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3 years ago

What are the bounds of integration?

2 answers:

7 0

I really hope this is right ! Pleas forgive me if it isn’t . A mathematical analysis of integration of intergal . So basically the region that is bounded . (Example [DX]

Marina CMI [18]3 years ago

3 0

Answer:

so the limits are 2 and 9

We want to express as a integral. To do this, we have to identify as a Riemann Sum that approximates the integral. (taking the limit makes the approximation equal to the value of the integral)

In general, to find a Riemann sum that approximates the integral of a function f over an interval [a,b] we can the interval in n subintervals of equal length and approximate the area (integral) with rectangles in each subinterval and them sum the areas. This is equal to

, where is a selected point of the subinterval.

In particular, if we select the ending point of each subinterval as the , the Riemann sum is:

Now, let's identify this in .

The integrand is x² so this is our function f. When k=n, the summand should be because the last selected point is b. The last summand is thus b=9 and b-a=7, then 9-a=7 which implies that a=2.

To verify our answer, note that if we substitute a=2, b=9 and f(x)=x² in the general Riemann Sum, we obtain the sum inside the limit as required.

You might be interested in

a recent survey shows that 16% of college students have dogs and 38% have an HBO subscription. assuming these two events are ind

Nataly_w [17]

Answer: $0.939\ or\ 93.9\%$

Step-by-step explanation:

Given

Survey shows that 16% of college students have dogs and 38% have HBO subscription

Probability that a random person have both is

$\Rightarrow P_o=0.16\times 0.38\quad [\text{As both events are independent}]\\\Rightarrow P_o=0.0608$

The probability that the random person has neither of the two is

$\Rightarrow P=1-P_o\\\Rightarrow P=1-0.0608\\\Rightarrow P=0.939$

3 0

3 years ago

What are the roots of the polynomial equation?

Andreas93 [3]

Answer:

The roots of the polynomial equation in this case would be the intersection of the 2 polynomial functions. which are at x = 4 and x = -3

Step-by-step explanation:

The roots are found by finding the x-values of the intersections of these two cubic polynomial functions.

We could try solving algebraically, but you have the graph.

6 0

3 years ago

It cost $5000 to feed

Mariulka [41]

Answer:

Okays so for 100 guests we can make the equation $5000 ÷ 100 = $50.00

For 100 guests at the wedding it would cost <u>$50.00</u> per plate

For 45 guests we can make the equation $2750 ÷ 45 = $61.111111111111, it would be a repeating decimal

For 45 guests at the wedding, it would cost <u>$61.111111111111</u>

I hope that this can help you! ^‿^

5 0

2 years ago

Evaluate each finite series for the specified number of terms. 1+2+4+...;n=5

zaharov [31]

Answer:

Step-by-step explanation:

The series are given as geometric series because these terms have common ratio and not common difference.

Our common ratio is 2 because:

1*2 = 2

2*2 = 4

The summation formula for geometric series (r ≠ 1) is:

$\displaystyle \large{S_n=\frac{a_1(r^n-1)}{r-1}}$ or $\displaystyle \large{S_n=\frac{a_1(1-r^n)}{1-r}}$

You may use either one of these formulas but I’ll use the first formula.

We are also given that n = 5, meaning we are adding up 5 terms in the series, substitute n = 5 in along with r = 2 and first term = 1.

$\displaystyle \large{S_5=\frac{1(2^5-1)}{2-1}}\\\displaystyle \large{S_5=\frac{2^5-1}{1}}\\\displaystyle \large{S_5=2^5-1}\\\displaystyle \large{S_5=32-1}\\\displaystyle \large{S_5=31}$

Therefore, the solution is 31.

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Summary

If the sequence has common ratio then the sequence or series is classified as geometric sequence/series.

Common Ratio can be found by either multiplying terms with common ratio to get the exact next sequence which can be expressed as $\displaystyle \large{a_{n-1} \cdot r = a_n}$ meaning “previous term times ratio = next term” or you can also get the next term to divide with previous term which can be expressed as: