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
garri49 [273]
3 years ago
11

                                             .....................................

Mathematics
1 answer:
Hatshy [7]3 years ago
4 0
... .. ... .... ... ... ..... .
You might be interested in
The following integral requires a preliminary step such as long division or a change of variables before using the method of par
shtirl [24]

Division yields

\dfrac{x^4+7}{x^3+2x} = x-\dfrac{2x^2-7}{x^3+2x}

Now for partial fractions: you're looking for constants <em>a</em>, <em>b</em>, and <em>c</em> such that

\dfrac{2x^2-7}{x(x^2+2)} = \dfrac ax + \dfrac{bx+c}{x^2+2}

\implies 2x^2 - 7 = a(x^2+2) + (bx+c)x = (a+b)x^2+cx + 2a

which gives <em>a</em> + <em>b</em> = 2, <em>c</em> = 0, and 2<em>a</em> = -7, so that <em>a</em> = -7/2 and <em>b</em> = 11/2. Then

\dfrac{2x^2-7}{x(x^2+2)} = -\dfrac7{2x} + \dfrac{11x}{2(x^2+2)}

Now, in the integral we get

\displaystyle\int\frac{x^4+7}{x^3+2x}\,\mathrm dx = \int\left(x+\frac7{2x} - \frac{11x}{2(x^2+2)}\right)\,\mathrm dx

The first two terms are trivial to integrate. For the third, substitute <em>y</em> = <em>x</em> ² + 2 and d<em>y</em> = 2<em>x</em> d<em>x</em> to get

\displaystyle \int x\,\mathrm dx + \frac72\int\frac{\mathrm dx}x - \frac{11}4 \int\frac{\mathrm dy}y \\\\ =\displaystyle \frac{x^2}2+\frac72\ln|x|-\frac{11}4\ln|y| + C \\\\ =\displaystyle \boxed{\frac{x^2}2 + \frac72\ln|x| - \frac{11}4 \ln(x^2+2) + C}

7 0
2 years ago
Modeling a Bicycle Wheel Complete the table
Sladkaya [172]

Answer:

a= 6

b= 7

c= 8

d= 7

e= 6

7 0
3 years ago
Read 2 more answers
Measuring the speed of sound in the ocean is an important part of marine research. One application is the study of climate chang
dalvyx [7]

Answer:

A linear formula for S as a function of D is S=17D+1534

Step-by-step explanation:

We are supposed to find a linear formula for S as a function of D.

Equation of line : y = mx+c

We are given that At the surface, the speed of sound is 1534 meters per second.

c = 1534

We are given that for each increase in depth by 1 km, the speed increases by 17 m/s

So, Slope = m = 17

Substitute the values in equation

y=17x+1534

x denotes depth

y denotes speed

We are given that Use D for depth and S for the speed of sound

So, S=17D+1534

Hence a linear formula for S as a function of D is S=17D+1534

7 0
3 years ago
The area of a rectangular field is 6052 m².
Aleonysh [2.5K]

Answer:

<h2>length = 89 m</h2>

Step-by-step explanation:

Area of a rectangle = l × w

where

l is the length

w is the width

From the question

Area = 6052 m²

width = 68 m

To find the length substitute the values into the above formula

6052 = 68l

Divide both sides by 68

We have the final answer as

<h3>length = 89 m</h3>

Hope this helps you

5 0
3 years ago
Read 2 more answers
What is the vertex of the quadratic function below?
likoan [24]

Answer:

(-2, 3)

Step-by-step explanation:

7 0
2 years ago
Other questions:
  • The formula for the volume of a cone is . find the radius, to the nearest hundredth, of a cone with a height of 3 in. and a volu
    13·1 answer
  • Bonita brought 3 bags of apples and 2 pounds of grapes to the picnic. Each bag of apples weighed 4 pounds. How many pounds of ap
    6·1 answer
  • What is the length of segment DC?
    5·1 answer
  • Community Gym charges a $60 membership fee and a $55 monthly fee. Workout Gym charges a $200 membership fee and a $45 monthly fe
    5·1 answer
  • Find w and y without a calculator, will give brainliest for the correct answer
    12·1 answer
  • The measure of an angle is 89º. Find the measure of its supplement
    13·2 answers
  • On,Saturday, Alexa babysat her neighbors kids for 180 minutes. Then, on Sunday she babysat her little brother for 2 hours.how ma
    8·1 answer
  • If a store is selling 3 bottles of water for $3.24. how much would 8 bottles of water cost
    8·1 answer
  • What is the solution to this system of equations?
    9·2 answers
  • Decide if the following biconditional statement is true or false:
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!