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2 years ago

The most accurate estimation of 5+4

Mathematics

2 answers:

NeTakaya2 years ago

8 0

The most accurate estimation is 9.

Levart [38]2 years ago

4 0

The most accurate estimate is 9 .

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Evaluate the Riemann sum for f(x) = 3 - 1/2 times x between 2 and 14 where the endpoints are included with six subintervals taki

Digiron [165]

Answer:

-6

Step-by-step explanation:

Given that :

we are to evaluate the Riemann sum for $f(x) = 3 - \dfrac{1}{2}x$ from 2 ≤ x ≤ 14

where the endpoints are included with six subintervals, taking the sample points to be the left endpoints.

The Riemann sum can be computed as follows:

$L_6 = \int ^{14}_{2}3- \dfrac{1}{2}x \dx = \lim_{n \to \infty} \sum \limits ^6 _{i=1} \ f (x_i -1) \Delta x$

where:

$\Delta x = \dfrac{b-a}{a}$

a = 2

b =14

n = 6

∴

$\Delta x = \dfrac{14-2}{6}$

$\Delta x = \dfrac{12}{6}$

$\Delta x =2$

Hence;

$x_0 = 2 \\ \\ x_1 = 2+2 =4\\ \\ x_2 = 2 + 2(2) \\ \\ x_i = 2 + 2i$

Here, we are using left end-points, then:

$x_i-1 = 2+ 2(i-1)$

Replacing it into Riemann equation;

$L_6 = \lim_{n \to \infty} \sum \imits ^{6}_{i=1} \begin {pmatrix}3 - \dfrac{1}{2} \begin {pmatrix} 2+2 (i-1) \end {pmatrix} \end {pmatrix}2$

$L_6 = \lim_{n \to \infty} \sum \imits ^{6}_{i=1} 6 - (2+2(i-1))$

$L_6 = \lim_{n \to \infty} \sum \imits ^{6}_{i=1} 6 - (2+2i-2)$

$L_6 = \lim_{n \to \infty} \sum \imits ^{6}_{i=1} 6 -2i$

$L_6 = \lim_{n \to \infty} \sum \imits ^{6}_{i=1} 6 - \lim_{n \to \infty} \sum \imits ^{6}_{i=1} 2i$

$L_6 = \lim_{n \to \infty} \sum \imits ^{6}_{i=1} 6 - 2 \lim_{n \to \infty} \sum \imits ^{6}_{i=1} i$

Estimating the integrals, we have :

$= 6n - 2 ( \dfrac{n(n-1)}{2})$

= 6n - n(n+1)

replacing thevalue of n = 6 (i.e the sub interval number), we have:

= 6(6) - 6(6+1)

= 36 - 36 -6

= -6

5 0

2 years ago

A survey of students in a school showed 1/2 of the students exercise regularly, 2/5 of the students exercise occasionally and th

Rashid [163]

Answer:

1/10 do not exercise at all.

Step-by-step explanation:

That would be 1 - 1/2 - 2/5

= 10/10 - 5/10 - 4/10

= 1/10.

5 0

2 years ago

An item cost 50 is marked up 20% off.Sales tax for the item is 8%.What is the final price including tax?

sashaice [31]

$64.80 50+20%+8% tax then you get 64.80

4 0

3 years ago

The yearbook club had a meeting. The meeting had 21 people, which is one-third of the club. How many people are in the club?

VladimirAG [237]

Answer:

63 because if 1/3 of the club is gone then we need to multiply 21 times 21 to find the total. Which is 63.

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3 years ago

What is five billion two hundred fifty four million seventy one thousand nine hundred twenty six written in standard form

lakkis [162]

5,254,071,926

Is the standard form

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2 years ago