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In an isosceles trapezoid the 5- cm altitude drawn from the endpoint of the shorter base to
the larger base divides the larger base in segments of 10 cm and 25 cm long. Compute for
the area of the trapezoid.
A region is bounded by y = square root of x, the x-axis, and x = 4. Write the integral that represents the volume of this region revolved about the line y = 3
Show that the length of the portion of any tangent line to the asteroid a𝑥^2/3 + 𝑦^2/3 = 𝑎^2/3 ,cut off by the coordinate axes is constant.
A cone of radius 𝑟 centimeters and height ℎ centimeters is lowered point first at
a rate of 1 cm/s into a tall cylinder of radius 𝑅 centimeters that is partially filled with
water. How fast is the water level rising at the instant the cone is completely
submerged?
Suppose 𝑓 is odd and differentiable everywhere. Prove that for every positive
number 𝑏, there exists a number 𝑐 in (−𝑏, 𝑏) such that 𝑓 ′(𝑐) = 𝑓(𝑏)/𝑏.
At which point on the following curve does the tangent line has the largest slope?
𝑦 = 1 + 40𝑥^3 − 3𝑥^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 ∞ ∑(-1)^n+1 5/7n+2 is conditionally convergent.
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
