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3 years ago

9

Mandis planned to spend RI 000 for shoes this week.

1 answer:

Alja [10]3 years ago

7 0

Answer:

733.05

Step-by-step explanation:

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For the function y=3x2: (a) Find the average rate of change of y with respect to x over the interval [3,6]. (b) Find the instant

nirvana33 [79]

Answer:

The instantaneous rate of change of $y$ with respect to $x$ at the value $x = 3$ is 18.

Step-by-step explanation:

a) Geometrically speaking, the average rate of change of $y$ with respect to $x$ over the interval by definition of secant line:

$r = \frac{y(b) -y(a)}{b-a}$ (1)

Where:

$a$ , $b$ - Lower and upper bounds of the interval.

$y(a)$ , $y(b)$ - Function exaluated at lower and upper bounds of the interval.

If we know that $y = 3\cdot x^{2}$ , $a = 3$ and $b = 6$ , then the average rate of change of $y$ with respect to $x$ over the interval is:

$r = \frac{3\cdot (6)^{2}-3\cdot (3)^{2}}{6-3}$

$r = 27$

The average rate of change of $y$ with respect to $x$ over the interval $[3,6]$ is 27.

b) The instantaneous rate of change can be determined by the following definition:

$y' = \lim_{h \to 0}\frac{y(x+h)-y(x)}{h}$ (2)

Where:

$h$ - Change rate.

$y(x)$ , $y(x+h)$ - Function evaluated at $x$ and $x+h$ .

If we know that $x = 3$ and $y = 3\cdot x^{2}$ , then the instantaneous rate of change of $y$ with respect to $x$ is:

$y' = \lim_{h \to 0} \frac{3\cdot (x+h)^{2}-3\cdot x^{2}}{h}$

$y' = 3\cdot \lim_{h \to 0} \frac{(x+h)^{2}-x^{2}}{h}$

$y' = 3\cdot \lim_{h \to 0} \frac{2\cdot h\cdot x +h^{2}}{h}$

$y' = 6\cdot \lim_{h \to 0} x +3\cdot \lim_{h \to 0} h$

$y' = 6\cdot x$

$y' = 6\cdot (3)$

$y' = 18$

The instantaneous rate of change of $y$ with respect to $x$ at the value $x = 3$ is 18.

5 0

3 years ago

Please help! Question below

Marysya12 [62]

152... cuz 28 is perpendicular so... 180-28

5 0

4 years ago

Jonathan and 5 of his friends are going to the park. they each bought a snack the cost the same, the total was 54.00 dollars. ho

egoroff_w [7]

Answer:

$9

Step-by-step explanation:

'Jonathan and 5 friends' would equal <u>6 people paying</u>

Since the total amount was 54 dollars, the equation will be:

$54 ÷ 6 friends

54 divided by 6 is $9

Check:

6 x 9 = 54

3 0

3 years ago

URGENT HELP (picture says everything you need to know)

seropon [69]

Answer:

I believe the quiz had 18 questions, with a 14:4 ratio

8 0

3 years ago

The general equation for an ellipse?

allochka39001 [22]

Answer:

The standard equation for an ellipse, x 2 / a 2 + y2 / b 2 = 1

Step-by-step explanation:

it represents an ellipse centered at the origin and with axes lying along the coordinate axes.

6 0

3 years ago