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MATH 212 Midterm: MATH212_ALL-SECTIONS_SPRING2006_0000_MID_EXAM_2

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turquoisegnu128

10 Jan 2019

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University of Maryland

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Draw a 2-d diagram which shows 2 (3 5) = (2 3) 5. Use the meaning of multiplication to explain how your picture depicts both expressions. 3(14). a) use the distributive property (several times) to show that. 15 32 = 10 30 + 10 2 + 5 30 + 5 2 (do not just cite this as foil!!!: draw a diagram showing why the above equality holds. Use the partial products algorithm to solve 46 times 234. A closet floor is 4 1/2 feet wide and 2 1/3 feet deep. a) find the area of the floor by changing the fractions to improper form and using the standard algorithm. 6(8). a) write the following number in scientific notation: 10. 56 b) write the following in its numeral form: 5. 7 10-7. 8(16). a) explain why the rule for multiplying decimals works using the example:

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Related Questions

Equations and Inequalities

Identifying Properties When Solving Equations

Independent Practice

1. The following pairs of equations are equivalent. Describe the operation that occurred in the second equation.

2. Complete the following table with the properties used to solve 4(x+3)=20.

Statement	Proof
4 (x+3) = 20	Given
4x + 12 = 20
4x = 8
x = 2

3. Complete the following table with the mathematical statements that correspond to the proofs used to solve

Statement	Proof
	Given
	Multiplication Property of Equality
	Distributive Property
	Addition Property of Equality
	Division Property of Equality

4. Consider the equations 5x + 10 = 30 and 5 (x+10) = 30.

Do they have the same solution? Why or why not?

5. Consider the equations 3x + 2 = 14 and 2+3x = 14.

Do they have the same solution? Why or why not?

6. Consider the equation 3 (x+2)+3x = 36

Without solving. Name all the properties that would be used to solve the equation.

7. Consider the equation

Part A: Write an equivalent equation using the multiplication property of equality.

Part B: What properties will you use next to solve the equation?

8. Solve the following equation. Justify each step.

0.2x + 3.1 - 2.1x = 0.3 (x-5) + 0.2

Trigonometric Substitution Rules

For v(a^2-u^2 ) let u = asin?? and v(a^2-u^2 ) = acos??
For v(a^2+ u^2 ) let u = atan? and v(a^2+u^2 ) = asec?
For v(u^2-a^2 ) let u = asec?? and v(u^2-a^2 ) = atan?

1. Integrate ?dx/v(25+4x^2 ). Identify the following:

a = u = du =

What adjustment, if any, needs to be made to the integral tocomplete the substitution in to u?

2. Rewrite the above integral so that it is all in u.

3. Which of the trig substitution rules above will we use to solvethis integral? Why? Draw and label the relevant right trianglediagram.

4. Use the rule you chose and the diagram to identify what you willreplace u, du and v(a^2+u^2 ) with.

5. Rewrite the integral from step 2 using the replacements fromstep 4. Did you use all the replacements? If not, why not? Can thisintegral be simplified? If so, do it?

6. Integrate the resulting trig function using a basicformula.

7. Use the information from steps 1 and 4 to rewrite the answer instep 6 in terms of the variable x.

u = 2x = 5tan? and v(a^2+u^2 )=v(25+4x^2 )=5sec?

8. How does knowing the trigonometric relationships as defined bythe three sides of a right triangle and the Pythagorean Theoremhelp us solve integrals using trig substitutions?

9. ?dx/(xv(49-9x^2 )) 10. ?dx/v(16x^2-1)

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