Answer:
0.082 = 8.2× 10^-2
Step-by-step explanation:
Given the decimal number 0.082, the expanded form using the power of 10 can be gotten by writing the decimal number in standard format(writing as a multiple of 10).
To do that we will shift the decimal point to the front up to the front of digit 8. This shows that the decimal point will be shifted 2times to the front. Since of is shifted 2times to the front, our power of 10 will be -2.
0.082 = 8.2× 10^-2
This gives the required answer.
Note that, the power of 10 is positive when decimals are shifted to the back and negative when shifted to the front(in this case).
Answer:
50 minutes
Step-by-step explanation:
she spent 1 hr and 30 minutes on homework
she spends 2/3 of an hour on the phone = 40 minutes
1 hr 30 min + 40 minutes = 2 hrs and 10 min
so she had 50 minutes to kill before bedtime since she goes to sleep 3 hrs after dinner
2hr 10 min + 50 min = 3 hrs.
the construction of fields of formal infinite series in several variables, generalizing the classical notion of formal Laurent series in one variable. Our discussion addresses the field operations for these series (addition, multiplication, and division), the composition, and includes an implicit function theorem.
(PDF) Formal Laurent series in several variables. Available from: https://www.researchgate.net/publication/259130653_Formal_Laurent_series_in_several_variables [accessed Oct 08 2018].
1) The function is
3(x + 2)³ - 32) The
end behaviour is the
limits when x approaches +/- infinity.3) Since the polynomial is of
odd degree you can predict that
the ends head off in opposite direction. The limits confirm that.
4) The limit when x approaches negative infinity is negative infinity, then
the left end of the function heads off downward (toward - ∞).
5) The limit when x approaches positive infinity is positivie infinity, then
the right end of the function heads off upward (toward + ∞).
6) To graph the function it is important to determine:
- x-intercepts
- y-intercepts
- critical points: local maxima, local minima, and inflection points.
7)
x-intercepts ⇒ y = 0⇒ <span>
3(x + 2)³ - 3 = 0 ⇒ (x + 2)³ - 1 = 0
</span>
<span>⇒ (x + 2)³ = -1 ⇒ x + 2 = 1 ⇒
x = - 1</span>
8)
y-intercepts ⇒ x = 0y = <span>3(x + 2)³ - 3 =
3(0 + 2)³ - 3 = 0 - 3×8 - 3 = 24 - 3 =
21</span><span>
</span><span>
</span><span>9)
Critical points ⇒ first derivative = 0</span><span>
</span><span>
</span><span>i) dy / dx = 9(x + 2)² = 0
</span><span>
</span><span>
</span><span>⇒ x + 2 = 0 ⇒
x = - 2</span><span>
</span><span>
</span><span>ii)
second derivative: to determine where x = - 2 is a local maximum, a local minimum, or an inflection point.
</span><span>
</span><span>
</span><span>
y'' = 18 (x + 2); x = - 2 ⇒ y'' = 0 ⇒ inflection point.</span><span>
</span><span>
</span><span>Then the function does not have local minimum nor maximum, but an
inflection point at x = -2.</span><span>
</span><span>
</span><span>Using all that information you can
graph the function, and I
attache the figure with the graph.
</span>