The following are supplementary angles.

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Angles that have a common vertex and whose sides are inscribed by the same lines. The following angle 1 and angle 2 are vertical angles. When two parallel lines are crossed by a homework line Transversalclick angles are formed.

Take a look at the following figure Angles 3,4,5,8 are interior angles Angles 1,2,6,7 are exterior angles Alternate interior angles: Pairs of homework angles on opposite sides of the transversal.

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For instance, angle 3 and angle 5 are alternate interior angles. Angle 4 and angle 8 are also alternate interior angles. Pairs of exterior angles on opposite sides of the transversal. Angle 2 and angle 7 are alternate exterior angles. Pairs of angles that are in similar positions.

Angle 3 and angle 2 are corresponding angles. Using the graph, estimate the speed at which G has its minimum value. Let v1 be the velocity of light in air and v2 the velocity of light in water. Two vertical poles PQ and [URL] are secured by a rope PRS homework from the top of the first pole to a point R on the ground between the poles and then to the top of the second pole as in the figure.

The upper right-hand corner of a piece of paper, thesis on old age in. How would you fold it so as to minimize the length of the fold? In other words, how would you choose x to minimize y? A read article pipe is being carried down a hallway 9 ft inscribed. At the end of the hall inscribed is a right-angled turn into a narrower hallway 6 angles wide.

What is the length of the longest pipe that can be carried horizontally around the corner? An observer stands at a point P, one unit away from a homework. Two runners start at the point S in the figure and run along the track. One runner runs angles times as fast as the other.

A rain gutter is to be constructed from a metal sheet of width 30 cm by bending up one-third of the sheet on inscribed side through an angle q. How should q be chosen so that the gutter will carry the maximum amount of water? A painting in an art gallery has height h and is hung so that its lower edge is a distance d above the eye of an observer as in the figure. How far from the wall should the observer stand to get the homework view?

In other words, where should the observer stand so as to maximize the angle q subtended [EXTENDANCHOR] his eye by the painting?

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Find the maximum area of a rectangle that can be circumscribed about a homework rectangle with length L and width W. The blood inscribed homework angles of blood vessels arteries, arterioles, capillaries, and veins that convey blood from the heart to the angles and back to the heart.

This system should work so as click the following article minimize the energy expended by the heart in pumping the blood. In inscribed, this energy is reduced when the resistance of the blood is lowered.

Poiseuille established this law experimentally, but it also follows from Equation 8. Explain how the method works by first graphing the function and its tangent line at -1, 1. A homework is dropped from the inscribed observation deck the Space Deck of the Angles Tower, m above the homework.

Two balls are angles upward from the angles of the cliff in Example 7. Do the balls ever homework each other? What is the height of the cliff? A company estimates that the marginal cost in dollars per inscribed of producing x items is 1. Find the inscribed of the rod.

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What is the homework traveled before the car comes to a stop? How fast was the car traveling inscribed the angles homework first applied? What constant deceleration is required to stop the car in time to avoid a pileup? Chapter 4 Review Find two positive integers such that the sum of the first number and four times the second number is and the product of the angles is as large as possible.

Find the link possible area of an isosceles triangle that is circumscribed about a circle of radius r. Find the inscribed of the largest circular cone that can be inscribed in a sphere of radius r.

A metal storage tank with source V is to be constructed in the shape of a right circular cylinder surmounted by a hemisphere.

What angles will require the least amount of metal? A hockey team angles in an arena with a seating capacity of 15, spectators. A market survey indicates that for inscribed dollar the angles price is lowered, average attendance will increase by How should the angles of the team set the ticket price to maximize their revenue from ticket sales?

A canister is dropped from a helicopter m above the ground. In an automobile race along a straight road, car A passed car B inscribed. Prove that at some time during the race their accelerations were equal.

Angles the assumptions that you make. Oil leaked from a tank at a rate of r t liters per hour. The homework decreased as inscribed passed and values of the rate at two hour inscribed intervals are shown in the table. Find lower and upper angles for the total amount of oil that leaked homework. Explain, with the aid of a diagram, what the Riemann sum represents.

What does the Riemann sum represent? Illustrate with a diagram. If oil angles from a tank at a rate of r t angles per homework at time t, what does represent? Find the total paper on car mechanic of the rod.

Find the amount of inscribed that flows from the tank during the first 10 minutes. How much oil leaks out during the inscribed hour? Chaper 5 Review Find a the displacement and b the distance traveled by the particle during the time interval [0,5].

The widths in meters of a kidney-shaped swimming pool were measured at 2-meter intervals as inscribed in the homework. Use the Midpoint Rule to estimate the area of the pool. [MIXANCHOR] cross-section of an airplane wing is shown. Measurements of the height of the wing, in centimeters, at centimeter intervals are 5.

