Jacob P.

Find the perimeter of a rhombus whose diagonals measure 14cm and 18cm. Express in simplest radical form.

A laser passing through air passes through an unknown liquid at an incident angle of 30 degrees. The laser is refracted such that the refracted angle is 20 degree relative to the normal line. What... more

Given the function f(x)=x^3−48x^2, determine all intervals on which f is both increasing and concave up. I am also confused about when my teacher tested values and stated whether or not a number... more

The radius of a cone is decreasing at a constant rate of 5 feet per second. The volume remains a constant 432 cubic feet. At the instant when the height of the cone is 66 feet, what is the rate of... more

(Calculator allowed)Identify the global extrema of the functionf(x) = -5x4 + 3x3 + 2x2 + x on the interval -1≤ x ≤ 1.A) This function has no global extremaB) Global maximum: x = 1, global minimum:... more

Find the order 3 Taylor polynomial T3(x) of the given function f(x) = (7x-6) 4/3 at a=4. Use exact values.

Consider a weighted graph representing the distances between cities. Nodes represent cities, and edges represent the roads connecting them with associated distances. If City A is connected to City... more

I've been told that this tricky integral is fairly easy to solve with Laplace transform:However, I am not sure on the solution itself after taking the Laplace transform of the integral. Could... more

I have this interesting integral to solve using residues. So far I have only noted that cos(x)=Re(eix), but I can't seem to arrive at the full solution. I would appreciate any help.

The average cost function, denoted as a(x), is defined as a(x) = c(x) / x, where c(x) represents the cost function, and x represents the number of units produced. The cost function is given as c(x)... more

Find the general solution to the non-homogeneous differential equation.y'' − 5y' + 4y = 3exthe homogenous part would be y(x) = C1e^x+C2e^4xfor yp would i guess Ae^x or Axe^x

Could you explain how to solve this to someone who has never learned this before? I'm having trouble explaining this to my younger sister.Find dy/dx at the point (pi, pi/4) when sin x + sin y = tan... more

At a certain location, Earth has a magnetic field of 0.60 × 10-4 T, pointing 75° below the horizontal in a north-south plane. A 10.0 m long straight wire carries a 15 A current. (a) If the current... more

Consider the equation below.r = 12/(3-sin(θ))The eccentricity is e = 1/3 and It is an ellipseGive an equation of the directrix (in Cartesian Coordinates)

For f(x) = sin^2x - cosx, and 0 ≤ x ≤ pi, find the value(s) of x for each condition listed belowa) number of local maxima and what they areb) number of local minima and what they arec) global... more