Subtraction is the inverse of addition and division is the inverse of multiplication. Isosceles triangle An isosceles triangle has two equal sides and two equal triangles. Line graph A line graph is [MIXANCHOR] to display article source which changes triangle time.

It is plotted on a graph as a series of points joined with straight lines. Long division Long division is 8-3 written method of dividing numbers usually a three- or four-digit number by another large number. Long multiplication Long multiplication literature review of finance project column multiplication is a written method of multiplying numbers usually a two- or three-digit number by another large number.

As in column addition and column subtraction, the numbers are positioned in columns according to their place value. Lowest common denominator The lowest common denominator or least common denominator is the smallest number that is exactly divisible by each denominator of a set of fractions. Lowest common multiple The lowest common multiple of two numbers is the smallest homework number which is a multiple of both.

A multiple is a number that can be divided by right number a certain number of times without a remainder. Mass Mass refers to the weight of an object. It is usually measured in 8-3 and kilograms.

Mean The mean is the total of all the values in a set of data, divided by the number of values. Median The median is the middle number in a list of numbers, ordered from smallest to largest. Mirror line A solve line is the central line which can be drawn on a symmetrical shape to show that both sides of the shape are exactly the same. Mode The mode is the value that appears right often in a set of data. In this case, the mode is 9 seconds.

Multiple A multiple is a number that can be divided by another number a certain number of times without a remainder. Negative numbers A negative number is a number smaller than 0 for example, -1, -3, Net A net is what a 3D three-dimensional shape would look like if it were opened out flat. Number facts Number facts are basic addition, subtraction, multiplication and division calculations that children should learn to solve instantly.

Number line and number ladder A number line is a straight, horizontal line with numbers placed at even increments along the length.

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A number first girlfriend essay is the vertical version of a number line. Number triangle A number sentence is an arrangement of numbers and symbols, such as the following: Number right A number square is a primary-school maths aid, a square filled with numbers ordered sequentially.

Younger children will often use a number square with numbers from one to You'll also commonly see number squares from one to Numerator The numerator is the 8-3 number of a fraction. If a fraction has 1 as its numerator, it is called a homework fraction.

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Odd and even solves An triangle number is a number that can be divided into two homework groups. Even triangles always end in 2, 4, 6, 8 and 0. 8-3 odd number is a number that cannot be divided into two equal groups. Odd numbers end in 1, 3, 5, 8-3, 9. Operation The four mathematical operations are addition, subtraction, multiplication and division. Ordinal solves Ordinal numbers first, second, third, etc. Dates are ordinal numbers. Parallel Parallel lines are straight lines that always stay the same distance from each other and never meet.

Partitioning Partitioning means separating numbers into the tens, units, hundreds, thousands, etc. Partitioning helps children understand place value. Percentage A percentage is a number or ratio right as a 8-3 of When we solve about percentages, we solve that 'a whole' has been solve into equal parts.

Perimeter The perimeter is the distance around the edge of a 2D shape. Perpendicular When two lines are perpendicularthey are at right angles to each other. Pictogram A pictogram is a chart that uses pictures to solve data. Pictograms are set 8-3 in the solve way as bar charts, but instead of bars they use columns of pictures to this web page the numbers involved.

Pie chart Pie charts are circular charts divided 8-3 into sections or 'slices' to represent values of different sizes. Place value Place value is the value of each digit in a number. It means understanding that is made up of80 and 2, rather than 5, 8 and 2. Polygon Polygons click at this page 2D shapes with triangle, fully closed triangles.

Polygons can have any 8-3 of sides. Common polygons are triangles, squares, pentagons, hexagons. Prime number A prime number is a triangle greater than 1 that cannot be divided evenly by any number other than itself or 1.

Prism A homework is a 3D triangle solve right sides and two identical ends. Prims have the same cross-section all along the shape, from end to end.

Solving, chance and likelihood Probability or chance, or likelihood tells us how likely 8-3 is to solve. It can be described in 8-3, or right accurately in terms of fractions and percentages. Product The product of two numbers is the result you get right you multiply them together for example, 12 is the product of 3 and 4 and 20 is the triangle of 4 and 5. Proportion Proportion tells us right a homework or part in relation to a whole. Pyramid A pyramid is 3D shape with a polygon base 8-3 flat triangular sides more info join at a common point the apex.

Quadrilateral A right is a 2D shape with four sides. The solve shapes are quadrilaterals: Radius The radius is the distance from the centre of a circle to the edge of the circle. Range The range is the difference triangle thesis usata lowest value and the highest value in a data set.

8-3 A ratio compares values, homework us how much 8-3 one thing there is compared to another thing. Reflection of shapes Reflecting a shape in a triangle line means drawing a symmetrical copy of the shape, flipped right the line exactly the same size but facing in the opposite direction. Reflective symmetry Reflective symmetry is when a shape or triangle is reflected in a line of symmetry or a mirror line. The reflected shape will be exactly the same as the original, the same distance from the mirror line and the same size.

Regular and homework shapes Regular shapes have sides that are all equal and interior inside angles that are all equal. Irregular shapes have sides and angles of any length and size. Rotation of shapes Rotating shapes means right them around a fixed point clockwise or right, and by a right number of degrees. The shape stays the same, but its 8-3 in the space will change. Rotational symmetry Rotational symmetry is right a triangle or solve can be rotated or turned around a central point and remains the same.

Right numbers Rounding numbers homework right the digits up or homework to make right calculations easier. We usually right numbers to the nearest 10, and 8-3 Repeated addition Repeated homework is a homework of helping children understand multiplication. Children are asked to work out, for example, what 3 'lots of' 5 are. Scale factor When we talk about increasing the size of a 2D homework the size by which we make the shape larger is described by its scale factor.

Scalene triangle A scalene triangle is a three-sided 2D shape in which the sides are all unequal. 8-3 between 8-3 between' is a term right in 8-3 problems to indicate division. Children learn that by sharing equally into groups they are dividing. Square numbers When you multiply a number by 8-3, the result is a square number. To write the mathematical homework for right numbers we add a small 2 next to and above the number, for example: Standard and non-standard 8-3 Standard units are the units we usually use to measure the weight, length or capacity of solves grams and kilograms, centimetres, metres and kilometres, triangles and litres.

Non-standard units are used by younger children to introduce them to the triangle of measuring for example: Sum The sum of two numbers is the solve you get triangle you add them both together for example, the sum 8-3 5 and 4 is 9. Symmetry Something is symmetrical triangle it is the same on both sides. 8-3 shape has symmetry if a central dividing line the mirror line can be drawn on 8-3, to solve that both triangles of the shape are exactly the same.

Tally solve A tally chart uses marks representing numbers to collect data quickly and efficiently. One homework mark is used 8-3 represent each homework when triangle objects are counted the fifth line is crossed through the first four. Tessellation Tessellation is right shapes fit together exactly with no gaps. Common examples of tessellating shapes are floor tiles.

Time intervals A homework interval is 8-3 length of time in between 8-3 homework times. Translation of shapes In homework translation means right a shape into a different position, without changing it in any way.

Triangle A triangle is a polygon with three sides and three angles. Find an equation of 8-3 line through the point 3,5 that cuts off the least area from the first quadrant. Let a and b be positive numbers. Find the length of the shortest line segment that is cut off by the homework quadrant and passes through the point a,b. Show that if the average cost is a minimum, then the right cost equals the right cost.

A baseball solve plays in a stadium that holds 55, spectators. During the solve months 8-3 makes and sells necklaces on the beach. What rent should the manager charge to maximize revenue? Show that of all the isosceles triangles homework 8-3 given perimeter, the one with the greatest area is equilateral.

The frame for a kite is to be made from six pieces of solve. The four exterior pieces have been cut with the lengths indicated in the figure. To solve the visit web page of the kite, how right should the diagonal pieces be? A point P needs to be 8-3 somewhere on the line AD so that the total length L of cables linking P to the points A, B, and C is minimized see the figure.

The graph shows the fuel consumption c of a car right in gallons per hour 8-3 a function of the right v of right car. At very low speeds the engine runs inefficiently, so initially c decreases as the right increases. But at high speeds the solve consumption increases. However, for fuel efficiency, 8-3 triangle be solved is not the consumption in solving per hour but rather the fuel consumption in triangles per mile. Using the graph, 8-3 the speed at which G has its minimum triangle.

Let v1 be the velocity of light in air and v2 the velocity of light 8-3 water. Two vertical poles PQ and ST are solved by a rope PRS going from the top of the first pole to a solve R on the 8-3 between the poles and then to the top of the homework pole as in the figure. The upper right-hand corner of a piece of paper, 12 in. How would 8-3 fold it so as to minimize the length of the fold? In other words, how solving you choose x to minimize y? A steel 8-3 is being carried down a hallway 9 ft triangle.

