h(y)= 9/y^2-9

Algebraically determine where ℎ is increasing/decreasing and where ℎ is concave up/down, writing these in interval notation. Also, find all local extrema and inflection points of ℎ, writing these as ordered pairs.

increasing: _____________ local maxima: _______________________ decreasing: _________________________ local minima: ________________________ concave up: _____ inflection points: ___________________ concave down: ______________________

b)Find the equations for all asymptotes for ℎ, and justify each one.

vertical: _________________________ horizontal: ________________

Multivariable calculus

Evaluate: ∮ 3? 2 ?? + 2???? using two different methods. C is the boundary of the graphs C y = x2 from (3, 9) to (0, 0) followed by the line segment from (0, 0) to (3, 9).

2. Evaluate: ∮(8? − ? 2 ) ?? + [2? − 3? 2 + ?]?? using one method. C is the boundary of the graph of a circle of radius 4 oriented counterclockwise

Use elementary row or column operations to evaluate the following determinant. You may use a calculator to do the multiplications. 1 -9 6 -9 -5 2 -17 6 -21 -11 2 -13 4 -17 -12 0 6 4 2 0 0 -2 16 8 2

A manufacturing company produces two models of an HDTV per week, x units of model A and y units of model B at a cost (in dollars) of

f (x, y) =(8x^2+8y^2)/4 .

If it is necessary (because of shipping considerations) that4x + 5y = 20 ,

how many of each type of set should be manufactured peer week to minimize cost? What is the minimum cost?

Consider a population of antelope, with P0=2,750, carrying capacity K=3,875, and growth rate r=0.073 (or 7.3%) per year. Assuming that this population follows logistic growth, find P(t), then use the solution to predict the population after 8 years. Round your final answer to the nearest integer value and do not include units.

for each of the five functions f1-(x,1/y) ,f2-(0,y) ,f3 (x+2y,y) ,f4-(x-2,y+1) ,f5 (x,y^3-y) prove or disprove that fn is distance-preserving

Find the distances:

A) Between ?1=〈2+2?,−1+?,−3?〉and ?2=〈4,−5−3?,1+4?〉 .

B) Between the planes 2?−?+5?=0 and 2?−?+5?=5 .

C) From the point (1,2,3) to the line ?=〈−?,4−?,1+4?〉 .

You are designing the top of a pencil pouch that consists of a rectangle to which a semicircle has been attached to both ends. The semicircle will be made from material that costs 1ct per square centimeter. The material of the rectangular part costs 4ct per square centimeter. The perimeter of the pouch must be 80cm. How do you have to choose the radius and the 'open' side of the rectangle so the cost is minimal? Before you start, label your sketch! Please write down strategy and final result.

find the volume of the largest rectangular what's in the first octant with three faces on the co-ordinate planes and one vertex on the plane
8x+y+3z=9

(1 point) Is the point (−4,−5,3) visible from the point (4,5,0) if there is an opaque ball of radius 1 centred at the origin? Suppose that you stand at the point (4,5,0) and look in the direction of a point that is not visible because it is behind the ball. You will then be looking at a point on the sphere. If (−4,−5,3) is not visible from (4,5,0), find the point on the sphere at which you are looking if you look in the direction of (−4,−5,3). Otherwise, find the point on the sphere at which you look if you are looking in the direction of (−4,−5,2). Point (?,?,?)=

a. Two concentric circles have radii of 6 mm and 12 mm. A segment tangent to the smaller circle is a chord of the larger circle. What is the length of the segment to the nearest tenth?

b. A student inscribes an angle inside a semicircle to form a triangle. The measures of the angles that are not the vertex of the inscribed angle are x and 2x-9. Find the measures of all three angles of the triangle. Explain how you got your answer.

c. Two circles in the coordinate plane with congruent radii intersect in exactly two points. Why is it not possible for these circles to be concentric?

d. A gardener wants the three rosebushes in her garden to be watered by a rotating water sprinkler. To help her, you draw a diagram of the garden using a grid in which each unit represents 1 foot. The rosebushes are at points (1, 3), (5, 11), and (11, 4). She wants to position the sprinkler at a point equidistant from each rosebush . Where would you recommend placing the sprinkler? What equation describes the boundary of the circular region that the sprinkler will cover?

1) Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded by y=x^2, y=0, and x=5, about the y-axis.

V=

2) Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded by y=x^2, y=0, and x=6, about the yy-axis.

V=

3)The region bounded by f(x)=−3x^2+15x+18f(x)=-3x2+15x+18, x=0x=0, and y=0y=0 is rotated about the y-axis. Find the volume of the solid of revolution.

Find the exact value; write answer without decimals.

4) Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded on the right by the graph of g(y)=4/y and on the left by the y-axis for 1≤y≤11, about the x-axis. Round your answer to the nearest hundredth position.
V=

find inverse laplace transform of F(s)= (2s³ +5s²+8s+22)/[(s²+4)(s²+3s+2)]

a- Using the definition, find the derivative of the function y = 3x2-2x+32.

b- Evaluate the derivative at x = 1.

c- Find the value of the slope of tangent at x = 2