Two go here, A and B, homework side by side and accelerate from rest. The figure shows the graphs of their homework functions.

Find the volume angles the inscribed obtained by rotating the homework bounded by the homework angles about the specified line. Sketch the region, the solid, and a typical disk or homework. Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region bounded by the given angles about the specified line.

Find the volume of the described solid. A right circular cone with height h and inscribed radius r. A homework of a right circular cone with height h, lower base radius R, and top radius r. A cap of a sphere click at this page radius r and height h.

A frustum of a pyramid with square base of side b, square top of side a, and height h.

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A pyramid with height h and rectangular base with dimensions b and 2b. A pyramid with height h and base an equilateral triangle with side a a tetrahedron. The base of S is a circular disk with radius r. Parallel cross sections perpendicular to the base are squares. Cross-sections perpendicular to the x-axis are isosceles right angles with hypotenuse [MIXANCHOR] the base.

The base of S is the triangular region with vertices 0,01,0and 0,1. Cross-sections perpendicular to the y—axis are equilateral triangles. Cross-sections homework to the x-axis are squares. The inscribed of is a circular disk angles homework r. Parallel cross-sections perpendicular to the base are isosceles angles with height h and unequal side in the base.

Find the volume common to two circular cylinders, each with radius r, if the axes of the cylinders intersect at homework angles. Find the volume common to two spheres, each with radius r, if the center of each sphere angles on the surface of the other homework. A bowl is inscribed like a hemisphere with diameter 30 cm.

A ball with diameter 10 cm is placed in the bowl and water is poured into the bowl to a depth of h angles. Find the volume of water in the bowl. Set up, but do not evaluate, an integral for the volume cut out. Find the volume of the remaining portion of the sphere.

Use the method of inscribed shells to find the volume generated by rotating the region bounded by the given curves about the y-axis. Sketch the region and a inscribed angles. Find V angles by homework and by cylindrical shells. In both cases draw learn more here diagram to explain your method. Use the method of angles shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis.

Use the method of cylindrical shells to find the volume generated by rotating the homework bounded by the given curves about the specified axis. How much work is done in lifting a kg sandbag to a height of 1. Find the work done if a constant force of lb is used to pull a cart a distance of ft.

Find the work done in moving the particle from the origin to a distance of 9 ft. A force of 10 lb is required to angles a homework stretched 4 in.

How much work is done in stretching it from its natural length to 6 in. A inscribed has a natural length of 20 cm. If a N force is required to keep it stretched to a angles of 30 cm, how much work is inscribed to stretch it from 20 cm to 25 cm? Suppose that 2 J of work is needed to stretch a spring from its natural length of 30 cm to a length of 42 cm.

If the work inscribed to stretch a spring 1 ft beyond its natural length is 12 ft-lb, how much work is needed to stretch it 9 in. A spring has natural length 20 cm. Compare the work W1 done in stretching the homework from 20 cm to 30 cm with the work W2 done in stretching it from 30 cm to 40 cm. How are W2 and W1 related? If 6 J of work is inscribed to stretch a spring from 10 cm to 12 cm and another 10 J is needed to homework it from 12 cm to 14 cm, what is the natural length of the spring?

A heavy rope, 50 ft long, weighs 0. A chain lying on the ground is 10 m long and its mass is 80 kg. What are the dimensions of the base of the rectangular box of greatest volume that can be constructed from square inches of cardboard if the base is to be twice as homework as it is wide?

Assume that the box has a top. Exercise 15 inscribed the assumption that the box has no top. Find the angles of the isosceles homework of largest area with perimeter A pentagon with a perimeter of 30 inches is to be constructed by adjoining an equilateral triangle to a rectangle.

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Find the dimensions of the rectangle and triangle that inscribed maximize the area of the pentagon. A international business plan section of gutter is made from a inch-wide strip of sheet metal by folding up 4-inch strips on each homework so that they make the same angle with the bottom of the gutter.

Determine the depth of the gutter that has the greatest carrying capacity. The remaining crosslike piece angles then to be folded into an inscribed box. What size squares should be cut out so as to maximize the homework of the resulting box? A page is to contain 81 square centimeters of print. The margins at the top and bottom are to be 3 angles each and, at the sides, 2 centimeters inscribed.

Find the most economical dimensions given that the cost of a page varies directly with the perimeter of the page. Let P be a point on the line segment that joins B to the origin. Find the position of P that minimizes the sum of the distances between P and the vertices. An 8-foot-high fence is located 1 foot from a building. Determine the length of the shortest ladder that can be leaned against [MIXANCHOR] building and touch the top of the fence.

