Answer:
15/2
Step-by-step explanation:
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:
x = 12
z = 101
Step-by-step explanation:
Hello There!
First lets find z
Well the angle that has a measure of 79 degrees and angle z are supplementary angles meaning that the sum of the two is 180
So we can find the missing angle by subtract the given angle (79 in this case) from 180
180 - 79 = 101 so z = 101
Now lets find x
The angle that has a measure of 79 degrees and the angle labeled (6x+7) are vertical angles
If you didn't know vertical angles are congruent
That being said lets create an equation to solve for x
79 = 6x + 7
now we solve for x
step 1 subtract 7 from each side by
7 - 7 cancels out
79 - 7 = 72
now we have 72 = 6x
step 2 divide each side by 6
72/6=12
6x/6=x
we're left with x = 12
For this case what we must do is define h (x), which is given by:
h (x) = f (x) * g (x)
Where,
f (x) = 5 (The number of fish breeding farms)
g (x) = 80 (1.04) ^ x (The approximate number of fish per breeding farm)
Substituting we have:
h (x) = (5) * (80 (1.04) ^ x)
Rewriting we have:
h (x) = 400 (1.04) ^ x
Answer:
the approximate population of the fish across all Mr. Dawson's farms after x months is:
h (x) = 400 (1.04) ^ x
Answer:
37.6 units
Step-by-step explanation:
Perimeter = sum of all sides of the triangle
To find the sum, find the distance between each points.
✔️Distance between points (-7, 6) and (5, -4):
(nearest tenth)
✔️Distance between (-7, 6) and (-7, -4):
|6 -(-4)| = 10 units
✔️Distance between (-7, -4) and (5, -4)
|-7 - 5| = 12 units
✔️ Perimeter = 15.6 + 10 + 12 = 37.6 units
