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x^{\msquare}  \log_{\msquare}  \sqrt{\square}  \nthroot[\msquare]{\square}  \le  \ge  \frac{\msquare}{\msquare}  \cdot  \div  x^{\circ}  \pi  
\left(\square\right)^{'}  \frac{d}{dx}  \frac{\partial}{\partial x}  \int  \int_{\msquare}^{\msquare}  \lim  \sum  \infty  \theta  (f\:\circ\:g)  f(x) 
▭\:\longdivision{▭}  \times \twostack{▭}{▭}  + \twostack{▭}{▭}   \twostack{▭}{▭}  \left(  \right)  \times  \square\frac{\square}{\square} 
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x^{\msquare}  \log_{\msquare}  \sqrt{\square}  \nthroot[\msquare]{\square}  \le  \ge  \frac{\msquare}{\msquare}  \cdot  \div  x^{\circ}  \pi  
\left(\square\right)^{'}  \frac{d}{dx}  \frac{\partial}{\partial x}  \int  \int_{\msquare}^{\msquare}  \lim  \sum  \infty  \theta  (f\:\circ\:g)  f(x) 
 \twostack{▭}{▭}  \lt  7  8  9  \div  AC 
+ \twostack{▭}{▭}  \gt  4  5  6  \times  \square\frac{\square}{\square} 
\times \twostack{▭}{▭}  \left(  1  2  3    x 
▭\:\longdivision{▭}  \right)  .  0  =  +  y 
Number Line
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 line\:(1,\:2),\:(3,\:1)
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Related Pages Common Core Math Resources, Lesson Plans And Worksheets Common Core Math Video Lessons, Math Worksheets and Games for Grade 5 Common Core Math Video Lessons, Math Worksheets and Games for all grades
Grade 5 Homework, Lesson Plans And Worksheets
Module 1 Topics and Objectives  

Standard: 5.NBT.1, 5.NBT.2, 5.MD.1 Days: 4 : Reason concretely and pictorially using place value understanding to relate adjacent base ten units from millions to thousandths. ( ) : Reason abstractly using place value understanding to relate adjacent base ten units from millions to thousandths. ( ) : Use exponents to name place value units and explain patterns in the placement of the decimal point. ( ) : Use exponents to denote powers of 10 with application to metric conversions. ( )  
Standard: 5.NBT.3 Days: 2 : Name decimal fractions in expanded, unit, and word forms by applying place value reasoning. ( ) : Compare decimal fractions to the thousandths using like units and express comparisons with >, <, =. ( )  
Standard: 5.NBT.4 Days: 2 , : Round a given decimal to any place using place value understanding and the vertical number line. ( ) ( )  
: Topics AC (assessment ½ day, return ½ day, remediation or further applications 1 day)  
Standard: 5.NBT.2, 5.NBT.3, 5.NBT.7 Days: 2 : Add decimals using place value strategies and relate those strategies to a written method. ( ) : Subtract decimals using place value strategies and relate those strategies to a written method. ( )  
Standard: 5.NBT.1, 5.NBT.3, 5.NBT.7 Days: 2 : Multiply a decimal fraction by singledigit whole numbers, relate to a written method through application of the area model and place value understanding, and explain the reasoning used. ( ) : Multiply a decimal fraction by singledigit whole numbers, including using estimation to confirm the placement of the decimal point. ( )  
Standard: 5.NBT.3, 5.NBT.7 Days: 4 : Divide decimals by singledigit whole numbers involving easily identifiable multiples using place value understanding and relate to a written method. ( ) : Divide decimals with a remainder using place value understanding and relate to a written method. ( ) : Divide decimals using place value understanding including remainders in the smallest unit. ( ) : Solve word problems using decimal operations. ( )  
: Topics AF (assessment ½ day, return ½ day, remediation or further applications 1 day)  
Module 2 Topics and Objectives  

Standard: 5.NBT.1, 5.NBT.2, 5.OA.1 Days: 2 : Multiply multidigit whole numbers and multiples of 10 using place value patterns and the distributive and associative properties. ( ) : Estimate multidigit products by rounding factors to a basic fact and using place value patterns. ( )  
Standard: 5.OA.1, 5.OA.2, 5.NBT.5 Days: 7 : Write and interpret numerical expressions and compare expressions using a visual model. ( ) : Convert numerical expressions into unit form as a mental strategy for multidigit multiplication. ( ) : Connect visual models and the distributive property to partial products of the standard algorithm without renaming. ( ) :Connect area diagrams and the distributive property to partial products of the standard algorithm without renaming. ( ) : Connect area diagrams and the distributive property to partial products of the standard algorithm with renaming. ( ) : Fluently multiply multidigit whole numbers using the standard algorithm and using estimation to check for reasonableness of the product. ( ) : Fluently multiply multidigit whole numbers using the standard algorithm to solve multistep word problems. ( )  
Standard: 5.NBT.7, 5.OA.1, 5.OA.2, 5.NBT.1 Days: 3 : Multiply decimal fractions with tenths by multidigit whole numbers using place value understanding to record partial products. ( ) : Multiply decimal fractions by multidigit whole numbers through conversion to a whole number problem and reasoning about the placement of the decimal. ( ) : Reason about the product of a whole number and a decimal with hundredths using place value understanding and estimation. ( )  
Standard: 5.NBT.7, 5.NBT.7, 5.MD.1 Days: 3 : Use whole number multiplication to express equivalent measurements. ( ) : Use decimal multiplication to express equivalent measurements. ( ) : Solve twostep word problems involving measurement and multidigit multiplication. ( )  
: Topics AD (assessment ½ day, return ½ day, remediation or further applications 2 days)  
Standard: 5.NBT.1, 5.NBT.2, 5.NBT.6 Days: 3 : Use patterns for multidigit whole number division. ( ) , : Use basic facts to approximate quotients with twodigit divisors. ( ) ( )  
Standard: 5.NBT.6 Days: 5 : Divide two and threedigit dividends by multiples of 10 with singledigit quotients and make connections to a written method. ( ) : Divide two and threedigit dividends by twodigit divisors with singledigit quotients and make connections to a written method. ( ) : Divide two and threedigit dividends by twodigit divisors with singledigit quotients and make connections to a written method. ( ) , : Divide three and fourdigit dividends by twodigit divisors resulting in two and threedigit quotients, reasoning about the decomposition of successive remainders in each place value. ( ) ( )  
Standard: 5.NBT.2, 5.NBT.7 Days: 4 : Divide decimal dividends by multiples of 10, reasoning about the placement of the decimal point and making connections to a written method. ( ) : Use basic facts to approximate decimal quotients with twodigit divisors, reasoning about the placement of the decimal point. ( ) , : Divide decimal dividends by twodigit divisors, estimating quotients, reasoning about the placement of the decimal point, and making connections to a written method. ( ) ( )  
Standard: 5.NBT.6, 5.NBT.7 Days: 2 , : Solve division word problems involving multidigit division with group size unknown and the number of groups unknown. ( ) ( )  
: Topics AH (assessment ½ day, return ½ day, remediation or further application 2 days)  
Module 3 Topics and Objectives  

Standard: 5.NF.1, 5.NF.3 Days: 2 : Make equivalent fractions with the number line, the area model, and numbers. ( ) : Make equivalent fractions with sums of fractions with like denominators. ( )  
Standard: 5.NF.1, 5.NF.2 Days: 5 : Add fractions with unlike units using the strategy of creating equivalent fractions. ( ) : Add fractions with sums between 1 and 2. ( ) : Subtract fractions with unlike units using the strategy of creating equivalent fractions. ( ) : Subtract fractions from numbers between 1 and 2. ( ) : Solve twostep word problems. ( )  
: Topics AB (assessment ½ day, return ½ day, remediation or further applications 2 day)  
Standard: 5.NF.1, 5.NF.2 Days: 5 : Add fractions to and subtract fractions from whole numbers using equivalence and the number line as strategies. ( ) : Add fractions making like units numerically. ( ) : Add fractions with sums greater than 2. ( ) : Subtract fractions making like units numerically. ( ) : Subtract fractions greater than or equal to one ( )  
Standard: 5.NF.1, 5.NF.2 Days: 4 : Use fraction benchmark numbers to assess reasonableness of addition and subtraction equations. ( ) : Strategize to solve multiterm problems. ( ) : Solve multistep word problems; assess reasonableness of solutions using benchmark numbers. ( ) : Explore part to whole relationships. ( )  
: Topics CD (assessment ½ day, return ½ day, remediation or further applications 2 day)  
Module 4 Topics and Objectives  

