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
lyudmila [28]
3 years ago
6

What is the average rate of change of the function fx= 2x2+ 3 over the interval [1,4]?

Mathematics
1 answer:
Molodets [167]3 years ago
6 0

Answer:

  10

Step-by-step explanation:

The average rate of change of f(x) on the interval [a, b] is found by ...

  m = (f(b) -f(a))/(b -a)

For your function, we have [a, b] = [1, 4}, so the rate of change is calculated as ...

  f(1) = 2·1² +3 = 5

  f(4) = 2·4² +3 = 35

  m = (35 -5)/(4 -1) = 30/3 = 10

The average rate of change on the interval is 10.

_____

<em>Comment on quadratic slope</em>

The slope of a quadratic curve changes continuously in linear fashion. The average slope on any interval is the slope at the midpoint of the interval. Using derivatives, we find the slope of the quadratic ax^2+bx+c to be given by 2ax+b. For the function given here, that is 4x. The midpoint of [1, 4] is x=2.5, so the slope at the midpoint is 4(2.5) = 10, as above.

You might be interested in
Given these angles: m∠3 = 82°, m∠4 = 98°.
RSB [31]
These angles are supplementary.
Complementary angles add up to 90 degrees. Supplementary angles add up to 180 degrees. 82 degrees + 98 degrees = 180 degrees.
8 0
2 years ago
Find the value of x in each case. PLEASE SHOW WORK!!!
myrzilka [38]
m\angle BCA=180^o-5x

\angle CAB=\angle ACD\\\\m\angle CAB=33^o

In the triangle ABC:

m\angle ABC+m\angle BCA+m\angle CAB=180^o\\\\2x+180^o-5x+33^o=180^o\\\\-3x+213^o=180^o\ \ \ |-213^o\\\\-3x=-33^o\ \ \ |:(-3)\\\\x=11^o

4 0
3 years ago
This question has four parts. Two football games were played at a stadium on the same day. Part A At the start of the first game
Leviafan [203]

Answer: ok so 66.66% of the seats were filled aka ocupied

Step-by-step explanation:

5 0
3 years ago
Write the first trigonometric expression in terms of the second expression. Cot(x); sin(x)
Alina [70]

The first trigonometric expression cot x and sin x in terms of the second expression is one over tan x and one over cosec x.

<h3>What is trigonometry?</h3>

Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.

Write the first trigonometric expression in terms of the second expression.

The cotangent can be written as

\cot x= \dfrac{1}{\tan x}

And the sine can be written as

\sin x = \dfrac{1}{\csc x}

More about the trigonometry link is given below.

brainly.com/question/22698523

#SPJ4

7 0
2 years ago
Suppose that the functions q and r are defined as follows.
satela [25.4K]

Answer:

(r o g)(2) = 4

(q o r)(2) = 14

Step-by-step explanation:

Given

g(x) = x^2 + 5

r(x) = \sqrt{x + 7}

Solving (a): (r o q)(2)

In function:

(r o g)(x) = r(g(x))

So, first we calculate g(2)

g(x) = x^2 + 5

g(2) = 2^2 + 5

g(2) = 4 + 5

g(2) = 9

Next, we calculate r(g(2))

Substitute 9 for g(2)in r(g(2))

r(q(2)) = r(9)

This gives:

r(x) = \sqrt{x + 7}

r(9) = \sqrt{9 +7{

r(9) = \sqrt{16}{

r(9) = 4

Hence:

(r o g)(2) = 4

Solving (b): (q o r)(2)

So, first we calculate r(2)

r(x) = \sqrt{x + 7}

r(2) = \sqrt{2 + 7}

r(2) = \sqrt{9}

r(2) = 3

Next, we calculate g(r(2))

Substitute 3 for r(2)in g(r(2))

g(r(2)) = g(3)

g(x) = x^2 + 5

g(3) = 3^2 + 5

g(3) = 9 + 5

g(3) = 14

Hence:

(q o r)(2) = 14

8 0
2 years ago
Other questions:
  • Help? (1# only)<br> In really confused :(
    11·1 answer
  • All I need is the answer and if you answer absolutely right you will be marked THE BRAINLIEST
    13·1 answer
  • Tim has 30 jellybeans, with equal numbers of three flavors—raspberry, pineapple, and orange. He likes raspberry the best. So far
    5·2 answers
  • Jimmy spent 55 minutes on solving 11 math questions. If it took him the same amount of time to solve each question how long woul
    9·2 answers
  • Simplify the following
    5·1 answer
  • Last month Alicia’s agency booked $14500 in airline fees on orbit airlines. If orbit pays agencies a commission of 4.1%, how muc
    7·1 answer
  • The figure shows the front side of a purse in the shape of a trapezoid.
    15·1 answer
  • On the grid below, which point is located in the quadrant where the x- and y-coordinates are both negative numbers?
    8·2 answers
  • A 4500.00 g bowling ball rolling at a 4.0m/s I NEED HELPPP ASAPPP
    14·1 answer
  • K= 35.50x + 42<br> k=991x + 27
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!