{zeC : -1< Re(z) < 1} under e ? a disk of radius 2 the annulus between the circle of radius 1 and circle of radius e O The annulus between the circle of radius 1/e and the radius of radius e The annulus between the circle of radius 1/e and the radius of radius 1
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- Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?Consider the following geometry problems in 3-spaceEnter T or F depending on whether the statement is true or false. 1. Two lines either intersect or are parallel 2. A plane and a line either intersect or are parallel 3. Two planes orthogonal to a third plane are parallel 4. Two lines orthogonal to a third line are parallel 5. Two planes parallel to a line are parallel 6. Two lines parallel to a third line are parallel 7. Two lines parallel to a plane are parallel 8. Two lines orthogonal to a plane are parallel 9. Two planes orthogonal to a line are parallel 10. Two planes either intersect or are parallel 11. Two planes parallel to a third plane are parallel2. Chapter 15 Review 33: Use polar coordinates to calculate sD√x2 + y2dA where D is the region inthe first quadrant bounded by the spiral r = θ, the circle r = 1, and the x-axis.
- where S is the sphere of radius 1 centered at the origin in R^3A rectangle ℛ with sides a and b is divided into two parts ℛ1 and ℛ2 by an arc of a parabola that has its vertex at one corner of ℛ and passes through the opposite corner. Find the centroids of both ℛ1 and ℛ2.Additional question: Where does the space curve lies, e.g. does the particle motion lie in a plane? If so, what does that imply about T, N, and B?
- Given a ray r(t) = (0; 0; 0) + t(1; 0; 0), t ≥ 0, and a set of spheres of unitradius and centered respectively at: (1) O = (0; 0; 0), (2) O = (3; 0; 0), (3) O = (1; 1; 0), (4) O = (-3; 0; 0), (5) O = (0; 3; 0). Which of the given spheres will be intersected from outside by the ray?Given: KL and KM are tangent and secant segments respectively of circle O drawn from exterior point K. KM intersects circle O at N. Prove: (KL)2 = KM x KN Statement Reason m ∠NLK = ½ m LN and m∠LMN = ½ m LN m ∠NLK = m∠LMN ∠NLK ≅ ∠LMN m ∠LNK = m∠NLM + m∠LMN KM x KN = |LK| 2Let S be the hyperboloid x 2 + y 2 = z2 + 1 and let P = (a, {3, 0) be a point on S in the (x, y )-plane. Show that there are precisely two lines through P entirely contained in S (Figure 18). Hint: Consider the line r(t) = (a +at, f3 + bt, t) through P. Show that r(t) is contained in S if (a, b) is one of the two points on the unit circle obtained by rotating (a, {3) through ± ~. This proves that a hyperboloid of one sheet is a doubly ruled surface, which means that it can be swept out by moving a line in space in two different ways.
- 1.A square with one side along the y-axis is rotated 360° about the y-axis. What is the resulting solid? 2. A family is buying a house and wants to pay less than $150$150 per square foot. The price of one 1,8001,800 square foot house is $242,000.$242,000. Which statement is true? A. If the family purchases the house, the family will stay within the limit of $150 per square foot and will be under by about $15.56 per square foot. B. If the family purchases the house, the family will stay within the limit of $150 per square foot and will be under by about $25.56 per square foot. C.If the family purchases the house, the family will not stay within the limit of $150 per square foot and will be over by about $15.56 per square foot. D.If the family purchases the house, the family will not stay within the limit of $150 per square foot and will be over by about $16.67 per square foot.The part of the surface z =1 + 3x+ 2y 2 that lies above the triangle with vertices (0, 0), (0, 1) and (2, 1)MTH 261 SECTION 2.4 220 alt DELTA COLLEGE Consider the points A(3, −1, 10), B(−1, 4, 1), C(5, −2, −1), and D(1, 1, 1) (a) Determine the volume of the parallelepiped P with adjacent sides−→ DA,−→ DB, and−→ DC. (b) To the nearest tenth of a unit, calculate the distance from D to the plane determined by A, B, and C. (c) To the nearest tenth of a unit, calculate the distance from A to the plane determined by D, B, and C. (d) To the nearest tenth of a degree, calculate the measures of the three acute angles between each pair of parallel faces of P. Solution: