1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kozerog [31]
3 years ago
12

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

aneous rate of change of y with respect to x at the value x=3. Average Rate of Change : Instantaneous Rate of Change at x=3:
Mathematics
1 answer:
nirvana33 [79]3 years ago
5 0

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.

You might be interested in
Mrs cousins works in a pool store and earns a 9.5% commission on every swimming pool she sells. how much commission did she earn
Dennis_Churaev [7]
She earned $532 for selling the pool
7 0
3 years ago
A rectangular prism has a length of 20 in a width of 2 in and a height of 3 1/4 in the prism is filled with cubes that have edge
Zinaida [17]
You can express the edge lengths in terms of "cubes" or you divide the total volume by the volume of a cube. It works either way.

Edge lengths are
.. 80 cubes by 8 cutes by 13 cubes
so total volume is
.. (80 * 8 * 13) = 8320 cubes


In cubic inches, the volume is
.. (20 in)*(2 in)*(3 1/4 in) = 130 in^3.
The volume of a 1/4-in cube is (1/4 in)^3 = 1/64 in^3.
Then the number of cubes that will fit in the prism is
.. (130 in^3)/(1/64 in^3) = 8320 . . . . cubes

8320 cubes are needed to fill the rectangular prism.
7 0
3 years ago
Quadratic Equations<br> How do I solve a quadratic equation?
malfutka [58]
There are different ways to solve a quadratic equation, the main ones that i'm thinking about right now are:
1) factor the equation as a product:
 ex:        x^2+ 4x + 3 =0
             (x+3) (x+1) = 0
              x=-3 and x=-1 are the solutions.
To find (x+p) and (x+q) you have to think that (p+q )have to be equal to the number that is multiplied by x, in my example it was 4 (3+1=4), (p times q) have to be equal to the last number of the quadratic equation, the one that is not multiplied by any x, that in my example is 3 (3 x 1= 3)

2) The other way to solve a quadratic function is by using a formula:
    given: ax^2 +bx +c=0
    x= (-b +/- <span>√(b^2 -</span> 4ac)) / 2a
    
 ex: 3x^2 + 4x -2=0
    x= (-4 +/- √16-4(3)(-2)) / 6= (-4 +/- √16+24)/6= (-4 +/- <span>√40) / 6
now there are 2 possibilities: x= (-4+</span><span>√40) /6
                                                        and
                                              x= (-4 - </span><span>√40) / 6
I hope the examples were clear enough also if i did't get very nice numbers. Look closely to the sings + and -, they are very important</span>
5 0
3 years ago
Please help me on these questions and explain it thanks
BlackZzzverrR [31]
For problem 2:

The answer would be B) Car A travels more miles per gallon of fuel than Car B.

This is because Car B is shown on the graph to travel the same number of miles as Car A using 16 gallons of fuel, while Car A uses only 4 gallons. Thus, Car A travels further with less fuel.

For problem 3:

Let's write out the equation and try to solve.
5x + 1 = 3x + 7

First, subtract 3x from both sides.
5x - 3x + 1 = 3x - 3x + 7
2x + 1 = 7
Now, subtract one from both sides.

2x + 1 - 1 = 7 - 1
2x = 6

Finally, divide both sides by 2.
2x/2 = 6/2

x = 3

You should only get B) One solution

Hope that helped!
8 0
3 years ago
Isla was researching kiwi birds. She categorized each bird she observed by species and gender. The two-way frequency table below
Ludmilka [50]

Answer:

A.

I hope it helps

8 0
3 years ago
Read 2 more answers
Other questions:
  • The temperature dropped from 38°F to 12°F in 13 hours. Find the average rate of change per hour.
    14·1 answer
  • Compare |−49| and |−52|. 50 POINTS HELP ASAP PLEASE ANYONE PLEASE A) |−49| |−52| D) |−49| ≥ |−52|
    10·2 answers
  • A wire is first bent into the shape of a triangle. Each side of the triangle is 24 inches long. Then the wire is unbent and resh
    10·2 answers
  • The two histograms below show the weights of dogs at two different veterinarian offices.
    13·1 answer
  • Bailey company purchased a new delivery truck for $35,000. the sales tax was $2,000. the logo of the company was painted on the
    6·1 answer
  • Enjoli is making cupcakes for a party. She needs 45 cupcakes but the recipe makes 15.
    15·2 answers
  • "Which shapes are topologically equivalent to Choice 2?
    14·1 answer
  • I need to know what to do
    9·1 answer
  • Can you guys help me find the mistake??
    8·2 answers
  • 2.5. For his homework Thulani defined a factor as: "Factors of a number are formed when the number is multiplied by 1; 2; 3; 4".
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!