Standard: 5.MD.2 Days: 1 : Measure and compare pencil lengths to the nearest 1/2, 1/4, and 1/8 of an inch, and analyze the data through line plots. ( )  
Standard: 5.NF.3 Days: 4 , : Interpret a fraction as division. ( )( ) : Use tape diagrams to model fractions as division. ( ) : Solve word problems involving the division of whole numbers with answers in the form of fractions or whole numbers. ( )  
Standard: 5.NF.4a Days: 4 : Relate fractions as division to fraction of a set. ( ) : Multiply any whole number by a fraction using tape diagrams. ( ) : Relate fraction of a set to the repeated addition interpretation of fraction multiplication. ( ) : Find a fraction of a measurement, and solve word problems. ( )  
Standard: 5.OA.1, 5.OA.2, 5.NF.4a, 5.NF.6 Days: 3 : Compare and evaluate expressions with parentheses. ( ) , : Solve and create fraction word problems involving addition, subtraction, and multiplication. ( )  
: Topics AD (assessment ½ day, return ½ day, remediation or further applications 1 day)  
Standard: 5.NBT.7, 5.NBT.4a, 5.NF.6, 5.MD.1 Days: 8 : Multiply unit fractions by unit fractions. ( : Multiply unit fractions by nonunit fractions. ( ) : Multiply nonunit fractions by nonunit fractions. ( ) : Solve word problems using tape diagrams and fractionbyfraction multiplication. ( ) , : Relate decimal and fraction multiplication. ( ) : Convert measures involving whole numbers, and solve multistep word problems. ( ) : Convert mixed unit measurements, and solve multistep word problems. ( )  
Standard: 5.NF.5, 5.NF.6 Days: 4 : Explain the size of the product, and relate fraction and decimal equivalence to multiplying a fraction by 1. ( ) , : Compare the size of the product to the size of the factors. ( ) : Solve word problems using fraction and decimal multiplication. ( )  
Standard: 5.OA.1, 5.NBT.7, 5.NF.7 Days: 7 : Divide a whole number by a unit fraction. ( ) : Divide a unit fraction by a whole number. ( ) : Solve problems involving fraction division. ( ) : Write equations and word problems corresponding to tape and number line diagrams. ( ) : Connect division by a unit fraction to division by 1 tenth and 1 hundredth. ( ) , : Divide decimal dividends by nonunit decimal divisors. ( )( )  
Standard: 5.OA.1, 5.OA.2 Days: 2 : Interpret and evaluate numerical expressions including the language of scaling and fraction division. ( ) : Create story contexts for numerical expressions and tape diagrams, and solve word problems. ( )  
: Topics AH (assessment ½ day, return ½ day, remediation or further applications 2 days)  
Module 5 Topics and Objectives  

Standard: 5.MD.3, 5.MD.4 Days: 3 : Explore volume by building with and counting unit cubes. ( ) : Find the volume of a right rectangular prism by packing with cubic units and counting.( ) : Compose and decompose right rectangular prisms using layers. ( )  
Standard: 5.MD.3, 5.MD.5 Days: 6 : Use multiplication to calculate volume. ( ) : Use multiplication to connect volume as with volume as . ( ) : Find the total volume of solid figures composed of two nonoverlapping rectangular prisms. ( ) : Solve word problems involving the volume of rectangular prisms with whole number edge lengths. ( ) , : Apply concepts and formulas of volume to design a sculpture using rectangular prisms within given parameters. ( )  
: Topics AB (assessment 1 day, return ½ day, remediation or further applications ½ day)  
Standard: 5.NF.4b, 5.NF.6 Days: 6 : Find the area of rectangles with wholebymixed and wholebyfractional number side lengths by tiling, record by drawing, and relate to fraction multiplication. ( ) : Find the area of rectangles with mixedbymixed and fractionbyfraction side lengths by tiling, record by drawing, and relate to fraction multiplication. ( ) : Measure to find the area of rectangles with fractional side lengths. ( ) : Multiply mixed number factors, and relate to the distributive property and the area model. ( ) , : Solve real world problems involving area of figures with fractional side lengths using visual models and/or equations. ( ) ( )  
Standard: 5.G.3, 5.G.4 Days: 6 : Draw trapezoids to clarify their attributes, and define trapezoids based on those attributes. ( ) : Draw parallelograms to clarify their attributes, and define parallelograms based on those attributes. ( ) : Draw rectangles and rhombuses to clarify their attributes, and define rectangles and rhombuses based on those attributes. ( ) : Draw kites and squares to clarify their attributes, and define kites and squares based on those attributes. ( ) : Classify twodimensional figures in a hierarchy based on properties. ( ) : Draw and identify varied twodimensional figures from given attributes. ( )  
: Topics AD (assessment 1 day, return ½ day, remediation or further applications ½ day)  
Module 6 Topics and Objectives  

