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
Annette [7]
3 years ago
12

Consider the curve defined by the equation y=6x2+14x. Set up an integral that represents the length of curve from the point (−2,

−4) to the point (1,20).
Mathematics
1 answer:
torisob [31]3 years ago
5 0

Answer:

32.66 units

Step-by-step explanation:

We are given that

y=6x^2+14x

Point A=(-2,-4) and point B=(1,20)

Differentiate w.r. t x

\frac{dy}{dx}=12x+14

We know that length of curve

s=\int_{a}^{b}\sqrt{1+(\frac{dy}{dx})^2}dx

We have a=-2 and b=1

Using the formula

Length of curve=s=\int_{-2}^{1}\sqrt{1+(12x+14)^2}dx

Using substitution method

Substitute t=12x+14

Differentiate w.r t. x

dt=12dx

dx=\frac{1}{12}dt

Length of curve=s=\frac{1}{12}\int_{-2}^{1}\sqrt{1+t^2}dt

We know that

\sqrt{x^2+a^2}dx=\frac{x\sqrt {x^2+a^2}}{2}+\frac{1}{2}\ln(x+\sqrt {x^2+a^2})+C

By using the formula

Length of curve=s=\frac{1}{12}[\frac{t}{2}\sqrt{1+t^2}+\frac{1}{2}ln(t+\sqrt{1+t^2})]^{1}_{-2}

Length of curve=s=\frac{1}{12}[\frac{12x+14}{2}\sqrt{1+(12x+14)^2}+\frac{1}{2}ln(12x+14+\sqrt{1+(12x+14)^2})]^{1}_{-2}

Length of curve=s=\frac{1}{12}(\frac{(12+14)\sqrt{1+(26)^2}}{2}+\frac{1}{2}ln(26+\sqrt{1+(26)^2})-\frac{12(-2)+14}{2}\sqrt{1+(-10)^2}-\frac{1}{2}ln(-10+\sqrt{1+(-10)^2})

Length of curve=s=\frac{1}{12}(13\sqrt{677}+\frac{1}{2}ln(26+\sqrt{677})+5\sqrt{101}-\frac{1}{2}ln(-10+\sqrt{101})

Length of curve=s=32.66

You might be interested in
What is 3x+8 if x=8
Mazyrski [523]

Answer:

y=32

Step-by-step explanation:

y=3(8)+8

y=24+8

24+8=32

y=32

4 0
3 years ago
Read 2 more answers
What series of transformations map triangle △ABC onto △EDF ​ to prove that ABC≅EDF ?
Nonamiya [84]
Hello!

The correct answer is A translation 3 units up then a reflection across the x-axis.

Translation: moving/sliding a figure
Reflection: taking a figure and flipping it over a line.
7 0
3 years ago
Read 2 more answers
A class has 36 students in it and 25% of the students wore hats to school. What fraction of the students wore hats?​
Setler79 [48]

Hi,

25/100 * 36 = 9

So it represents 9/36 = 1/4 of students

8 0
3 years ago
5/6k=-20 what is the correct answer ??
damaskus [11]
<span>5/6k=-20

k=-24

Hope this helps
</span>
4 0
3 years ago
Read 2 more answers
What is the remainder of f(x)=x^4-2x^3-27x^2-9x+18 when divided by binomial x+4
givi [52]

Answer:

The remainder will be 6.

Step-by-step explanation:

We have the function:

f(x)=x^4-2x^3-27x^2-9x+18

And we want to find the remainder after it is divided by the binomial:

x+4

We can use the Polynomial Remainder Theorem. According to the PRT, if we have a polynomial P(x) being divided by a binomial in the form (<em>x</em> - <em>a</em>), then the remainder will be given by P(a).

Here, our divisor is (<em>x</em> + 4). We can rewrite this as (<em>x</em> - (-4)).

Therefore, <em>a</em> = -4.

Then according to the PRT, the remainder will be:

f(-4)=(-4)^4-2(-4)^3-27(-4)^2-9(-4)+18=6

The remainder will be 6.

4 0
3 years ago
Other questions:
  • Derek can type 75 words in 15 minutes. How many words is he able to type in 7 minutes?
    9·1 answer
  • The graph below represents two varying sized triangles plotted in the coordinate plane.
    7·1 answer
  • Angle relationships worksheet #2
    12·1 answer
  • The vertices of a rectangle are R(-5,-5), S(-1,-5), T(-1,1) and U(-5,1). After translation R' is the point (-3,-8). What are the
    8·1 answer
  • Find the sum: <br> -21 + (-13) + (-9). <br> A. -43 <br> B. -25 <br> C. 1 <br> D. 4
    8·2 answers
  • How do i find the area of this regular hexagon? picture is included
    13·1 answer
  • Does the equation y=14x show a proportional relationship between x and​ y? Explain.
    15·1 answer
  • If the sum of the interior angles of a polygon is 1800 how many sides does it have?
    14·2 answers
  • Name the altitudes of right triangle in the Pythagorean triplet (9, 12, 15).
    15·1 answer
  • A farmer rotates wheat, corn, and soybean crops on her farm the farmer produces 293 bushels of produce and sells them for a tota
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!