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A tank initially contains 59 gal of brine, in which 6 lb of salt is dissolved. Brine containing 1 lb of dissolved salt per gallon flows into the tank at the rate of 6 gal/min, and the well-stirred mixture flows out of the tank at the same rate. How much salt is present in the tank at the end of 14 min? (Round your answer to one decimal place.)
A graph is outerplanar if it can be embedded in the plane so that every vertex lies on the boundary of the exterior region. Prove the following:
Consider the curve 5x3+8xy+5y2 = 45. Use implicit differentiation to calculate the derivative dy/dx. Hence determine the point/s which has/have a horizontal tangent.
Find the nodes x_i and the weights w_i so that the Gaussian quadrature of the sum from i=1 to 2 of (w_i) f(x_i) approximating the integral from -1 to 1 of f(x)dx is exact when f(x) is a polynomial of as high degree as possible.
Make the appropriate test statistics & the rejection of your test.
Estimate the area under the graph of f(x)=2sinx between x=0 and x=pi/2 using five approximating rectangles of equal withs and right endpoints as sample points.
Find the probability on poisson distribution.
Find a matrix A that admits no LU decomposition, even if we only require that L is lower triangular ( not necessarily unit!) and U is upper triangular.
In a circle of radius 6 centimeters, find the area of the segment bound by an arc of measure 120 degrees and the chord joining the endpoints of the arc. Round your answer to nearest tenth.
Describe the object, include details on how you went about performing the calculation, and determine the slope. Be sure to include the unit of measurement (inches, feet, yards, etc.).
Show that if a convergent series of real numbers contains only a finite number of negative terms, then it is absolutely convergent.
Find the range of angles that trace out the full graph and determine and graph the equations of the tangent lines at each relative maximum of r
Recall that S_N (f)(x)= sum (n=-N to N) c_n e^{inx}= 1/2pi integral (from -pi to pi) f(x-t)sin ((N+1/2)t)/sin(t/2) dt
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