Find the area of the quadrilateral shown in the figure. Two angles that share a common side and have the same vertex. The rate at which water is flowing into a tank is r(t) gallons/minute, with t in minutes. Sum of (3 + 6^n)/(6^n) from n = 1 to infinity. If f(2) = 14, f prime is continuous, and integral from 2 to 5 of f prime (x) dx = 20, find the value of f(5). Introduction: In the real world of building construction there are many rich problems which can be used to build sense making and reasoning skills for students. Go ahead and ask it. Mathematics in Construction . One day, he noticed that the animals had a total of 12 heads and 44 feet. Find the radius and interval of convergence of the series sum of (n(x + 2)^n)/(3^(n + 1)) from n = 0 to infinity. Find the interval of convergence. y double prime + 3y = 9x, y(0) = 0, y(1) + y prime (1) = 0. Sum of (x^n)/(n*10^n) from n = 1 to infinity. Visual Maths Resources Ltd is a company registered in England and Wales with a company no. Find the series' radius of convergence. Show that the following series is divergent. Find the expansions of (3 - 2 x) (2 x + 7) (2 x + 1). Find the sum of the series for those value of x. What are the two coins? The semicircle of area 1250 π centimeters is inscribed inside a rectangle. Evaluate the limit using L'Hospital's rule if necessary. (Use C as the arbitrary constant.). Suppose we are trying to model Y as a polynomial of X. Find the average value of f(x, y) over the region R. f(x, y) = x^2 + y^2 R: square with vertices (0, 0), (4, 0), (4, 4), (0, 4). For example…, Assorted Concepts in Math Part 1 | New SAT, Assorted Concepts in Math Part 2 | New SAT, Trade Term Vocabulary (Module 2: Construction Math), any angle between 0 degrees and 90 degrees, Angles that have the same vertex and one side in common, A shape made by two straight lines coming together at a point.…, The surface or amount of space occupied by a two-dimensional o…, Any angle between 0 degrees and 90 degrees, the shape made by two straight lines coming together at a poin…, This is an angle whose measure is between 0 degrees and 90 deg…, A triangle in which all of the angles are smaller than 90° is…, These are two angles in a plane which share a common vertex an…, These are two angles that add up to 180° that share a common v…, angles that have the same vertex and one side in common, Your job as a carpenter pays $20/hour and you worked 40 hours…, When you add larger, 2-digit numbers in a column you may need…. Consider the vector \mathbf F(x,y,z) = (2x+4y)\mathbf i +(4z+4x) \mathbf j + (4y + 2x) \mathbf k . Let f(x) = 2x^2 - 2 and let g(x) = 5x + 1. A 14 foot ladder is leaning against a vertical wall. Angles that have the same vertex and one side in common. (Your answer should be a function of x. This model assumes that populations are competing for a single limiting resource and reproduce at discrete moments in time. Calculate the average value of f(x) = 5 x sec^2 x on the interval [0, pi/4], For u = e^x cos y, (a) Verify that {partial^2 u} / {partial x partial y} = {partial^2 u} / {partial y partial x} ; (b) Verify that {partial^2 u} / {partial x^2} + {partial^2 u} / {partial y^2} = 0. \int_{-1}^{2}\int_{2}^{3}\int_{1}^{e}\frac{xy^2}{z} dz dx dy \\\int_{-1}^{2}\int_{2}^{3}\int_{1}^{e}\frac{xy^2}{z} dz dx dy = \boxed{\space} (Simplify your answer. f(x) = sqrt (x). (Give your answer in interval notation.). \cos^2 \theta = 3(1 -\sin \theta). B) The series converges, but is not absolutely convergent. Find an equation for the plane consisting of all points that are equidistant from the points (-6, 2, 3) and (2, 4, 7). The diameter of the semicircle coincides with the length of the rectangle. (NOTE: figure not drawn to scale). Convert 122^o 37' to radians. What is the number? Solve the differential equation 2y'' -5y' -3y =0 with the initial conditions y(0) = 1, y'(0) =10, Find curl F(x,y,z) , when F(x,y,z) = x^3yz i +xy^3z j + xyz^3 k, Evaluate the integral \int \frac{1}{64x^2-9} \,dx. What is the average of the function g(x) = [x(ln x)^2]^(-1) over the interval x is element of [e, e^2]? What kinds of pre-discussion activities facilitate student discourse about math?