Hello from MrBillDoesMath!
Answer:
a(n) = -3n , n>= 1
Discussion:
a(1) = -3
a(2) = -6
a(3) = -9
a(4) = -12
The pattern looks like a(n) = -3n
Thank you,
MrB
9514 1404 393
Answer:
4) 6x
5) 2x +3
Step-by-step explanation:
We can work both these problems at once by finding an applicable rule.
where O(h²) is the series of terms involving h² and higher powers. When divided by h, each term has h as a multiplier, so the series sums to zero when h approaches zero. Of course, if n < 2, there are no O(h²) terms in the expansion, so that can be ignored.
This can be referred to as the <em>power rule</em>.
Note that for the quadratic f(x) = ax^2 +bx +c, the limit of the sum is the sum of the limits, so this applies to the terms individually:
lim[h→0](f(x+h)-f(x))/h = 2ax +b
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4. The gradient of 3x^2 is 3(2)x^(2-1) = 6x.
5. The gradient of x^2 +3x +1 is 2x +3.
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If you need to "show work" for these problems individually, use the appropriate values for 'a' and 'n' in the above derivation of the power rule.
Answer:
(4/2 × 2/2 × 3/2) in.³ =3 in.³
Step-by-step explanation:
Answer:
The shaded area is 314.2 cm²
Step-by-step explanation:
Here we have the diameter, d₁ of the smaller semicircles as 10 cm
We note that the larger semicircle is subtended (bounded) by the two smaller semicircles;
1 shaded small semicircle and the other is blank
Therefore, the diameter, d₂ of the large semicircle = 10 + 10 = 20 cm
Also the area of the shaded figure consists of the removal of one small semicircle and the addition of the other semicircle to the area of the larger semicircle such that the area of the shaded figure is as follows
Shaded area of figure = π·d₂²/4 + π·d₁²/4 - π·d₁²/4 = π·d₂²/4 = π×20²/4 = 100×3.142 = 314.2 cm²
Shaded area = 314.2 cm².
Answer:
1.01
Step-by-step explanation:
Mean with outliner = (39.55 + 40.51 + 41.01 + 37.76+ 35.32 + 33.28 + 34.38 + 36.48 + 39.87 + 50.32 + 40.59 + 41.71)/12 = 39.23 seconds.
In this case, the outlier comes to be the data: 50.32. If we don't consider that data point, the mean equals:
Mean wihout outliner = (39.55 + 40.51 + 41.01 + 37.76+ 35.32 + 33.28 + 34.38 + 36.48 + 39.87 + 40.59 + 41.71)/11 = 38.22
The difference is: 39.23 - 38.22 = 1.01
