕ at point (1, 2, 3).

When analyzing motions in 2D, what vectors should be described in terms of time (t), and x & y components?

Vector A is 3 units in length and points along the positive x-axis, vector B is 4 units in length and points along a direction 31 degrees from the positive x-axis, and vector C is 9 units and points along a direction 160 degrees. What is the direction of the resulatant with respect to the positive x-axis in degrees?

If F1=2N, and F2= 3.4N, α1=500, α2=400.  The value of  FR by  Cos law is:

A cockroach is crawling along the walls inside a cubical room that has anedge length of 3 m. If the cockroach starts from the back lower left-hand corner of the cube andfinishes at the front upper right hand corner, what is the magnitude of the displacement of thecockroach? What is the distance covered by the cockroach?

“An object is moving at a speed of v(t)= 3(t^2-1)+5tan (7t), where V is in m / s and t in seconds. What is your acceleration during the first two seconds? To answer this question, in mathematical terms, what are you asked to calculate an integral, a derivative, or a rate of change?

If , and , find the unknown constants a and b such that .

In SI units, speeds are measured in meters per second (m/s). But, depending on where you live, you’re probably mole comfortable of thinking of speeds in terms of either kilometers per hour (km/h) or miles per hour (mi/h). In this problem, you will see that 1 m/s is roughly 4 km/h or 2 mi/h, which is handy to use when developing your physical Intuition. More precisely, show that (a) 1.0m/s=3.6km/h and 1.0m/s=2.2mi/h .