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Is $(2,\,9)$ a solution to this system of inequalities? $\newline$ y > x + 7 $\newline$ y > 3x + 3 $\newline$ Choices: $\newline$ (A)yes $\newline$ (B)no

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Is (x, y) a solution to the system of inequalities?

Full solution

Q. Is

(2,\,9)

a solution to this system of inequalities?

\newline

y > x + 7

\newline

y > 3x + 3

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Check Point Coordinates: Does the point $(2, 9)$ satisfy the inequality y > x + 7? $\newline$ Substitute $x = 2$ and $y = 9$ into the inequality y > x + 7. $\newline$ 9 > 2 + 7 $\newline$ 9 > 9 $\newline$ This is not true because $9$ is not greater than $9$ , it is equal to $9$ .

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Question

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Question

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Question

10\text{-kg}

bucket is lifted from the ground to a height of

14\, \text{m}

at a constant speed with a rope that weighs

0.6\, \text{kg/m}

. Initially the bucket contains

42\, \text{kg}

of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the

14\, \text{m}

level. How much work is done? (Use

9.8\, \text{m/s}^2

g

.) Show how to approximate the required work (in

\text{J}

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x

be the height in meters above the ground. Enter

x_i^*

x_i

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Question

10-\mathrm{kg}

bucket is lifted from the ground to a height of

14

m at a constant speed with a rope that weighs

0.6 \mathrm{~kg} / \mathrm{m}

. Initially the bucket contains

42

kg of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the

14-\mathrm{m}

level. How much work is done? (Use

9.8 \mathrm{~m} / \mathrm{s}^{2}

\newline

Show how to approximate the required work (in J) by a Riemann sum. (Let

x

be the height in meters above the ground. Enter

x_{i}^{* *}

x_{i}

\newline

\lim _{n \rightarrow \infty} \sum_{i=1}^{n}\left(\boxed{98+35.28 x_{i}}\right) \Delta x

\newline

Express the work (in J) as an integral in terms of

x

\newline

\int_{0}^{14}(98+35.28 x

\newline

Evaluate the integral (in J). (Round your answer to the nearest integer.)

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