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
Whitepunk [10]
3 years ago
5

Calculus help! Using the mean value theorem!

Mathematics
1 answer:
marta [7]3 years ago
8 0
f is differentiable across its domain, so the MVT says there is some value of c in the open interval (a,b) such that

f'(c)=\dfrac{f(b)-f(a)}{b-a}

You have

f(x)=Ax^2+Bx+C\implies f'(x)=2Ax+B

so the equation above becomes

2Ac+B=\dfrac{(Ab^2+Bb+C)-(Aa^2+Ba+C)}{b-a}

Solve for c.

2Ac+B=\dfrac{A(b^2-a^2)+B(b-a)}{b-a}
2Ac+B=A(b+a)+B
2Ac=A(b+a)
c=\dfrac{b+a}2

so c is indeed the average of the endpoints, i.e. the midpoint.
You might be interested in
Which fraction is the simplest form of 16/34
Alex_Xolod [135]

Answer:

Good Morning you answer is 8/17

Step-by-step explanation:

you halve 16 and 34 getting 8 and 17

17 is a prime number so you can not divide any more

6 0
3 years ago
Read 2 more answers
a random sample of 4 claims are selected from a lot of 12 that has 3 nonconforming units. using the hypergeometric distribution
Sloan [31]

Answer:

The probability that the sample will contain exactly 0 nonconforming units is P=0.25.

The probability that the sample will contain exactly 1 nonconforming units is P=0.51.

.

Step-by-step explanation:

We have a sample of size n=4, taken out of a lot of N=12 units, where K=3 are non-conforming units.

We can write the probability mass function as:

P(x=k)=\frac{\binom{K}{k}\binom{N-K}{n-k}}{\binom{N}{n}}

where k is the number of non-conforming units on the sample of n=4.

We can calculate the probability of getting no non-conforming units (k=0) as:

P(x=0)=\frac{\binom{3}{0}\binom{9}{4}}{\binom{12}{4}}=\frac{1*126}{495}=\frac{126}{495} = 0.25

We can calculate the probability of getting one non-conforming units (k=1) as:

P(x=1)=\frac{\binom{3}{1}\binom{9}{3}}{\binom{12}{4}}=\frac{3*84}{495}=\frac{252}{495} = 0.51

5 0
3 years ago
Water comes out of a pipe at a rate of 30 gallons per minute.
Lyrx [107]

Answer:

90

Step-by-step explanation:

30x3=90

3 0
3 years ago
Read 2 more answers
Lines a and b are parallel.
VashaNatasha [74]
I have added a screenshot with the complete question along with a diagram representing the scenario.

<u><em>Answer:</em></u>
s = 22°

<u><em>Explanation:</em></u>
<u>1- getting the top right angle of line B:</u>
We are given that:
the top right angle of line A = 158°
Since lines A and B are parallel, therefore, the top right angle of line A and the top right angle of line B are corresponding angles which means that they are equal
This means that:
<u>Top right angle of line B = 158°</u>

<u>2- getting the value of s:</u>
Now, taking a look at line B, we can note that:
angle s and the top right angle form a straight angle. This means that the sum of these two angles is 180°
Therefore:
180 = s + 158
s = 180 - 158
<u>s = 22°</u>

Hope this helps :)

8 0
3 years ago
Which graph is generated by this table of values?<br> PLS HURRY
viva [34]
Use two points to find the slope
8 0
2 years ago
Read 2 more answers
Other questions:
  • What is the derivative of Sec^2(3x)
    6·1 answer
  • How would I work This Problem out and solve it thank you!
    13·1 answer
  • A blue die and a green die are rolled what is the probobility of rolling a number less than 7 and 4
    8·1 answer
  • Christian has a collection of 18 shark teeth. He identified them as 6 tiger shark teeth, 8 sand shark teeth, and the rest as bul
    9·2 answers
  • The automatic opening device of a military cargo parachute has been designed to open when the parachute is 200 m above the groun
    10·1 answer
  • (5y+5)+(7y-9)=(6x+50)+2(5x-5)
    14·2 answers
  • Please help me with this thankyou​
    12·1 answer
  • Write a conjecture using the information provided.
    6·1 answer
  • Hhhhhhhhhhheeeeeeelp
    11·1 answer
  • Jessica borrows $1500 at 7% simple interest per week. If she ends up owing $2235, how may weeks did it take her to pay back the
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!