Explanation

To form a differential equation from a given function containing arbitrary constants:

• If the function has 'n' arbitrary constants, differentiate the equation 'n' times with respect to the independent variable.
• This process removes the arbitrary constants, leaving a differential equation.

Explanation

Explanation

We have two equations:

x + y = 99 ... (1)

x - y = 9 ... (2)

Add (1) and (2) to eliminate y:

2x = 108

Divide by 2:

x = 54

Now, substitute x into (1) to find y:

54 + y = 99

Subtract 54 from both sides:

y = 45

So, the values are x = 54 and y = 45.

Explanation

 We are given:

To find $q$, divide both sides by 0.87:

Explanation

If a/2+4 = 7/2, the a =?

A/ 2+4 = 7/2

a/ 4 = 7

4 - 7 =  a

-3 =  a

 -3/ 3 = a

-1 = a

ND-21-5-2023

Explanation

12 - 5x = x + 30

Add 5x to both sides:

12 = 6x + 30

Subtract 30 from both sides:

-18 = 6x

Divide both sides by -6:

x = -18/6

x = -3

So, the value of x is -3.

Explanation

To evaluate the expression 2^2n + 1, we need to follow the order of operations (PEMDAS):

Calculate the exponent: 2^2n = 2^(2*3) = 2^6

Calculate the value of 2^6: 2^6 = 64

Add 1 to the result: 64 + 1 = 65

Therefore, the correct answer is: 65

Explanation

Given:

xy = 35

x + y = 12

To find x² + y²:

(x + y)² = x² + 2xy + y²

144 = x² + 2(35) + y²

144 = x² + 70 + y²

x² + y² = 144 - 70

= 74

Explanation

Explanation

Given x + 1/x = 3

To find x³ + 1/x³:

(x + 1/x)³ = x³ + 3(x²)(1/x) + 3(x)(1/x)² + 1/x³

= x³ + 3x + 3/x + 1/x³

= x³ + 1/x³ + 3(x + 1/x)

(x + 1/x)³ = x³ + 1/x³ + 3(3)

27 = x³ + 1/x³ + 9

x³ + 1/x³ = 27 - 9

= 18