If 2/5n+4=20, what is the value of n?

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

2 years ago

6.8 (-0.5) - 2 (5.8)

Zina [86]

Answer:

- 15

Step-by-step explanation:

6 0

3 years ago

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What is the volume of the sphere that has a diameter of 3? use 3.14 for pie

aev [14]

Hey ! there

Answer:

113.04 unit cube

Step-by-step explanation:

In this question we are provided with a sphere having radius 3 units and value of π is 3.14 . And we're asked to find the volume of sphere .

For finding volume of sphere , we need to know its formula . So ,

$\qquad \qquad \: \underline{\boxed{ \frak{Volume_{(Sphere)} = \dfrac{4}{3} \pi r {}^{3} }}}$

Where ,

π refers to 3.14

r refers to radius of sphere

Solution : -

Now , we are substituting value of π and radius in the formula ,

$\quad \longrightarrow \qquad \: \dfrac{4}{3} \times 3.14 \times (3) {}^{3}$

Simplifying it ,

$\quad \longrightarrow \qquad \: \dfrac{4}{3} \times 3.14 \times 3 \times 3 \times 3$

Cancelling 3 with 3 :

$\quad \longrightarrow \qquad \: \dfrac{4}{ \cancel{3}} \times 3.14 \times 3 \times 3 \times \cancel{3}$

We get ,

$\quad \longrightarrow \qquad \:4 \times 3.14 \times 9$

Multiplying 4 and 3.14 :

$\quad \longrightarrow \qquad \:12.56 \times 9$

Multiplying 12.56 and 9 :

$\quad \longrightarrow \qquad \: \pink{\underline{\boxed{\frak{113.04 \: unit \: cube}}}} \quad \bigstar$

Henceforth , volume of sphere having radius 3 units is 113 .04 units cube .

<h2>#Keep Learning</h2>

5 0

1 year ago

Write an expression for the calculation 4 added to 12 times 19 plus 24

harina [27]

Answer:

4 + 12 × 19 + 24

Step-by-step explanation:

Hullo!

Words like "added or sum", represent addition.

Words like "times", represent multiplication.

Words like "subtracted or took away", represent subtraction.

Words like "divided or split up", represent division.

Therefore, we can express the equation 4 added to 12 times 19 plus 24 can be rewritten as $\boxed{4 + 12 \cdot 19 + 24}$ in expression format.

Hope this helps!

8 0

3 years ago

Brianna needs to contact members of the softball league. She calls 4 members in the morning. Those 4 people each call 4 more peo

charle [14.2K]

Answer:

...

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers