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4 years ago

Find the antiderivative of the function: (x^4+2x^2)/x^3

Mathematics

2 answers:

Pie4 years ago

4 0

Answer: Either it is 3x to the 12 power or x+2x to the 2 power

Step-by-step explanation:

dividing exponents is the equivalent to subtracting

this leaves us with x+2x to the 2 power. then you just add. I might be wrong about breaking it down that far.

dangina [55]4 years ago

3 0

Set the function up in integral form and evaluate to find the integral.
F(x)=F(x)=12x2−ln(|x|)−1x2+C

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Find the area of a circle with radius, r = 5.64m.

Tpy6a [65]

Answer:

99.93 $m^{2}$

Step-by-step explanation:

1. The area of a circle is defined by the equation: A = $\pi r^{2}$

2. We can plug in the radius and solve the equation: A = $\pi *5.64^{2}$

3. A = π * 31.8096

4. A = 99.932

5. A = 99.93

3 0

2 years ago

Is 23 a prime, composite or neither

Juli2301 [7.4K]

23 is an prime number because it has 2 factors 1 and itself

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3 years ago

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Find the vertex of the parabola<br> y= x^2-2x-1<br> vertex (?,?)

SpyIntel [72]

$y=ax^2+bx+c\\\\vertex:(x_v;\ y_v)\\\\x_v=\frac{-b}{2a}\ and\ y_v=f(x_v)$

$y=x^2-2x-1\\\\a=1;\ b=-2;\ c=-1\\\\x_v=\frac{-(-2)}{2\cdot1}=\frac{2}{2}=1\\\\y_v=1^2-2\cdot1-1=1-2-1=-2\\\\Answer:(1;-2)$

5 0

3 years ago

Read 2 more answers

Make a fraction become a decimal

JulijaS [17]

Answer:

1. 0.18333333333

2. 1.5

3. 0.55555556

4. 2.75

5. 0.81818181818

6. 4.1111111111

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3 years ago

There are 17 portable mini suites (a.k.a. cages) in a row at the paws and claws holiday pet resort. they are neatly labeled with

DiKsa [7]

Given that there are 17 portable mini suites (a.k.a. cages) in a row at the Paws and Claws Holiday Pet Resort. They are neatly labeled with their guests' names. There are 8 poodles and 9 tabbies. How many ways can the "suites" be arranged if: a) there are no restrictions.

b) cats and dogs must alternate.

c) dogs must be next to each other.

d) dogs must be next to each other and cats must be next to each other.

Part A:

If there are no restrictions, then the number of ways the "suites" can be arranged is given by:

$17!=17\times16\times15\times14\times13\times12\times11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1=355,687,428,096,000 \ ways$

Part B:

If cats and dogs must alternate, then the number of ways the "suites" can be arranged is given by:

$9!\times8!=9\times8\times7\times6\times5\times4\times3\times2\times1\times8\times7\times6\times5\times4\times3\times2\times1=14,631,321,600 \ ways$

Part C:

If dogs must be next to each other, then the group of dogs are taken as 1 object and there are now 10 objects to arrange. The number of ways to arrange 10 objects is given by:

$10!=10\times9\times8\times7\times6\times5\times4\times3\times2\times1=3,628,800
 \ ways$

Also, the group of dogs can be arranged in:

$8!=8\times7\times6\times5\times4\times3\times2\times1=40,320
 \ ways$

Therefore, the total number of ways the "suites" can be arranged is given by:

$10!\times8!=3,628,800\times40,320=146,313,216,000 \ ways$

Part D:

If dogs must be next to each other and cats must be next to each other, then the group of dogs are taken as 1 object and the group of cats are taken as 1 object, then there are now 2 objects to arrange.

The number of ways to arrange two objects is given by:

$2!=2\times1=2$

The number of ways the 9 dogs are to be arranged is given by:

$9!=9\times8\times7\times6\times5\times4\times3\times2\times1=362,880$

The number of ways the 8 cats are to be arranged is given by:
$8!=8\times7\times6\times5\times4\times3\times2\times1=40,320$

Therefore, the total number of ways the "suites" can be arranged is given by:

$2!\times9!\times8!=2\times362,880\times40,320=29,262,643,200 \ ways$

4 0

3 years ago