Answer:
B
Step-by-step explanation:
let the angles be 3k,10k,2k
then 3k+10k+2k=180
15k=180
k=180/15=12
x=10k=10×12=120°
Let p(x) be a polynomial, and suppose that a is any real
number. Prove that
lim x→a p(x) = p(a) .
Solution. Notice that
2(−1)4 − 3(−1)3 − 4(−1)2 − (−1) − 1 = 1 .
So x − (−1) must divide 2x^4 − 3x^3 − 4x^2 − x − 2. Do polynomial
long division to get 2x^4 − 3x^3 − 4x^2 – x – 2 / (x − (−1)) = 2x^3 − 5x^2 + x –
2.
Let ε > 0. Set δ = min{ ε/40 , 1}. Let x be a real number
such that 0 < |x−(−1)| < δ. Then |x + 1| < ε/40 . Also, |x + 1| <
1, so −2 < x < 0. In particular |x| < 2. So
|2x^3 − 5x^2 + x − 2| ≤ |2x^3 | + | − 5x^2 | + |x| + | − 2|
= 2|x|^3 + 5|x|^2 + |x| + 2
< 2(2)^3 + 5(2)^2 + (2) + 2
= 40
Thus, |2x^4 − 3x^3 − 4x^2 − x − 2| = |x + 1| · |2x^3 − 5x^2
+ x − 2| < ε/40 · 40 = ε.
Answer:
c. 18
Step-by-step explanation:
First, you would find the total sum of the 60 numbers. The average is always the sum of the numbers divided by the number of numbers.
35*18=630
15*10=150
Now we do not know how many numbers the last group has. However, we can find it out doing 60-35-15 to see how many numbers are left. There would be 10 numbers left
10*30=300
630+150+300=1080
1080/60=18
Hence, the answer is C(18)
Answer:
= 184/5
Step-by-step explanation:
converting mixed numbers to fractions, our initial equation becomes,
44/5 × 2/11
Applying the fractions formula for multiplication you get,
= 924/5
Simplifying 924/5, the answer is
=184 4/5
Answer:
632
Step-by-step explanation:
