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2 years ago

Please help me with this :)

Mathematics

1 answer:

Elena L [17]2 years ago

8 0

Answer:

i think :

3 hours and 35 min

2 hours and 45 min

4 hours and 30 min

4 hours and 5 min

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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

2 years ago

Anyone know how to do this

Oxana [17]

Answer:

9 sqrt(2) /2 = PQ

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp/ hypotenuse

sin 45 = PQ = 9

9 sin 45 = PQ

9 sqrt(2) /2 = PQ

4 0

3 years ago

Read 2 more answers

How do you find volume of a circle

Sauron [17]

Answer:

V = 4/3 pi r^3 for a sphere

Step-by-step explanation:

You can't a circle is a two dimensional object.

The volume of a sphere, which is the three dimensional form of a circle is found by

V = 4/3 pi r^3

Where r is the radius

5 0

3 years ago

Two lines are intersecting. What is the value of x? Enter your answer in the box.

Romashka-Z-Leto [24]

Answer:

x = 19

Step-by-step explanation:

To find the value of x, you set the equations as equal to each other:

$x+23 = 2x+4$

Then you simplify:

$23 = 2x + 4 - x\\23 = x + 4\\23-4 = x\\19=x$

4 0

2 years ago

Using sum or difference formulas, find the exact value of sin(165∘)

Nikitich [7]

$\bf \textit{Sum and Difference Identities}
\\ \quad \\
sin({{ \alpha}} + {{ \beta}})=sin({{ \alpha}})cos({{ \beta}}) + cos({{ \alpha}})sin({{ \beta}})
\\ \quad \\
sin({{ \alpha}} - {{ \beta}})=sin({{ \alpha}})cos({{ \beta}})- cos({{ \alpha}})sin({{ \beta}})\\\\
-------------------------------\\\\$

$\bf sin(165^o)\implies sin(120^o+45^o)
\\\\\\
sin(120^o)cos(45^o)~+~cos(120^o)sin(45^o)\implies \cfrac{\sqrt{3}}{2}\cdot \cfrac{\sqrt{2}}{2}~+~\cfrac{-1}{2}\cdot \cfrac{\sqrt{2}}{2}
\\\\\\
\cfrac{\sqrt{6}}{4}~-~\cfrac{\sqrt{2}}{4}\implies \cfrac{\sqrt{6}-\sqrt{2}}{4}$

6 0

2 years ago