A. solve the differential equation y prime equals the product of 4 times x and the square root of the quantity 1 minus y squared. b. explain why the initial value problem y prime equals the product of 4 times x and the square root of the quantity 1 minus y squared with y(0) = 4 does not have a solution.

Step-by-step explanation:

Given is a differential equation as:

We can solve this by separation of variables method

To find C:

Given y(0) =4

Substitute x=0 and y =4

sin inverse of 4 = C

But sin inverse is valid only for values between -1 and 1

Hence C is not a real value

No solution for this.

Pentagon : Order of rational symmetry of 7.

Rectangle : Order of rational symmetry of 2.

Explanation:

The order of rotational symmetry of a geometric figure is the number of times you can rotate the geometric figure so that its looks exactly the same as the original figure. You can only rotate the figure up to 360° degrees

Regular Pentagon:

We rotated a Pentagon 72° degrees each time to get the right shape.That sum up to 7 times in 360° which means symmetry order of 7.

Rectangle :

We rotated a rectangle 180° degrees each time to get to the right shape. That sum up to 2 times in 360° which means symmetry order of 2.