Let 2a > -1, If the area of the region of the plane defined by {(x,y)...

Let 2a > -1, If the area of the region of the plane defined by {(x,y) : x ≥ 0, 2y-x ≥ 0, ax+y-3 ≤ 0} is equal to 3, then the value of a, lies in
Answer key: (0.75, 1.5)

Expert Solution

Colby Messinger answered 2 years ago

1. The base of a solid is the region in the x-y plane bounded by the...

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let R be a region bounded by x = 0 and x =1 and y =...

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find the area of the region bounded by the curves √ x + √y = 1...

find the area of the region bounded by the curves √ x + √y = 1 and the coordinate axis.

Let A = R x R, and let a relation S be defined as: “(x1, y1)...

Let A = R x R, and let a relation S be defined as: “(x1, y1) S (x2, y2) ⬄ points (x1, y1) and (x2, y2)are 5 units apart.” Determine whether S is reflexive, symmetric, or transitive. If the answer is “yes,” give a justification (full proof is not needed); if the answer is “no” you must give a counterexample.

Let f(x, y) = 2x^3 − 6xy + 3y^2 be a function defined on xy-plane (a)...

Let f(x, y) = 2x^3 − 6xy + 3y^2 be a function defined on xy-plane (a) Find first and second partial derivatives of. (b) Determine the local extreme points of f (max., min., saddle points) if there are any. (c) Find the absolute max. and absolute min. values of f over the closed region bounded by the lines x = 2, y = 0, and y = x

Find the area of the region enclosed by the graphs of x=(1/2)(y^2)-3 and y=x-1

a) Find the area of the region bounded by the line y = x and the...

a) Find the area of the region bounded by the line y = x and the curve y = 2 - x^2. Include a sketch. Find the volume of the solid created when rotating the region in part a) about the line x = 1, in two ways.

Let the joint pmf of X and Y be defined by f (x, y) = c(x...

Let the joint pmf of X and Y be defined by f (x, y) = c(x + y), x =0, 1, 2, y = 0, 1, with y ≤ x. 1. Are X and Y independent or dependent? Why or why not? 2. Find g(x | y) and draw a figure depicting the conditional pmfs for y =0 and 1. 3. Find h(y | x) and draw a figure depicting the conditional pmfs for x = 0, 1 and2. 4....

Let the joint pmf of X and Y be defined by f (x, y) = c(x...

Let the joint pmf of X and Y be defined by f (x, y) = c(x + y), x =0, 1, 2, y = 0, 1, with y ≤ x. 1. Find g(x | y) and draw a figure depicting the conditional pmfs for y =0 and 1. 2. Find h(y | x) and draw a figure depicting the conditional pmfs for x = 0, 1 and2. 3. Find P(0 < X <2 |Y = 0), P(X ≤ 2 |Y...

Let R be the region inside x ^2 /9 + y^2 /25 = 1, with x...

Let R be the region inside x ^2 /9 + y^2 /25 = 1, with x ≥ 0. (That is, R is the right-hand side of the ellipse below.) (a) (15 pts) Use the change of variables x = 3u, y = 5v to transform ∫ ∫ R x dxdy to a polar coordinate integral. 3 −5 5 R (b) (5 pts) Evaluate the polar coordinate integral

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Let 2a > -1, If the area of the region of the plane defined by {(x,y)...

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