Standard: 5.G.1 Days: 6 : Construct a coordinate system on a line. ( ) : Construct a coordinate system on a plane. ( ) , : Name points using coordinate pairs, and use the coordinate pairs to plot points. ( ) , : Investigate patterns in vertical and horizontal lines, and interpret points on the plane as distances from the axes. ( )( )  
Standard: 5.OA.2, 5.OA.3, 5.G.1 Days: 6 : Plot points, use them to draw lines in the plane, and describe patterns within the coordinate pairs. ( ) : Generate a number pattern from a given rule, and plot the points. ( ) : Generate two number patterns from given rules, plot the points, and analyze the patterns. ( ) : Compare the lines and patterns generated by addition rules and multiplication rules. ( ) : Analyze number patterns created from mixed operations. ( ) : Create a rule to generate a number pattern, and plot the points.( )  
: Topics AB (assessment 1 day, return 1 day, remediation or further applications 1 day)  
Standard: 5.G.1, 5.G.2 Days: 5 : Construct parallel line segments on a rectangular grid. ( ) : Construct parallel line segments, and analyze relationships of the coordinate pairs. ( ) : Construct perpendicular line segments on a rectangular grid. ( ) : Construct perpendicular line segments, and analyze relationships of the coordinate pairs. ( ) : Draw symmetric figures using distance and angle measure from the line of symmetry. ( )  
Standard: 5.OA.3, 5.G.2 Days: 3 : Draw symmetric figures on the coordinate plane. ( ) : Plot data on line graphs and analyze trends.( ) : Use coordinate systems to solve real world problems. ( )  
: Topics AD (assessment 1 day, return 1 day, remediation or further applications 1 day)  
Standard: 5.NF.2, 5.NF.3, 5.NF.6, 5.NF.7c, 5.MD.1, 5.MD.5, 5.G.2 Days: 5 , , , , : Make sense of complex, multistep problems and persevere in solving them. Share and critique peer solutions. ( )  
Days: 9 , : Solidify writing and interpreting numerical expressions. ( ) : Solidify fluency with Grade 5 skills. , : Solidify the vocabulary of geometry. ( ) : Explore the Fibonacci sequence. : Explore patterns in saving money. ( ) , : Design and construct boxes to house materials for summer use. ( )  
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 Write Equation of Line from the Slope and 1 Point
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 Equation of Line Parallel to Another Line and Through a Point
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ME 274: Basic Mechanics II
Homework h1.j  fa24.

DISCUSSION THREAD
Ask or answer questions here. You can learn from either.
DISCUSSION and HINTS Since the cable does not stretch (R_dot = R_ddot = 0), an observer on aircraft A will see a circular path for B, although the true path of B is more complicated than that. Since θ_dot = constant, then θ_ddot = 0.
It is recommended that you write down the relative motion kinematics equations relating the motions of A and B:
v B = v A + v B/A a B = a A + a B/A
and use a set of polar coordinates to describe v B/A and a B/A :
v B/A = R_dot* e R + R*theta_dot* e θ = R*theta_dot* e θ a B/A = (R_ddot  R*theta_dot^2)* e R + (R*theta_ddot +2*R_dot*theta_dot)* e θ =  R*theta_dot^2* e R
5 thoughts on “Homework H1.J  Fa24”
Since velocity and accleration for a are given on the x axis, do we need to convert them to the polar coordinates before we can add them to the vB/A expression?
I would recommend converting the polar coordinates from vB/A to i and j to find the velocity of the glider.
Also, is there a reason why the angle is in degrees and the change in angle is in radians per second?
It's given in rad/s because that's how you would convert an angular velocity to velocity (rather than some degrees per second)
Does it matter if our final answer is in polar or cartesian?
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