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Keith_Richards [23]
2 years ago
6

FIRST ANSWER GETS BRAINLIEST!! (sorry for the colors on the picture)

Mathematics
2 answers:
Karo-lina-s [1.5K]2 years ago
8 0

It is the 3rd answer

Advocard [28]2 years ago
5 0
Its 3rd……! obviously
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Hi! I need help with the attached question in calc. Thank you:)
Elena L [17]

Answer:

3π square units.

Step-by-step explanation:

We can use the disk method.

Since we are revolving around AB, we have a vertical axis of revolution.

So, our representative rectangle will be horizontal.

R₁ is bounded by y = 9x.

So, x = y/9.

Our radius since our axis is AB will be 1 - x or 1 - y/9.

And we are integrating from y = 0 to y = 9.

By the disk method (for a vertical axis of revolution):

\displaystyle V=\pi \int_a^b [R(y)]^2\, dy

So:

\displaystyle V=\pi\int_0^9\Big(1-\frac{y}{9}\Big)^2\, dy

Simplify:

\displaystyle V=\pi\int_0^9(1-\frac{2y}{9}+\frac{y^2}{81})\, dy

Integrate:

\displaystyle V=\pi\Big[y-\frac{1}{9}y^2+\frac{1}{243}y^3\Big|_0^9\Big]

Evaluate (I ignored the 0):

\displaystyle V=\pi[9-\frac{1}{9}(9)^2+\frac{1}{243}(9^3)]=3\pi

The volume of the solid is 3π square units.

Note:

You can do this without calculus. Notice that R₁ revolved around AB is simply a right cone with radius 1 and height 9. Then by the volume for a cone formula:

\displaystyle V=\frac{1}{3}\pi(1)^2(9)=3\pi

We acquire the exact same answer.

8 0
2 years ago
The weights (in ounces) of 14 different apples are shown below. Find Q 3. 5.7 5.5 4.7 4.4 6.8 5.7 5.5 6.9 6.0 4.4 5.7 6.9 4.4 4.
elena55 [62]
I Think 5.7 I’m Not Sure
6 0
3 years ago
Solve 6n + 10 < 4n + 16
BartSMP [9]

Answer:

n < 3

Step-by-step explanation:

6n + 10 < 4n + 16

( Minus 4n from both sides to isolate + 16 )

2n + 10 < 16

( Minus 10 from both sides to isolate 2n )

2n < 6

( Divide both sides by 2 to isolate n )

n < 3

3 0
3 years ago
Read 2 more answers
Integration of ∫(cos3x+3sinx)dx ​
Murljashka [212]

Answer:

\boxed{\pink{\tt I =  \dfrac{1}{3}sin(3x)  - 3cos(x) + C}}

Step-by-step explanation:

We need to integrate the given expression. Let I be the answer .

\implies\displaystyle\sf I = \int (cos(3x) + 3sin(x) )dx \\\\\implies\displaystyle I = \int cos(3x) + \int sin(x)\  dx

  • Let u = 3x , then du = 3dx . Henceforth 1/3 du = dx .
  • Now , Rewrite using du and u .

\implies\displaystyle\sf I = \int cos\ u \dfrac{1}{3}du + \int 3sin \ x \ dx \\\\\implies\displaystyle \sf I = \int \dfrac{cos\ u}{3} du + \int 3sin\ x \ dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3}\int \dfrac{cos(u)}{3} + \int 3sin(x) dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3} sin(u) + C +\int 3sin(x) dx \\\\\implies\displaystyle \sf I = \dfrac{1}{3}sin(u) + C + 3\int sin(x) \ dx \\\\\implies\displaystyle\sf I =  \dfrac{1}{3}sin(u) + C + 3(-cos(x)+C) \\\\\implies \underset{\blue{\sf Required\ Answer }}{\underbrace{\boxed{\boxed{\displaystyle\red{\sf I =  \dfrac{1}{3}sin(3x)  - 3cos(x) + C }}}}}

6 0
3 years ago
A=12/35<br> B=35/37<br> C=35/12<br> D=12/37
Scrat [10]

Answer: D= 12/37

Step-by-step explanation:

To find sin of angle A, you take the opposite angle over the hypotenuse. 12 is opposite of A and 37is the hypotenuse.

3 0
3 years ago
Read 2 more answers
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