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3 years ago

The volume of a cylinder is found by:

Mathematics

1 answer:

densk [106]3 years ago

3 0

Answer:

D. multiplying the area of the base by the height

Calculate the area of the base (which is a circle) by using the equation πr². Then, multiply the area of the base by the height of the cylinder to find the volume.

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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

Brainiest <br><br><br>I Am Struggling With Two Questions :?<br> This is one of the two

Eddi Din [679]

Answer:

Sine of an angle =

opposite / hypotenuse

I this figure

AB is the opposite which is 12

BC is the hypotenuse which is 13

sine ∅ = 12/13

Therefore the sine ratio of the angle is

12/13

Hope this helps

7 0

3 years ago

?! if you make $360 a week what is your yearly wage ?

yKpoI14uk [10]

Answer:

18,720

Step-by-step explanation:

there are approximately 52 weeks in a year

7 0

3 years ago

Read 2 more answers

Noah sold 26 hot dogs during the pregame show at a football game. During the game he sells an average of 31 hot dogs per hour. W

shepuryov [24]

Answer:

26+31=h

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

This si more tiring than actually doing the work

DENIUS [597]

Answer:

D(WZ║XY)

Step-by-step explanation:

The definition of a trapezoid is "a quadrilateral with only one pair of parallel sides". WX and ZY are obviously not parrelel, so you need WZ and XY to be parellel to follow the criteria of a trapezoid.

6 0

3 years ago