### Hyperspheres : Volume of a Sphere with Radius 'r'

Finding formulas for the volume enclosed by a hypersphere in n-dimensional space. a) Use a triple integral and trigonometric substitution to find the volume of a sphere with radius r.

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Finding formulas for the volume enclosed by a hypersphere in n-dimensional space. a) Use a triple integral and trigonometric substitution to find the volume of a sphere with radius r.

Lim of theta as theta approaches zero of (cos theta - 1) / sin theta Please provide a detailed, step-by-step solution so that I can understand what is happening and will be able to solve similar problems in the future on my own. Thank you.

Q1. A glass crystal sculpture is made in the shape of a regular octagonal prism with 10 cm sides. Each of the lateral faces is square. To avoid breakage in shipment, the piece is padded with plastic foam beads when it is packed in its square-based rectangular box. The layer of beads must be at least 1 cm thick on all sides of

A force of 800 lbs acts in an upward direction of 40 degrees with the floor. Draw this force as a vector and determine its horizontal and vertical components.

A handicap ramp is 5.26 meters above the ground. What will the length of the ramp if it makes an angle of 23 degrees with the floor?

A beam 25 feet long leans against a wall. If the top of the beam rests at a point on the wall 17.5 feet above the floor, what is the angle the beam makes with the wall?

A length of rope 168 feet stretches from a bolt in the floor to the peak of an 87 foot radio tower. What is the distance from the floor at the radio tower base to the bolt? What angle does the rope make with the floor?

Problem: Construct a one-to-one function from (-1,2) into [0,1]. No need to prove.

G(x) = (4-cos3x)/(x^2) Could you please include steps so that I may learn to do it myself? Thanks.

Show step by step work and explanation of the solution. (Answer is provided in the attachment.) Just #8, please.

To measure the height of a mountain a surveyor takes two sightings of the peak at a distance of 900 meters apart on a direct line to the mountain (see attached picture). The first observation results in an angle of elevation of 47 degrees, whereas the second results an angle of elevation of 35 degrees. If the transit is 2 meters

Solve the triangle, if possible. C = 35°30' a = 18.76 c = 16.15 Which is the correct answer? A = 42°25', B = 102°05', b = 25.19 No solution A = 42°25', B = 102°05', b = 27.20; A' = 137°35', B' = 6°55', b' = 3.35 A = 102°05', B = 42°25', b = 17.52; A' = 6°55', B' = 137°35', b' = 26.19.

Solve the triangle, if possible. B = 24.4° C = 102.9° b = 38.62 Which is the correct answer? A = 50.7°, a = 93.13, c = 76.37 A = 50.7°, a = 91.13, c = 74.37 A = 52.7°, a = 76.37, c = 93.13 A = 52.7°, a = 74.37, c = 91.13

Find the missing parts of the triangle. (Find angles to the nearest hundredth of a degree.) a = 162 yd b = 185 yd c = 323 yd Which is the correct answer? A = 19.99, B = 11.49, C = 148.52 A = 19.99, B = 22.98, C = 137.03 A = 22.98, B = 19.99, C = 137.03 No triangle satisfies the given conditions.

A plane flying a straight course observes a mountain at a bearing of 35.3° to the right of its course. At that time the plane is 9 km from the mountain. A short time later, the bearing to the mountain becomes 45.3°. How far is the plane from the mountain when the second bearing is taken (to the nearest tenth of a km)?

Starting at point A, a ship sails 24 km on a bearing of 211°, then turns and sails 33 km on a bearing of 302°. Find the distance of the ship from point A. Which is the correct answer? 57 km 73 km 16 km 40 km

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in [0,360°]. (√2,-1) Which one is the correct answer? √3; 305.3 3; 324.7 √3; 324.7 3; 125.3

Please see the attached file for the fully formatted problems. 1. Find the indicated part of each triangle ABC. C = 118°, b = 130km, a = 75km; find c The correct answer to this problem is 180 km how did they come up with that answer? 2. Height of a Balloon: The angles of elevation of a balloon from two points A and B on

Solve the equation for the interval [0, 2л). sin^2 x - cos^2 x = 0 Which is the correct answer? x = л/4, л/3 x = л/4, 3л/4, 5л/4, 7л/4 x = л/4 x = л/4, л/6

Solve the equation for solutions in the interval [0, 360). cos 2x= √3/2 Which is the correct answer? x = 15, 165, 195, 345 x = 30, 90, 150, 270 x = 0, 120, 180, 240 x = 105, 165, 285, 345.

Find the exact value, given that sin A = -4/5 with A in quadrant IV tan 2A Which is the correct answer? - 7/24 24/7 - 24/7 7/24

Solve the equation for solutions in the interval [0, 360). tan 4x = 0 Which is the correct answer? x = 33, 57, 147, 237, 327 x = 0, 90, 180, 270 x = 0, 45, 90, 135, 180, 225, 270 x = 0, 45, 90, 135, 180, 225, 270, 315

1. Solve csc^2θ - 2 cot θ = 4 for solutions over the interval [0°, 360°]. Express approximate solutions to the nearest tenth of a degree. Could you please show me step by step to see how to get the correct answer? The correct answers are (18.4°, 135°, 198.4°, 315°)

Graph the attached function (which of the graph options are correct?)

Match the attached functions with their graphs. Thank you.. Match the function with its graph. Which is the correct answer? 1) y = 1 + sin x 2) y = 1 + cos x 3) y = -1 + sin x 4) y = -1 + cos x A B C D 1A, 2D, 3C, 4B 1A, 2B, 3C, 4D 1A, 2C, 3D, 4

Factor the trigonometric expression. Which is the correct answer? sin2x + sin2x cot2x cot2x - 1 sin2x + 1 cot2x + 1 1.

Give the amplitude or period as requested. Which is the correct answer? Amplitude of y = 4 sin x 4л л/4 4 2л

Use trigonometric identities to find the exact value of the attached equation. Which of the attached answers is correct?

1) Prove from the unit circle that sin²⊖ + cos²⊖ = 1. Using the result describe the equation for which x = 3 + 2cos⊖, y = 1 + 3sin⊖. 2) Using problem one simplify sin²⊖/(1 + cos⊖) + sin²⊖/(1 - cos⊖)

If you would please give me each step to solve these problems so I can get a better understanding how to solve these types of problems would be very helpful. Thanks. Graph each expression and use the graph to conjecture an identity. Then verify your conjecture algebraically. 1. sec x - sin x tan x Verify that each equat