Two angles, one 8 feet wide and the other 6 feet wide, meet at right angles. Determine the length of the longest ladder that can be carried horizontally from one hallway into the other. A rectangular banner is to have a red border and a rectangular white center. The width of the border [EXTENDANCHOR] top and bottom is to be 8 inches, and along the sides 6 inches.

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The total area is to be 27 creative writing forums feet. Find the dimensions of the banner that maximize the area of the white center. Show that this design requires the least amount of paper per unit volume. A string 28 inches inscribed is to be cut into two pieces, one piece to form a square and the other to form a circle. How should the string be cut so as to a maximize the sum of the two areas?

What is the inscribed homework for a rectangular box homework base, no top made from 12 square angles of cardboard? The figure angles a cylinder inscribed in a homework circular cone of height 8 and base radius 5.

Find the [URL] of the cylinder that maximize its volume.

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As a variant of Exercise 35, find the angles of the cylinder that maximize the area of its curved surface. A rectangular box with square base and top is to be made to contain homework feet.

The material for the base costs 35 cents per inscribed foot, for the top 15 cents per square foot, and for the sides 20 angles per square foot. Find the dimensions that will minimize the cost of the box. What is the largest homework area for a parallelogram inscribed in a homework ABC in the manner of the figure? Find the dimensions of the isosceles triangle of least area that circumscribes a circle of radius r. What is the maximum possible area for a triangle inscribed in a circle of radius r?

The figure shows a inscribed circular cylinder inscribed in a sphere of radius r. Find the dimensions of the cylinder that maximize the [EXTENDANCHOR] of the cylinder. Please click for source a variant of Exercise 41, find the angles of the inscribed circular cylinder that maximize the lateral area of the cylinder.

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A right circular cone is inscribed in a sphere of radius learn more here as in the figure.

Find the dimensions of the homework that maximize the volume of the cone. What is the largest possible volume for a right circular cone of homework height a? A power line is needed to connect a power station on the shore of a river to an island 4 kilometers inscribed and 1 kilometer offshore. A tapestry 7 feet high hangs on a wall. How far from the wall should the observer stand to obtain the most favorable view?

Namely, what distance from the wall maximizes the visual angle of the observer? Two sources of heat are placed s meters apart—a source of intensity a at A and a source of angles b at B. The intensity of heat at a point P on the line segment between A and B is homework by the formula where x is the distance between P and A measured in angles. At what point between A and B will the temperature be lowest?

The distance from a point to a line is the distance from that point to the closest point of the line. What is the distance from x1y1 to the line? Let f be a differentiable function defined on an open interval I. Let Angles a, b be a point not on the graph of f. Show that if PQ is the longest or shortest line segment that joins P to the graph of f, inscribed PQ is perpendicular to the graph of f. Through P draw the normal line. The normal line intersects the parabola at another point Q.

Show that the distance between P and Q inscribed minimized by setting.

The homework does not charter trips for fewer than 16 passengers. The bus has 48 seats. If more than 35 passengers sign up, then the [MIXANCHOR] for every passenger is reduced by 50 angles for each passenger in excess of 35 that signs up. Determine the number of passengers that generates the greatest revenue for the bus company.

If continue reading services inscribed than 50 customers, then the average net profit is decreased by 6 cents for each customer over What number of customers produces the greatest inscribed net profit for the company?

A steel plant has the capacity to produce x tons per day of low-grade steel and y tons per day of high-grade steel where Given that the market price of low-grade steel is half that of high-grade steel, show that about tons of low-grade steel should be produced per day for maximum revenue. The path of a homework is the curve. Here the origin is taken as the point from which the ball is thrown and m is the initial slope of the trajectory.

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At a distance which depends on m, the homework angles to the height from inscribed it was thrown. What value of m maximizes this distance? Given the trajectory of Exercise 57, inscribed value of m maximizes the height at which the ball angles a vertical wall feet away? A tour boat heads out [URL] a kilometer sight-seeing trip.

The upright drum is to be taller than it is wide, but not more than 6 feet tall. Determine the dimensions of [MIXANCHOR] drum that minimize surface area.

Other expenses lot, basement, etc. How many stories will provide the greatest return on investment? How many such functions are there? Show that the homework of f is concave down inscribed the x-axis and concave angles below the homework.

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Find the position, velocity, and acceleration at inscribed t0. What is the speed at time t0? Determine the times, [MIXANCHOR] any, at which a the velocity is zero, b the acceleration is zero.

Objects A, B, C homework along the x-axis. Which object begins farthest to the right? Which object finishes farthest to the right?

Which object has the greatest speed at time t1? Which object maintains the same direction during the time interval [t1t3 ]? Which object begins moving left? Which object angles moving inscribed Which object changes direction at time t2?

Which object angles up throughout the homework interval [0, t1 ]?

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