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Lisa [10]
3 years ago
13

How many terms are in the arithmetic sequence 9, 2, −5, . . . , −187?

Mathematics
1 answer:
8090 [49]3 years ago
4 0
A(n) = 9 - 7(n-1)

The sequence decreases by -7 each time.

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Express the integral as a limit of Riemann sums. Do not evaluate the limit. (Use the right endpoints of each subinterval as your
Darina [25.2K]

Answer:

Given definite  integral as a limit of Riemann sums is:

\lim_{n \to \infty} \sum^{n} _{i=1}3[\frac{9}{n^{3}}i^{3}+\frac{36}{n^{2}}i^{2}+\frac{97}{2n}i+22]

Step-by-step explanation:

Given definite integral is:

\int\limits^7_4 {\frac{x}{2}+x^{3}} \, dx \\f(x)=\frac{x}{2}+x^{3}---(1)\\\Delta x=\frac{b-a}{n}\\\\\Delta x=\frac{7-4}{n}=\frac{3}{n}\\\\x_{i}=a+\Delta xi\\a= Lower Limit=4\\\implies x_{i}=4+\frac{3}{n}i---(2)\\\\then\\f(x_{i})=\frac{x_{i}}{2}+x_{i}^{3}

Substituting (2) in above

f(x_{i})=\frac{1}{2}(4+\frac{3}{n}i)+(4+\frac{3}{n}i)^{3}\\\\f(x_{i})=(2+\frac{3}{2n}i)+(64+\frac{27}{n^{3}}i^{3}+3(16)\frac{3}{n}i+3(4)\frac{9}{n^{2}}i^{2})\\\\f(x_{i})=\frac{27}{n^{3}}i^{3}+\frac{108}{n^{2}}i^{2}+\frac{3}{2n}i+\frac{144}{n}i+66\\\\f(x_{i})=\frac{27}{n^{3}}i^{3}+\frac{108}{n^{2}}i^{2}+\frac{291}{2n}i+66\\\\f(x_{i})=3[\frac{9}{n^{3}}i^{3}+\frac{36}{n^{2}}i^{2}+\frac{97}{2n}i+22]

Riemann sum is:

= \lim_{n \to \infty} \sum^{n} _{i=1}3[\frac{9}{n^{3}}i^{3}+\frac{36}{n^{2}}i^{2}+\frac{97}{2n}i+22]

4 0
3 years ago
If a regular polygon has exterior angles that measure approximately 17.14º each, how many sides does the polygon have?
mr Goodwill [35]
Exterior angles for n sides = 360/n = 17.14, n = 360/17.14 = <span>21 sides</span>
6 0
2 years ago
The length and width of a living room is 5.5 m and 4.8 m with an uncertainty of 0.1 m in each measurement. The perimeter of the
olga_2 [115]

Answer:

The perimeter of room is (20.6 \pm 0.4)~m

Step-by-step explanation:

We are given the following in the question:

The length and width of a room are measured with uncertainties.

There is  uncertainty of 0.1 m in each measurement.

Length = (5.5 \pm 0.1)~m

Width = (4.8 \pm 0.1)~m

Formula:

The perimeter of room is given by:

P = 2\times (\text{Length + Width})\\P = 2\times ((5.5\pm 0.1)+ (4.8\pm 0.1))\\= 2\times (10.3\pm 0.2)\\P = (20.6 \pm 0.4)~m

The uncertainties are also added and multiplied.

Thus,the perimeter of room is (20.6 \pm 0.4)~m

7 0
3 years ago
Write863.141 In expanded form
skad [1K]

Answer:

800+60+3+0.1+0.04+0.001

6 0
3 years ago
What is the solution to the system of equations below?
nata0808 [166]

Answer:

The answer is B

Step-by-step explanation:

5 0
2 years ago
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