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Need number 4 answered

Answer:

Step-by-step explanation:

5. dy/dx = y³/x²

Seperate similar variables

dy/y³ = dx/x²

Integrating both sides

y^(-3+1) /(-3+1) = x^(-2+1) /(-2+1)  + C 

y^-2 / -2 = -1/x + C 

Now, given that y(3) =2 

Putting x=3 and y = 2 

-1/8 = -1/3 + C 

C = 1/3 -1/8 = 5/24 

Therefore solution is 

y^-2 / -2 = -1/x + 5/24 

y^-2 = 2/x + 5/12

Answer:

Step-by-step explanation:

a) integration from 3 to 0 f(x) dx = +4 

b) integration from 3 to 3 f(x) dx = 0

c) integration from 3 to 7 6f(x) dx = 

6 times integration from 3 to 7 f(x) dx 

= 6 x 2 = 12

Answer:

Step-by-step explanation:

8) (24x⁵)^½ = √(2x²)².6x 

= 2x²√6x 

12) (81n^12)^ 1/3 = 3^(4×1/3) n^(12×1/3)

= 3n⁴.3^(1/3)

20) (8x)^3/2 = (2√2x)³ 

= 8.2x.√2x 

= 16x√2x

Answer:

Step-by-step explanation:

Problem 3:

To find the coterminal angles for the given angles, we need to add or subtract a multiple of 360 degrees (or 2π radians) until we get an angle between 0 and 360 degrees (or 0 and 2π radians).

(a) -2023 degrees:

Adding 360 degrees repeatedly until we get an angle between 0 and 360 degrees:

-2023 + 360 = -1663 -1663 + 360 = -1303 -1303 + 360 = -943 -943 + 360 = -583 -583 + 360 = -223

So, one coterminal angle for -2023 degrees between 0 and 360 degrees is -223 degrees.

(b) 44π/9 radians:

To find the coterminal angles in radians, we need to add or subtract a multiple of 2π radians until we get an angle between 0 and 2π radians.

We can simplify 44π/9 radians by dividing both numerator and denominator by 4:

44π/9 = (11π/2) / (9/4)

We can see that 11π/2 is a multiple of 2π, so any multiple of 2π radians can be added or subtracted to get a coterminal angle. Also, 9/4 is the same as 2π/9 radians.

Adding or subtracting a multiple of 2π radians:

11π/2 + 2π = 15π/2 11π/2 - 2π = 7π/2

So, one coterminal angle for 44π/9 radians between 0 and 2π radians is 15π/2 radians (or 7.5π radians), and another is 7π/2 radians (or 3.5π radians).

Answer:

Step-by-step explanation:

Side 1: 3x² -4x -1

Side 2: 4x - x² + 5 

the length of two sides, 1 and 2, of the triangle = side 1 + side 2 

= 3x² -4x - 1 + 4x - x² + 5 

= 2x² +4  

Answer:

Step-by-step explanation:

Answer given in the picture below 

Answer:

Step-by-step explanation:

1.To find the average value of the function f(x) = 4 - x^2 over the interval [-2,2],

 we need to evaluate the definite integral of the function over the interval, and then divide by the length of the interval.

The definite integral of the function over the interval [-2,2] is given by:

∫(from -2 to 2) (4 - x^2) dx = [4x - (x^3)/3] (from -2 to 2) = [32/3]

The length of the interval is 2 - (-2) = 4.

Therefore, the average value of the function over the interval [-2,2] is:

[32/3] / 4 = 8/3

So the answer is: 8/3

2)

The definite integral of the function over the interval [1,3] is given by:

∫(from 1 to 3) 4(x^2+1)/x^2 dx

= ∫(from 1 to 3) 4 + 4/x^2 dx

= [4x + 4(-1)/x] (from 1 to 3)

= 8 + 4/3

= 28/3

The length of the interval is 3 - 1 = 2.

Therefore, the average value of the function over the interval [1,3] is:

(28/3) / 2 = 14/3

So the answer is: 14/3

3)The definite integral of the function over the interval [0,pi] is given by:

∫(from 0 to pi) sin(x) dx = [-cos(x)] (from 0 to pi) = 2

The length of the interval is pi - 0 = pi.

Therefore, the average value of the function over the interval [0,pi] is:

2 / pi

So the answer is: 2/pi

4) The definite integral of the function over the interval [0,pi/2] is given by:

∫(from 0 to pi/2) cos(x) dx = [sin(x)] (from 0 to pi/2) = 1

The length of the interval is pi/2 - 0 = pi/2.

Therefore, the average value of the function over the interval [0,pi/2] is:

1 / (pi/2)

Simplifying, we get:

2/pi

So the answer is: 2/pi

5)The definite integral of the function over the interval [1,3] is given by:

∫(from 1 to 3) 9/x^2 dx = [-9/x] (from 1 to 3) = 3 - (-9) = 12

The length of the interval is 3 - 1 = 2.

Therefore, the average value of the function over the interval [1,3] is:

12 / 2 = 6

So the answer is: 6

6) The definite integral of the function over the interval [1,4] is given by:

∫(from 1 to 4) x^2 dx = [x^3/3] (from 1 to 4) = (4^3/3) - (1^3/3) = 21

The length of the interval is 4 - 1 = 3.

Therefore, the average value of the function over the interval [1,4] is:

21 / 3 = 7

So the answer is: 7

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45 

The answer is in the image 

The total nom of  code that can be used is equal to 5+3 = 8