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
PLEASEEEEE HELPPPPPP ASAPPPPPPPP
natta225 [31]

9514 1404 393

Answer:

  64r -48r -144

Step-by-step explanation:

The January cost expression is ...

  62p -48p -144 -432 = profit

The cost is identified as having 3 components, so the profit will have 4 components:

  (selling price)×p - ((cost per unit)×p +(fixed monthly cost)) -(first month startup cost) = profit

Comparing this to the given equation, we identify the components as ...

  selling price = 62

  cost per unit = 48

  fixed monthly cost = 144

  first month startup cost = 432

We note that 432 = 3×144, so is consistent with the description of startup costs.

Increasing the selling price by $2 will raise it from 62 to 64. In February, the initial month startup cost disappears, so the profit equation becomes ...

  (selling price)×r - ((cost per unit)×r +(fixed monthly cost)) = profit

  64r -48r -144 = profit

5 0
3 years ago
I need help please slope
loris [4]

Answer:

Step-by-step explanation:

The formula for slope is y2-y1/x2-x1 where y2 and x2 are the x and y coordinates from a coordinate pair and y1 and x1 are the coordinates from another coordinate pair. In this case, 2 coordinate pairs are given: (30,75) and (10, 35)  75-35/30-10 would be your slope, or, 40/20, or simplified, 2.

Your slope is 2

3 0
3 years ago
Kandace drives 48 miles each way to work.She works 5 days a week.Her car gets 32 miles per gallon of gas.If gas costs $3.79 per
Lorico [155]
48 * 5 = 240
240 / 32 = 7.5 gallons a week ( $28.42)
6 0
3 years ago
Find the exact value of cos(arcsin(1/4)). For full credit, explain your reasoning.
Westkost [7]
First way
arcsin(1/4) means that 1/4 sin of the angle.

sin(α)=1/4
sin²α+cos²α=1
(1/4)²+cos²α=1
cos²α=1-1/16 =15/16
cosα=+/-(√15)/4

<span>Second way
</span>
sin(α)=1/4 =opposite leg/hipotenuse
cos(α)=adjacent leg/hypothenuse
adjacent leg =√(hypotenuse²- Opposite²)=√(16-1)=√15
cosα=+/-√15/4

For one value of sinα, possible 2 values of cosα.

5 0
2 years ago
Evaluate V= bh divided by 3 for B= 9 in 2 and h=32 in
Luba_88 [7]
It would be 96 because V=(9)(32)= 288/3=96
8 0
3 years ago
Other questions:
  • 36.00 with a 7% sales tax
    11·1 answer
  • Acelynn borrows $1337 to buy a four wheeler. The interest rate is 4% for the 14 year loan. Q: A: How much interest will she pay
    11·1 answer
  • Check out this rectangular prism. Find the surface area of the rectangle prism (above)) using its net (below)
    10·1 answer
  • What is the length of the legs of a hypotenuse of a right triangle whose legs measure 30in and 72in
    15·1 answer
  • 11a-8b-9a-3b=
    13·1 answer
  • The picture below shows a pole and its shadow: A pole is shown with a right triangle side. The right triangle has hypotenuse 221
    10·1 answer
  • Sheila is climbin on a latter that is attached against the side of a jungle gym.she is 5 feet off the ground and 3 feet horizont
    14·1 answer
  • In math class help!!!!!
    13·1 answer
  • (2x−6)+4(x−3) =<br><br> Answer now or I eat ur cookies
    5·1 answer
  • - The Fun Guys game rental store charges an annual fee of $5 plus $5.50 per game rented. The Game Bank charges an annual fee of
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!