Basic Math question and answers for August 12, 2023
- Q 1) Determine the distance between the point (-2,6) and the line 3x -4y -10 = 02) Determine the distance between the point (4,-1) and the line 3x -4y +12 =...
- Q What is the length of the hypotenuse in the image below? Round your answer to 1 decimal place, units not required.
- Q What is the power series representation of ln(1-2x)?What is its radius of convergence?
- Q Consider the scalar functionsf(x,y,z)g(x,y,z)=x^2+y^2+z^2,g(x,y,z)=xy+xz+yz,and=h(x,y,z)=√xyzWhich of the three vector fields ∇f∇f, ∇g∇g and ∇h∇h areconservative?
- Q Find the equation of the tangent line to the curve at the givenpoint using implicit differentiation.Cardioid(x2 + y2 + y)2 = x2+ y2  at  (−1, 0)
- Q Inthe picture below, the blue and red crosspieces of the kite areperpendicular. The length of the horizontal red crosspiece is 3/2times the length of a side, or 3/2s. What is...
- Q A model rocket is fired vertically upward from rest. Itsacceleration for the first three seconds is given by a(t) = 60tft/s2 , at which time the fuel is exhausted and...
- Q  1. You invested $ 10,000 in a mutual fund, and after 10 years, the original investment has doubled. Find use   a). - Find the yearly percentage growth rateb).- The rate of...
- Q Find the arc length of the curve on the given interval.x= lnt , y = t + 1, 1 ≤ t ≤ 2
- Q Optimization:a) You are attempting to use 1000 yards of fencing to make onerectangular pasture. What’s the largest pasture you can make, andwhat are the lengths of the sides of the...
- Q Â 1. Consider the following curve f(x)= X^3 - 5x^2 +7x-5 Find the coordinates of the minimum and the maximum.2. The curve y= x^3 + ax^2 + bx + c has...
- Q Evaluate the surface integral  SF · dSfor the given vector field F and the orientedsurface S. In other words, find the flux ofF across S. For closed surfaces, use thepositive (outward)...
- Q Find the derivativea)y=(1+x)(x+3)/2x-1b)y=(1+x3)(3-4x2)+x+6
- Q The illumination of an object by a light source is directlyproportional to the strength of the source and inverselyproportional to the square of the distance from the source. If twolight...
- Q Find the area of the region enclosed between ?(?)=?2−3?+13 and?(?)=2?2−3?−3.
- Q Suppose that one factory inputs its goods from two differentplants, A and B, with different costs, 4 and 6 each respective. Andsuppose the price function in the market is decided...
- Q howmany local extrema of each type does f(x,y) have if f(x,y)=4x-((x^3))+3y-y^3?
- Q Consider the following one-dimensional partial differentiationwave equation. Produce the solution u(x, t) of this equation. 4Uxx= Utt 0 < x 0 Boundary Conditions: u (0, t) = u (2Ï€, t)...
- Q Find the local maximum and minimum values and saddle point(s) ofthe function. If you have three-dimensional graphing software,graph the function with a domain and viewpoint that reveal all theimportant aspects...
- Q A real estate office handles a 60-unit apartment complex. Whenthe rent is $530 per month, all units are occupied. For each $25increase in rent, however, an average of one unit...
- Q Margot is walking in a straight line from a point 40 feet dueeast of a statue in a park toward a point 34 feet due north of thestatue. She walks...
- Q 1. True or False:If we know that f(x) is increasing on an interval, then f ''(x)should be positive on that interval.2. True or False:If f '(x) is increasing on a...
- Q A man won ​$5 million by scoring 16 goals in 23 seconds in acontest at a sports game that was sponsored by a business. Did thebusiness risk the ​$ ​million?...
- Q Solve the following equations:3cos(x)+1=cos(x)3cosâ¡(x)+1=cosâ¡(x), where x is in the interval[0,2Ï€)[0,2Ï€)x=?sin(2x)=−12sinâ¡(2x)=−12, where x is in the interval[0,2Ï€)[0,2Ï€).  x=?
- Q Solve the following problems:(a) y'' - 2y' + 5y = 0 with y(0) = 1 and y'(0) = 2.(b) y(3) - 3y' + 2y = 0 with y(0) = 5,...
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