Answer:
1.5 unit^2
Step-by-step explanation:
Solution:-
- A graphing utility was used to plot the following equations:
- The plot is given in the document attached.
- We are to determine the area bounded by the above function f ( x ) subjected boundary equations ( y = 0 , x = -1 , x = - 2 ).
- We will utilize the double integral formulations to determine the area bounded by f ( x ) and boundary equations.
We will first perform integration in the y-direction ( dy ) which has a lower bounded of ( a = y = 0 ) and an upper bound of the function ( b = f ( x ) ) itself. Next we will proceed by integrating with respect to ( dx ) with lower limit defined by the boundary equation ( c = x = -2 ) and upper bound ( d = x = - 1 ).
The double integration formulation can be written as:
Answer: 1.5 unit^2 is the amount of area bounded by the given curve f ( x ) and the boundary equations.
![\bf \sqrt{n}< \sqrt{2n+5}\implies \stackrel{\textit{squaring both sides}}{n< 2n+5}\implies 0\leqslant 2n - n + 5 \\\\\\ 0 < n+5\implies \boxed{-5 < n} \\\\\\ \stackrel{-5\leqslant n < 2}{\boxed{-5}\rule[0.35em]{10em}{0.25pt}0\rule[0.35em]{3em}{0.25pt}2}](https://tex.z-dn.net/?f=%5Cbf%20%5Csqrt%7Bn%7D%3C%20%5Csqrt%7B2n%2B5%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bsquaring%20both%20sides%7D%7D%7Bn%3C%202n%2B5%7D%5Cimplies%200%5Cleqslant%202n%20-%20n%20%2B%205%20%5C%5C%5C%5C%5C%5C%200%20%3C%20n%2B5%5Cimplies%20%5Cboxed%7B-5%20%3C%20n%7D%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B-5%5Cleqslant%20n%20%3C%202%7D%7B%5Cboxed%7B-5%7D%5Crule%5B0.35em%5D%7B10em%7D%7B0.25pt%7D0%5Crule%5B0.35em%5D%7B3em%7D%7B0.25pt%7D2%7D)
namely, -5, -4, -3, -2, -1, 0, 1. Excluding "2" because n < 2.
Answer:
Khan Academy
The robot uses the expected amount of energy, but it doesn't filter the expected amount of air and water.
Step-by-step explanation:
Answer:
Here's one way to do it.
Step-by-step explanation:
-24 ÷ (-4)
-24 is the final number on the number line
-4 means you count by 4s on the number line moving backwards.
- Start at 0 facing forward.
- Move backwards in steps of four units from 0 to -24.
- Count the number of steps you took (six).
Answer: +6 (The sign is + because you are still facing forward).
Answer: d
Step-by-step explanation:
The probability of not being purple is the probability of the three other colors. Suppose the number of purple marbles is x. Then we have 20+30+40+x = 90 + x marbles. Then the probability of not being purple is 90/(90+x). If this fraction can have a lowest term for some value of x, then the numerator of this lowest term must be a factor of 90.
Checking through the options, only option D has a non-factor of 90 as its numerator.
