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3 years ago

7

the height of a cylinder is 5 units less than 3 times it’s radius, which expression represents the height of the cylinder in ter

ms of its radius

1 answer:

Nezavi [6.7K]3 years ago

8 0

Answer:

3r - 5 = h

Step-by-step explanation:

The statement basically says the equation, so all that is needed is interpretation. First, look at the "three times". If the height is just three times the radius, it will look like 3r = h, because if any number is put into r, then h will be three times larger. Then it says "5 units less", which can be put as r - 5 = h with the same logic as the previous explanation. Combining those two gives us, lo and behold, 3r - 5 = h.

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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.

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2 years ago

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Andru [333]

Answer:

(d) The functions are not inverses because for each ordered pair (x, y) for one function, there is no corresponding ordered pair (y, x) for the other function.

Step-by-step explanation:

If functions are represented by a table of ordered pairs, their inverse function is the set of ordered pairs with the x- and y-values swapped.

Here, for (x, y) = (0.75, 1038.18), the pair from the other table that begins to correspond is (y, x) = (0.75, 1057.81). These reversed pairs are not the same, so the functions are not inverses of each other.

_____

<em>Comment on the tables</em>

Table A is for a 5-year investment; table B is for a 7.5 year investment. They cannot be inverses of each other.

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