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
SOVA2 [1]
2 years ago
14

Find the numbers b such that the average value of f(x) = 4 + 10x − 6x2 on the interval [0, b] is equal to 5.

Mathematics
1 answer:
Tju [1.3M]2 years ago
6 0

Answer:

  b = (5±√17)/4 ≈ {0.2192, 2.2808}

Step-by-step explanation:

The average on the interval is found from the integral ...

  \frac{1}{b}\int\limits^b_0 {(4+10x-6x^2)} \, dx =\frac{1}{b}(4b+5b^2-2b^3)\\\\=-2b^2+5b+4

We want the value of this integral to be 5, so we want to find b such that ...

  5 = -2b^2 +5b +4

  2b^2 -5b +1 = 0

  b^2 -5/2b = -1/2

  b^2 -5/2b +25/16 = -1/2 +25/16

  (b -5/4)^2 = 17/16

  b = (5±√17)/4

The average value of f(x) is 5 on the intervals ...

  [0, (5-√17)/4] and [0, (5+√17)/4]

You might be interested in
kai owns a bakery and uses 25 grams of sugar for every 75 grams of butter in a pastry recipe. Using this information, complete t
eduard
50/150, 75/225, 100/300, 125/375.
8 0
3 years ago
Read 2 more answers
My Christmas present to you​
oksano4ka [1.4K]

Answer:

Step-by-step explanation:

if you need help let me know

8 0
2 years ago
Read 2 more answers
For integers a, b, and c, consider the linear Diophantine equation ax C by D c: Suppose integers x0 and y0 satisfy the equation;
Dmitrij [34]

Answer:

a.

x = x_1+r(\frac{b}{gcd(a, b)} )\\y=y_1-r(\frac{a}{gcd(a, b)} )

b. x = -8 and y = 4

Step-by-step explanation:

This question is incomplete. I will type the complete question below before giving my solution.

For integers a, b, c, consider the linear Diophantine equation

ax+by=c

Suppose integers x0 and yo satisfy the equation; that is,

ax_0+by_0 = c

what other values

x = x_0+h and y=y_0+k

also satisfy ax + by = c? Formulate a conjecture that answers this question.

Devise some numerical examples to ground your exploration. For example, 6(-3) + 15*2 = 12.

Can you find other integers x and y such that 6x + 15y = 12?

How many other pairs of integers x and y can you find ?

Can you find infinitely many other solutions?

From the Extended Euclidean Algorithm, given any integers a and b, integers s and t can be found such that

as+bt=gcd(a,b)

the numbers s and t are not unique, but you only need one pair. Once s and t are found, since we are assuming that gcd(a,b) divides c, there exists an integer k such that gcd(a,b)k = c.

Multiplying as + bt = gcd(a,b) through by k you get

a(sk) + b(tk) = gcd(a,b)k = c

So this gives one solution, with x = sk and y = tk.

Now assuming that ax1 + by1 = c is a solution, and ax + by = c is some other solution. Taking the difference between the two, we get

a(x_1-x) + b(y_1-y)=0

Therefore,

a(x_1-x) = b(y-y_1)

This means that a divides b(y−y1), and therefore a/gcd(a,b) divides y−y1. Hence,

y = y_1+r(\frac{a}{gcd(a, b)})  for some integer r. Substituting into the equation

a(x_1-x)=rb(\frac{a}{gcd(a, b)} )\\gcd(a, b)*a(x_1-x)=rba

or

x = x_1-r(\frac{b}{gcd(a, b)} )

Thus if ax1 + by1 = c is any solution, then all solutions are of the form

x = x_1+r(\frac{b}{gcd(a, b)} )\\y=y_1-r(\frac{a}{gcd(a, b)} )

In order to find all integer solutions to 6x + 15y = 12

we first use the Euclidean algorithm to find gcd(15,6); the parenthetical equation is how we will use this equality after we complete the computation.

15 = 6*2+3\\6=3*2+0

Therefore gcd(6,15) = 3. Since 3|12, the equation has integral solutions.

We then find a way of representing 3 as a linear combination of 6 and 15, using the Euclidean algorithm computation and the equalities, we have,

3 = 15-6*2

Because 4 multiplies 3 to give 12, we multiply by 4

12 = 15*4-6*8

So one solution is

x=-8 & y = 4

All other solutions will have the form

x=-8+\frac{15r}{3} = -8+5r\\y=4-\frac{6r}{3} =4-2r

where r ∈ Ζ

Hence by putting r values, we get many (x, y)

3 0
3 years ago
What’s 4%x56? 2 A.2.24 B.1.12 or C.0.448
MissTica

Answer:

A. 2.24

Step-by-step explanation:

Multiply 56 by 0.04

56(0.04)

= 2.24

6 0
3 years ago
Read 2 more answers
Sove for the Indicated varlable. Include all of your work in your answer. Submit your solution.
nika2105 [10]

Answer:

c=2r

divide both sides by 2

c/2=r

if you forgot the pi

c=2pir

divide by 2pi

c/(2pi)=r

Step-by-step explanation:

4 0
2 years ago
Other questions:
  • What are adjacent angles?
    8·1 answer
  • Which of the following groups of numbers are all prime numbers? 
    13·1 answer
  • Which model shows the correct factorization of x2 – x – 2? Image for option 1 Image for option 2 Image for option 3 Image for op
    13·2 answers
  • What is the sum of the exterior angle measures for an irregular convex hexagonal?
    10·1 answer
  • Find the length of the third side. If necessary, round to the nearest tenth.<br> 2<br> 3
    14·1 answer
  • PLEasE HELPPP WITH THISSSSS IF U KNOW THE ANSWER PLS TELL ME LIKE THIS :
    8·1 answer
  • 8 3/5 = -4x + 5 3/5 ??<br> Solution??
    5·2 answers
  • PLZZZ HURRY TIMED TEST NO LINKS!!!!
    8·1 answer
  • (PLEASE HELP FAST) What does the y-intercept of this relationship represent?
    12·2 answers
  • How to evaluate this question
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!