PLEASEE HELPP MEE IN MATHH!!!! NUMBERS 6 AND 7!!!!

Mathematics

1 answer:

Tomtit [17]2 years ago

5 0

Answer:

6.) angle 1 = 61 degrees. angle 2 = 61 degrees. . 7.) angle 1 = 44 degrees

angle 2 = 44 degrees

Step-by-step explanation:

main reason is that because of Alternate Interior angles theorem angle 1 = angle 2

for both questions 6 and 7.

Also the angles that form a straight line sum to 180 degrees

so 61 + 58 + 61 = 180

and for 7

90 = 46 + 44

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I need help with part b. I feel like there’s a catch, I want to do the first derivative test, however, I feel like there is a be

Sladkaya [172]

Answer:

The fifth degree Taylor polynomial of g(x) is increasing around x=-1

Step-by-step explanation:

Yes, you can do the derivative of the fifth degree Taylor polynomial, but notice that its derivative evaluated at x =-1 will give zero for all its terms except for the one of first order, so the calculation becomes simple:

$P_5(x)=g(-1)+g'(-1)\,(x+1)+g"(-1)\, \frac{(x+1)^2}{2!} +g^{(3)}(-1)\, \frac{(x+1)^3}{3!} + g^{(4)}(-1)\, \frac{(x+1)^4}{4!} +g^{(5)}(-1)\, \frac{(x+1)^5}{5!}$

and when you do its derivative:

1) the constant term renders zero,

2) the following term (term of order 1, the linear term) renders: $g'(-1)\,(1)$ since the derivative of (x+1) is one,

3) all other terms will keep at least one factor (x+1) in their derivative, and this evaluated at x = -1 will render zero

Therefore, the only term that would give you something different from zero once evaluated at x = -1 is the derivative of that linear term. and that only non-zero term is: $g'(-1)= 7$ as per the information given. Therefore, the function has derivative larger than zero, then it is increasing in the vicinity of x = -1