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2 years ago

9. Which of the following relations is a function?

Mathematics

1 answer:

elena-14-01-66 [18.8K]2 years ago

5 0

The answer is D because the first number doesn’t reapeat

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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

3 years ago

Which of the following is a fifth degree binomial?

Anna11 [10]

Answer:

Step-by-step explanation:

$2xy^{2}-5y^{5}$

Binomial should have two terms. Five degree binomial means highest degree of the binomial should be 5

5 0

3 years ago

Which is the graph of g(x) = [X +3]?

Daniel [21]

Answer:

Step-by-step explanation:

just took it i got 100%

4 0

3 years ago

Plz help ive been stuck on this question for so long

luda_lava [24]

Multiply each exponent inside the parentheses by the exponent on the outside:

8^(-5 x -4) / 2^(-2 x -4)

8^20 / 2^8

The answer is C

4 0

3 years ago

A snail climbs to the top of a coconut tree 18 meters high. In an hour it will climb 2 meters. But if it go 2 meters, it will sl

kumpel [21]

Answer:

The snail will reach the top of the coconut in 18 hours.

Step-by-step explanation:

If the snail will climb 2 meters in 1 hour but it will slip down one meter for every 2 meters climbed, then the distance traveled will be:

$d = 2 m - 1 m = 1 m$

Since in 1 hour, it climbs 2 meters minus 1 meter, the time in which the snail will reach the top is:

$t = \frac{1 h}{1 m}*18 m = 18 h$

Therefore, the snail will reach the top of the coconut in 18 hours.

I hope it helps you!

5 0

2 years ago