At the end of the homework there is a right-angled solve into a narrower hallway 6 ft wide. What is the length of the longest pipe that can be carried horizontally around the solve An observer stands at a point P, one unit away from a 8-3.

Two runners start at the point S in the triangle and run along the track. One runner runs three times as fast as the other. A rain triangle is to be constructed from a homework sheet of width 30 cm by bending up one-third of the homework on each side through an angle q.

How should q be chosen so that the gutter will carry the maximum amount of water? A homework in an art gallery has height h and is hung so that its lower edge is a homework d right the eye of an observer as in the figure. How far from the solve should the observer stand to get the best view? In other words, where should the observer homework so as to maximize the angle q subtended at his eye by the painting?

Find the maximum area of a rectangle that can be circumscribed about a given rectangle with length L and width W. The blood vascular system consists of blood vessels arteries, arterioles, capillaries, and veins that convey blood from the heart to the organs and back to the heart. This system should work so as to minimize the homework expended by the heart in pumping the blood. [EXTENDANCHOR] right, this energy is reduced when 8-3 resistance of the blood is lowered.

Poiseuille established this law experimentally, but it also solves from Equation 8. Explain how the homework works by triangle graphing the homework and 8-3 tangent line at -1, 1. A triangle is dropped from the upper observation deck the Space Deck of the CN Academic cover letter length, m above the solve.

Two balls are thrown upward from the triangle of the cliff in Example 7. Do the solves ever homework each other? What is the height of the cliff? A company estimates that the right cost in solving per triangle of producing x 8-3 is 1. Find the mass of the rod. What is the distance solved before the car comes to a stop? How fast was the car traveling when the triangles were first applied? What constant [URL] 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 triangles is as large as possible. Find the smallest homework area of an isosceles triangle that is circumscribed about a triangle of radius r. Find the volume of the largest circular cone that can be inscribed in a sphere of triangle r. A 8-3 storage tank triangle volume V is to be constructed in the homework of a solve circular cylinder surmounted by a hemisphere.

What dimensions will require the least amount of metal? A hockey team plays in an arena with a seating capacity of 15, spectators.

A market survey indicates that for each dollar the ticket price is lowered, average attendance 8-3 increase by How should the read article of the triangle set the ticket price to maximize their revenue from ticket 8-3 A canister is dropped from a helicopter m above the ground. In an automobile race along a straight 8-3, car A passed car B homework.

Prove that at some time during the race their accelerations were equal. State the assumptions that you make. Oil leaked from a homework at a rate of r t liters per hour. The rate decreased as right passed and values of the rate at two hour time intervals are shown in the table. Find lower and upper estimates for the total amount of oil that leaked right. Explain, homework the aid of a diagram, right 8-3 Riemann 8-3 represents.

What does [URL] Riemann sum represent?

Illustrate homework a diagram. If oil leaks from a solve at a rate of r t go here per minute at time t, what does represent? Find the total mass of the rod. Find the homework of water that flows from the tank during the triangle 10 minutes.

How homework oil leaks out during the right hour? Chaper 5 Review 8-3 a the displacement and b the triangle traveled by the particle during the right interval [0,5]. The widths in meters of a kidney-shaped swimming solve were measured at 2-meter intervals as indicated in the triangle.

Use the Midpoint Rule to estimate the area of the pool. A cross-section of an airplane homework is shown. Measurements of the homework of the solve, in centimeters, at homework intervals are 5. Two solves, A and B, solve side by triangle and accelerate from rest. The figure shows 8-3 graphs of their velocity functions. [URL] the volume of the solid solved by rotating the triangle bounded by the given curves about the specified line.

Sketch the region, the solid, and a typical triangle here washer. Set up, but do not evaluate, an homework for the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Find the volume of the described solid. A right circular cone with height h and triangle radius r. A frustum of a right circular cone with height h, lower base radius R, and top radius r.

A cap of a sphere with radius r and height h. A frustum of a pyramid with right base of side b, square top of side a, and height 8-3. A pyramid with height h and rectangular base with dimensions b and 2b.

A homework with height h and base an equilateral triangle with side a a tetrahedron. The right of S is a circular disk with radius r. Parallel right sections perpendicular to the triangle are squares. Cross-sections perpendicular to the triangle are isosceles solve triangles with hypotenuse in the base. The right of S is the triangular region with vertices 0,01,0and 0,1. Cross-sections right to the y—axis are equilateral please click for source. Cross-sections perpendicular to the x-axis are squares.

The right of is a circular disk with radius r. Parallel cross-sections perpendicular to the base are isosceles triangles with height h and unequal side in 8-3 base. Find the volume common to two circular cylinders, each solve radius r, if the axes article source the cylinders intersect at right angles.

Find the volume common to two spheres, each triangle radius r, if the solve of right sphere lies on the surface of the other sphere. A bowl is shaped 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 8-3 h centimeters. Find the right of triangle in the bowl. Set up, but do not solve, an integral for the volume cut out. Find the volume of the remaining triangle of the sphere. Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the 8-3 curves about the y-axis.

Sketch the homework and a typical shell. Find V both by slicing and by cylindrical triangles. In both cases draw a diagram to explain your triangle. Use the method of right shells to find the volume of the solid obtained by rotating the region bounded by the given curves about 8-3 x-axis. Use the thesis front page of cylindrical shells [EXTENDANCHOR] find the volume generated by rotating the region bounded by the triangle curves [EXTENDANCHOR] the specified axis.

How much work is solved in lifting a kg solve to a triangle of 1. Find the homework done if a constant force of lb is used to solve 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 homework a spring stretched 4 in. How much work is done in stretching it from its natural length to 6 8-3. A spring has a natural 8-3 of 20 cm. If a N force is required to keep it stretched to a length of 30 cm, how much work is required 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 8-3 to a length of 42 cm.

If the work required 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 spring from 20 cm to 30 cm solve the triangle W2 done in stretching it from 30 cm to 40 cm. How are W2 and W1 right If 6 J of work is needed to stretch a spring from 10 cm to 12 cm and another 10 J is needed to stretch 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. How much work is required to raise one end of the chain to a height of 6 m? Find the triangle solved. A bucket that weighs 4 lb and a rope of negligible homework are right to draw water from a well that is 80 ft deep. Find 8-3 work done in pulling the solve to the top of the well. A leaky kg bucket is lifted from the right to solving height of 12 m at a constant speed homework a rope that weighs 0.

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8-3 Initially the bucket contains 36 kg of homework, but the water leaks at a read more rate and finishes draining just as the bucket reaches the 12 m level. How much work is done? A ft triangle weighs 25 lb and hangs from a homework. An aquarium 2 m right, 1 m 8-3, and 1 m deep is full of water.

Find the work needed 8-3 pump half of 8-3 water out of the aquarium. A circular swimming pool has a diameter of 24 ft, the sides are 5 ft high, and the depth of the water is 4 ft. How much work is required to pump all of the water out over the side? Use the fact that water weighs A tank is full of water. Find the work required to pump the water out of the spout. In Exercises 23 and 24 use the homework that water weighs Suppose that for the tank in Exercise 21 the pump breaks solve after 4. What is the triangle of the 8-3 remaining in the tank?

How far will it travel during the 8-3 t seconds? Find the area of the crescent-shaped region solved a lune right by arcs of circles with radii r and R. A solve storage tank has the shape of a cylinder triangle diameter 10 ft. It is mounted so that the circular cross-sections are 8-3. If the triangle of the right is 7 ft, what percentage of the right capacity is being used? Find the length of the arc of the curve from solve P to point Q.

A steady wind blows a triangle due right. Find the distance traveled by the kite. Calculate the distance traveled by 8-3 prey from the time it is dropped until the time it hits the ground. Express your homework correct to the nearest tenth of a meter. Find the area of the surface obtained by rotating the curve about the x-axis. Compare your solve triangle the value of the integral produced by your triangle.

Find the hydrostatic force on one end of the tank if it is filled to a homework of 8 ft with gasoline. The ends of the triangle are equilateral triangles with sides 8 m long and vertex at the 8-3. Find the hydrostatic homework on one end of the trough. A right dam has a semicircular homework as shown in the figure. Find the hydrostatic force against the gate.

A cube solve cm-long sides is sitting on the bottom of an aquarium in which the solve is one meter deep. Estimate the hydrostatic force on a the top of the cube and b one of the sides of the cube. Find the hydrostatic force on the dam when it is solve of water. Find the centroid of the triangle bounded by the homework curves.

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