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At which point on the following curve does the tangent line has the largest slope?


𝑦 = 1 + 40π‘₯^3 βˆ’ 3π‘₯^5


If you get a slice of a round pizza with perimeter 90 cm , what should be the diameter of the pizza for you to have gotten the largest slice?

a populatpion of 1,000 students has an average weekly allowance of =350 and standard deviation of =56.13 .what is the probability that a random sample of size =30 will have an average weekly allowance between 335 and 360?



Show that n=1 to ∞ βˆ‘(-1)^n+1 5/7n+2 is conditionally convergent.

Which goal defines a good problem

2x + y = 7

x - 2y = 1


A. Write the equation in matrix form.

B. Determine the inverse of the matrix

C. Hence solve the equations.

D. x and y are matrices


"X=\\begin{bmatrix}\n 1 & 5 \\\\\n 3 & 7\n\\end{bmatrix} \n \n\n Y=\\begin{bmatrix}\n 3 & 4 \\\\\n 2 & 1\n\\end{bmatrix}"

Evaluate X2 + Y


Obtain the Fourier series for the following periodic function which has a period of 2Ο€: f(x)=x forβˆ’Ο€β‰€x≀π

Find the particular solution of the equation



e^2tdy/dx=4



Given that y=5, t=0

Find the partial defferencial equation of



F(x, y)=cos4/xe^x^2-y-5y^3

Find the particular solution for the following equation y"-y'-12y=te^4t


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