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
Vladimir [108]
3 years ago
12

Find the area of the region under the graph of f on [a, b]. f(x) = x2 − 8x + 17; [−1, 2]

Mathematics
1 answer:
Harman [31]3 years ago
5 0

Answer:

The area is 42 area units.

Step-by-step explanation:

The area of a function f(x) on an interval [a,b] is given by:

A = \int\limits^a_b {f(x)} \, dx

Applying to this question:

A = \int\limits^-1_2 {x^2 - 8x + 17} \, dx

Then

F(x) = \frac{x^{3}}{3} - 4x^{2} + 17x

A = F(2) - F(-1)

F(2) = frac{2^{3}}{3} - 4*2^{2} + 17*2 = \frac{8}{3} + 18 = \frac{8 + 3*18}{3} = \frac{62}[3}

F(-1) = frac{(-1)^{3}}{3} - 4*(-1)^{2} + 17*(-1) = -\frac{1}{3} - 21 = \frac{-1 - 21*3}{3} = -\frac{64}[3}

A = F(2) - F(-1) = \frac{62}[3} - (-\frac{64}[3}) = \frac{62+64}{3} = 42

The area is 42 area units.

You might be interested in
Please helppppp!!!!!!!!
Drupady [299]

Answer:

128 cm^2

Step-by-step explanation:

The area of a trapezoid is given by

A = 1/2 (b1+b2) h

where b1 and b2 are the lengths of the bases and h is the height

A =1/2( 10+22) * 8

A = 1/2 (32)8

  = 128

7 0
2 years ago
Read 2 more answers
Help needed pleaseee
ohaa [14]

Answer:

A

Step-by-step explanation:

Since we're dealing with perpendicular lines, we take the recipricol of the m value of the original equation.

So the slope we're dealing with is 1/2.

And the equation we have so far is

y = 1/2x + b

Now we solve for b by plugging in the point (4,2).

2 = 1/2(4) + b

2 = 2 + b

b = 0

So the final equation is

y = 1/2x

8 0
2 years ago
In a family there was give sons. The oldest son is 11 3/4 years old, and every next younger brother is younger than the next by
aleksklad [387]

Answer:

5.5

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
En Colima se lleva acabo la conferencia sobre la energética eólica a la cual asistieron 120 representantes de Latinoamérica y Su
andriy [413]
The first thing we must do for this case is to see how many representatives from each country attended.
 We have then:
 Argentines = (1/6) * (120) = 20
 Chileans = (1/5) * (120) = 24
 Bolivians = (1/4) * (120) = 30
 Venezuelans = (1/4) * (120) = 30
 Adding we have:
 20 + 24 + 30 + 30 = 104
 Therefore the number of Americans is:
 120-104 = 16
 Answer:
 16 Americans attended the wind energy conference
4 0
3 years ago
Can some show the steps and the answer please I really need help tell me how you get it and the answer
Lana71 [14]

Answer:

Step-by-step explanation:

so this is about triangles..  sooo the following is a bit of helpful reminders that I keep on my computer to help me remember how to fit the trig functions to triangles..  I strongly suggest you copy it and keep it where you can look at it often.

Use SOH CAH TOA to recall how the trig functions fit on a triangle

SOH: Sin(Ф)= Opp / Hyp

CAH: Cos(Ф)= Adj / Hyp

TOA: Tan(Ф) = Opp / Adj

I use this anytime I run into triangles or need some help with sin or cos

now the problem , 3 ladder  10, 12, & 15 feet.   Alex wants to get to 8 feet.

the problems is also telling you that   you can use   t.....   and then , the words are cut off.. but I know they were going to say   Tan ... next.. :P

b/c Tan is how you figure out problems with the adjacent side and the opposite side.  like this problem.    Look at  TOA  above.  use that to recall how the parts fit in the formula

Tan(∅) = Opp / Adj

they give us the Opp side of 8 feet in the problem

then they also tell us the Hyp of the triangle which is each of the ladders length.  Then they ask us what is the Adj sides length?

So we also need to solve the triangle with the know hyp  (ladder length).. uggg, this problem is long. Then we can solve the dist. from the wall or Adj side length.

it's two steps, if you want to think of it that way.   You're supposed to be pretty confident with trig functions.   I'm guessing this is a trig class.. right?

let's solve for the 3 different angles that the ladders make , each going to 8 feel.  Obviously, nobody would really do this with a ladder they would just lean it against the wall . and if it's taller than where they want to climb, they would just go up part way.   so anyway,     find the 3 different angles.  

look above to see which formula to use.

I like SOH b/c it seems to have all the pieces of the triangle we want to work with.

ladder 1  ( 10')

Sin(∅) = Opp / Hyp

Sin(∅) = 8 / 10

∅ = arcSin (4/5)

[ first, yes, I just reduced the fraction, then I did the arcSin on both sides, I think you might know how to do that already ? ]

∅ = 53.13010 °

( yes, I used my calculator to find that,  calculators are okay to use when figuring out non standard angles )

ladder 2 (12')

Sin(∅) = 8/12

∅ = arcSin (2/3)

∅ = 41.81031°

ladder 3 (15')

Sin(∅) = 8/15

∅ = arcSin (8/15)

∅ = 32.230952°

now use our Tan function to find the Adjacent side which is the distance from the wall

Tan(∅)= Opp / Adj

Adj = Opp / Tan(∅)

( I did some quick algebra to move the side we want to solve for, now plug and chug all 3 angles  )

ladder 1

Adj = 8 / Tan(53.13010)

Adj = 6.0000005    

ladder 2

Adj = 8 / Tan(41.81031)

Adj = 8.94427

ladder 3

Adj = 8 / Tan(32.230952)

Adj = 12.688577

so the 10' ladder is 6 feet from the wall

the 12' ladder is 8.9 feet from the wall

the 15 foot ladder is 12.7 feet from the wall.

I really don't think that 15' ladder is going to stay on the wall.. if Alex climbs it... it's way way too far out... it will just fall straight down the wall  :/   Maybe another math problem for the forces involved  :P

5 0
2 years ago
Other questions:
  • What is the equation of the line that goes through the point (-1,6) and (5,-4)
    11·1 answer
  • At the track meet, Justin won the 100 meter race in 12.61 seconds. Shawn won the 200-meter race in 26.38 seconds. Which runner r
    8·1 answer
  • Choose the answer.
    14·2 answers
  • Which relation graphed below is also a function?
    9·1 answer
  • O(●︿●)o ! <br> -1/3 x (-3/7)
    9·2 answers
  • Dr. Cyril conducts a simple random sample of 500 men who became fathers for the first time in the past year. He finds that 23% o
    9·1 answer
  • Has a slope of -2 and has a y-intercept of (0, -3)
    10·1 answer
  • What is the solution for -3x ≥ 36?
    13·2 answers
  • In the general population, the mean IQ is 100 with a standard deviation of 15. Dr. Robbins wants to see if a class of statistics
    6·1 answer
  • A sample of 50 11th graders were asked to select a favorite pattern out of 6 choices. The data list below shows what their favor
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!