I am writing this question only to see how smart the community on Brainly is.What is the 3rd derivative of $f(x)=sin(x)x^3+x^2tan(x)$

Answers

Answer 1

Answer: I am very confused as to why you posed this question in the way you did. People would have answered your question regardless.

First derivative:
f'(x) = 3x^2sin(x) + x^3cos(x) + 2xtan(x) + x^2sec^2(x)

Second derivative:
f''(x) = 6xsin(x) + 3x^2cos(X) + 3x^2cos(x) - x^3sin(x) + 2tan(x) + 2xsec^2(x) + 2xsec^2(x) + 2x^2sec^2(x)tan(x)

f''(x) = 6xsin(x) + 6x^2cos(x) - x^3sin(x) + 2tan(x) + 4xsec^2(x) +

Third Derivative:
f'''(x) = 6sin(x) + 6xcos(x) + 12xcos(x) - 6x^2sin(x) - 3x^2sin(x) - x^3cos(x) + 2sec^2(x) + 8xsec^2(x)tan(x) + 4sec^2(x) + 4x^2sec^2(x)tan^2(x) + 4xsec^2(x)tan(x) + 2x^2sec^4(x)

f'''(x) = 6sin(x) + 18xcos(x) - 9x^2sin(x) - x^3cos(x) + 12xsec^2(x)tan(x) + 6sec^2(x) + 4x^2sec^2(x)tan^2(x) + 2x^2sec^4(x)

f'''(x) = (6 - 9x^2)sin(x) + (18x - x^3)cos(x) + 12xsec^2(x)tan(x) + 6sec^2(x) + 4x^2sec^2(x)tan^2(x) + 2x^2sec^4(x)

There are many more ways this can be factored, but if this is just to test whether someone knows the basics of calculus, this should be sufficient.

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The LCD for the fractions 1/3, 3/4, 5/32, and 8/9 is

Answers

we know that

The LCD is the LCM (least common multiple) of all the denominators.

we have

$1/3, 3/4, 5/32, 8/9$

$3=3^(1) \n 4=2^(2) \n 32=2^(5) \n 9=3^(2)$

$LCM=2^(5) *3^(2) \n LCM=32*9\n LCM=288$

The LCM of $3, 4, 32, 9$ is $288$ ,

which is the multiple of the highest power of prime factors from all of the given numbers

therefore

the answer is

$288$

The LCD for the fractions $(1)/(3)$ , $(3)/(4)$ , $(5)/(32)$ and $(8)/(9)$ is $\boxed{288}$ .

Further explanation:

The LCD (least common denominator) is least common multiples of denominators.

The least common multiple is defined as the smallest number that divides all the given numbers.

Prime factorization is defined as the factors of the given number are only prime number.

Prime number is defined as a numbers that has only two factors one and itself.

Given:

The given numbers are $(1)/(3)$ , $(3)/(4)$ , $(5)/(32)$ and $(8)/(9)$ .

Explanation:

First we have to find the prime factors of the denominators of all the numbers.

The prime factors of $3$ can be expressed as,

$3 = {3^1}$

The prime factors of $4$ can be expressed as,

$4 = {2^2}$

The prime factors of $32$ can be expressed as,

$32 = {2^5}$

The prime factors of $9$ can be expressed as,

$9 = {3^2}$

The least common factors are ${2^5}$ and ${3^2}$ .

The least common denominator can be calculated as,

$\begin{aligned}\text{LCD} &= {2^5} * {3^2} \n &= 32 * 9\n&= 288\n \end{aligned}$

The LCD for the fractions $(1)/(3)$ , $(3)/(4)$ , $(5)/(32)$ and $(8)/(9)$ is $\boxed{288}$ .

Learn more:

1. Learn more about addition of two numbers brainly.com/question/894273

2. Learn more about multiplication brainly.com/question/4892332

Answer details:

Grade: Junior School

Subject: Mathematics

Chapter: Number system

Keywords: prime numbers, Least common denominator, LCD, Least common multiple, LCM, divide, prime factors, factorization, Prime factorization, factors, fraction, $(1)/(3)$ , $(3)/(4)$ , $(5)/(32)$ , $(8)/(9)$ .

Use elimination to solve this system of equations. 2r + 3s= 9 and 3r + 2s= 12

Answers

2r + 3s= 9 <=> -6r -9s = -27;
3r + 2s= 12 <=> 6r + 4s = 24;
=> 0*r -5*s = -3 => s = 3/5;

2*r + 3*(3/5) = 9<=> 10*r + 9 = 45 <=> 10*r = 36 => r = 18/5;

Answer:

(18/5,3/5)

Step-by-step explanation:

Felipe has saved $625. He is starting a part-time job that pays him $150 a week, and he plans to save all of the money he earns. Which algebraic expression represents Felipe's total savings after x weeks? A.625x + 125 B.775x C.150x + 625 D.125x - 650

Answers

The answer is C, 150x+625
Where x is the number of weeks

Answer:

The correct answer is C. 150x + 625 because x equals the total number of weeks. Hope this helps!

Two spheres have are such that the radius of the bigger sphere is 3 times bigger than the smaller. What is the ratio of the area?

Answers

Answer:

1 : 27

Step-by-step explanation:

Radius of sphere one = r₁ = x units

Radius of sphere 2 = r₂ = 3*x = 3x units

Ratio of area of two sphere's = r₁³ : r₂³

= x³ : (3x)³

$= (x^(3))/(3^(3)*x^(3))\n\n= (1)/(3^(3))\n\n= (1)/(27)$

= 1 : 27

A 3 pound package of ground beef sells for $6. At this rate, if John buys 10 pounds ofground beef, how much would he pay?

Answers

Answer:

$20

Step-by-step explanation:

3 pounds of beef is 6 dollars.

6 divided by 3 is 2. Therefore, each pound cost $2.

He wants to buy 10 pounds of beef.

9 pounds would be $18.

Add 1 pound, which is $2 and you will get $20.

Therefore, he would pay $20!~

Hope this helps!~~ <3

Solve the absolute value equation. |3x-4|=5

Answers

Absolute values are a way of finding a distant from zero, which means there will be 2 answers; one will be positive, and the other will be negative.

$|3x-4|=5 and |3x-4|=—5$ Because you need 2 answers, you have to make 5 positive and negative.

Another way to write this equation would be...
5=|3x-4|=—5

Now lets continue...
5=3x-4=—5

Add 4 to both sides...
9=3x=—1

Now divide by 3...
3=x= $- (1)/(3)$

So the solution is...
X={ $-(1)/(3)$ , 3}

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