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MAT136H1 Study Guide - Quiz Guide: Differential Equation, Slope Field, Gie

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ultramarineelephant806

25 Jul 2018

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Al- Faisal, Faisal

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MAT136H1 Full Course Notes

MAT136H1 Full Course Notes

Document Summary

Question: true or false? a solution, but not the most general solution to the differential equations. (cid:1843)=(cid:888)(cid:1857)4 is the most general solution to the differential equations (cid:1856)(cid:1843)(cid:1856)=(cid:886)(cid:1843). We can get other solutions by changing the 6 in (cid:1843)=(cid:888)(cid:1857)4 to othe(cid:396) (cid:374)u(cid:373)(cid:271)e(cid:396)s. it"s o(cid:374)ly. If (cid:1856)(cid:1876)(cid:1856)=(cid:883)(cid:1876) and (cid:1876)=(cid:885) when t=(cid:882),then (cid:1876) is an increasing function of . (cid:1856)(cid:1876)(cid:1856)>(cid:882),so the function increasing there, When (cid:1876)=(cid:885), but you also want know if it s increasing everywhere. (cid:1856)(cid:1876)(cid:1856)=(cid:883)(cid:1876) (cid:1876)(cid:1856)(cid:1876)= (cid:1856) (cid:1876)2(cid:884)=+(cid:1855) graph of (cid:1876)= (cid:884) +(cid:1855) general form not (cid:1876)= (cid:884) +(cid:1855) Square-rooting x could give both (cid:884) +(cid:1855), but (cid:1876)= (cid:884) +(cid:1855) is not a function since it (cid:449)o(cid:374)"t pass the (cid:448)e(cid:396)ti(cid:272)al li(cid:374)e test. Ho(cid:449)e(cid:448)e(cid:396), it (cid:272)ould gi(cid:448)e eithe(cid:396) (cid:884) +(cid:1855) or (cid:884) +(cid:1855) since either one of them would be a function, but for this situation, it has to be (cid:884) +(cid:1855) in other. Example: with (cid:1856)(cid:1876)(cid:1856)=+(cid:883),the solution is (cid:1876)= 22++(cid:1855),which is a polynomial.

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Related Questions

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1. Factor out the GCF from thepolynomial.
20m^9 + 6m^7 + 20m^5

2(10m^9 + 3m^7 +10m^5)
No common factor
m^5 (20m^4 + 6m^2 +20)
2m^5 (10m^4 + 3m^2 +10)

2. Find the solution to the system by addition(elimination) method.
4x + 15y = 15
8x - 3y = -3

(1, 0)
(0, 0)
(0, 1)
(1, 1)

3. (11p + 4)(11p - 4)

p^2 - 16
121p^2 + 88p - 16
121p^2 - 16
121p^2 - 88p -16

4. Find the solution to the system by addition(elimination) method.
2x + 15y = -91
9x + 5y = 28

(-5, 7)
(7, -7)
(9, -9)
(-7, 7)

5. Factor by grouping.
18x^3 + 15x^2 + 12x + 10

(3x^2 + 2)(6x + 5)
(18x^2 - 2)(x - 5)
(3x^2 - 2)(6x - 5)
x(18x + 2)(x +5)

6. (x + 3y)(x + 5y)

x^2 + 5xy + 15y^2
x^2 + 8xy + 8y^2
x^2 + 8xy + 15y^2
x + 8xy + 15y

7. 6x^7 (9x^7 + 12x^2 - 7)

54x^7 + 72x^2 - 42
54x^14 + 72x^9
54x^14 + 72x^9 -42x^7
54x^14 + 12x^2 -7

8. 15x^2 - 12x + 10x - 8

(15x + 2)(x - 4)
(15x - 2)(x + 4)
(3x - 2)(5x + 4)
(3x + 2)(5x -4)

9. For the polynomial, state the degree andwhether or not the polynomial is a monomial, a binomial, or atrinomial.
5x^3y^4 - 8x^5y^6 + 8

Binomial, degree 7
Trinomial, degree 3
Trinomial, degree18
Trinomial, degree11

10. (3x^8 + 2x^7 - 4x^6 + 8) + (7x^8 - 4x^7 +8x^6 + 1)

10x^8 - 2x^7 + 4x^6 +9
12x^42 + 9
10x^26 - 2x^14 + 4x^12 +9
4x^8 + 4x^7 + 4x^6 +9

11. (2n^5 - 3n^3 - 6) - (5n^5 - 14n^3 -3)

-3n^5 + 2n^3 - 9
-3n^5 + 11n^3 - 3
5n^8
-3n^5 + 11n^3 -9

12. Use the substitution method to solve thesystem.
x - 4y = -13
7x - 5y = -22

(1, 4)
(-2, 4)
(-1, 3)
No solution

13. Use the substitution method to solve thesystem.
8x - 6y = 32
2x - 2y = 8

(3, 1)
(4, 1)
(4, 0)
No solution

14. Terms in a polynomial are separated byaddition or subtraction.

15. A polynomial is an algebraic expression ofone or more terms.

16. A solution of two linear equations in twovariables is an ordered pair that is a solution to eachequation.

17. The greatest common factor will always begreater than the largest factor of each term of theexpression.

18. A system of equations in two variables mayhave infinite solutions.

19. When two or more algebraic expressions aremultiplied, each expression is called a term.

20. Factoring is multiplication inreverse.