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
Aleksandr [31]
2 years ago
9

Need help question #3. Show steps please

Mathematics
1 answer:
Oksana_A [137]2 years ago
8 0

Answer:

B.

Step-by-step explanation:

We are given:

\displaystyle \int \sqrt{x}\Big(9x^3-2\sqrt{x}+\frac{8}{x}\Big)\, dx

And we want to select its equivalent form.

Note that A is not valid. No integration property allows us to separate factors unless that factor is a constant.

We can simply rewrite and then distribute. First, by rewriting:

\displaystyle =\int x^{1/2}\Big(9x^3-2x^{1/2}+8x^{-1}\Big)\, dx

Distribute. Recall exponent properties;

\displaystyle =\int(9x^{3+1/2}-2x^{1/2+1/2}+8x^{-1+1/2})\, dx

Simplify:

\displaystyle=\int9x^{7/2}-2x+8x^{1/2}\, dx

This can then be separated (since its addition/subtraction) and integrated individually.

Hence, our answer is B.

You might be interested in
Please put a serious answer
aksik [14]

Answer:

x=12

Step-by-step explanation:

9x-14=2(3x+11)

9x-14=6x+22

9x-6x=22+14

3x=36

x=36/3=12

8 0
3 years ago
Please people i will give you lots of points and please give me the correct answer
cupoosta [38]

Answer:

15

Step-by-step explanation:

30 subtract 15 = 15 and both the 10 and the other 10 are the same

5 0
3 years ago
(-1 + 6) Squared + (4+5) squared
nalin [4]
(-1 + 6)^2 <span>+ (4+5)^2 = </span>106
3 0
3 years ago
Find the volume of the wedge with vertices at points (0,0,0), (1,0,0), (0,1,0), (0,0,1) by integrating the area of cross-section
Angelina_Jolie [31]

Answer:

V = 1/6 cubic units

Step-by-step explanation:

Applying the concept of integrals for volume calculation:

V = \int\limits^b_a {S(x)} \, dx          (1)

V = volume of the solid bounded by x = a and x = b

S(x) = cross section area of the solid, perpendicular to the x axis

From the figure we have that S is the area of a triangle that has base Z and height Y

Area of the triangle = S(x)=\frac{y(x)*z(x)}{2}          (2)

Calculation of y(x) and z(x)

We apply the equation of the point-slope line (plane xy):

Slope = m = \frac{y_{2} - y_{1} }{x_{2} - x_{1}}          (3)

Equation of the line = y - y_{1} =m(x-x_{1} )          (4)

Replacing the points (1,0) and (0,1) in (3):

m=\frac{1-0}{0-1} =-1

Replacing the point (1,0) and m = -1 in (4):

y-0=(-1)(x-1)

y(x) = -x + 1 (Line A-B)          (5)

We apply the equation of the point-slope line (plane xz):

Slope = m = \frac{z_{2} - z_{1} }{x_{2} - x_{1}}          (6)

Equation of the line = z - z_{1} =m(x-x_{1} )          (7)

Replacing the points (1,0) and (0,1) in (6):

m=\frac{1-0}{0-1} =-1

Replacing the point (1,0) and m = -1 in (7):

z-0=(-1)(x-1)

z(x) = -x + 1 (Line A-C)        (8)

Replacing (5) and (8) in (2)

S(x) = \frac{(-x + 1) * (-x + 1)}{2} =\frac{(-x + 1)^{2} }{2}          (9)

Replacing (9) in (1) and knowing that a = 0 and b = 1:

V = \int\limits^1_0 {\frac{(-x + 1)^{2} }{2}} \, dx = \int\limits^1_0 {\frac{x^{2}-2x+1 }{2}} \, dx

V =\frac{1}{2} (\frac{x^{3} }{3} -2\frac{x^{2} }{2} +x)  evaluated from x=0 to x=1

V= \frac{1}{2} (\frac{1}{3} -1 +1) = \frac{1}{6}

3 0
3 years ago
What is the radius of a circle with an area of 50.24 cubic inches?<br><br> Use 3.14 for pi.
OverLord2011 [107]
Hope this helps you..!!!

3 0
3 years ago
Other questions:
  • What is the answer of 7/4(-4)?
    10·2 answers
  • I have a question on a homework problem. Select the function that represents an arithmetic sequence.
    13·1 answer
  • What is the product of 5.86 × 10–7 and 3.1 × 104 What is the value of n in the scientific notation of the product?
    14·2 answers
  • Translate and solve: 94% of what number is 611?
    9·1 answer
  • School newspaper staff went to three different sports games to survey students on their favorite sport, and the results are show
    6·1 answer
  • Which lines must be parallel? <br><br> A)r and s<br> B)p and q<br> C)p and r<br> D)q and s
    13·2 answers
  • You decide to purchase a used car for $14,000. You have to take out a loan from the bank. If your loan is compounded semi-annual
    12·1 answer
  • I seriously need help
    9·1 answer
  • What times 1/11 equals 1?
    15·1 answer
  • Can you please help me with#11?I'm not sure how to find the answer.​
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!