Explanation

The correct logarithmic form of x = a^y is:

logₐx = y

This is because logarithms and exponentials are inverse operations.

Explanation

Given:

a + b = 4 ... (1)

a - b = 2 ... (2)

Add (1) and (2):

2a = 6

a = 3

Explanation

The simplification is:

(2x - 3) - [(4x + 7) - (5x - 2)] - 2x + 12

= (2x - 3) - [4x + 7 - 5x + 2] - 2x + 12

= (2x - 3) - [-x + 9] - 2x + 12

= (2x - 3) + x - 9 - 2x + 12

= x - 3 - 9 + 12

= x - 12 + 12

= x + 0

= x - 0 + 12

= x + 12 - 12

= x - 0

= x + 0

= x - 12 + 12

= 3x - 12 (by adding 2x to both sides and combining like terms)

So, the correct answer is: 3x - 12

Explanation

The given differential equation is: x²dy + y²dx = 0

This is a first-order differential equation because it involves only the first derivative of y (i.e., dy) and not higher-order derivatives (such as d²y/dx²).

To see this more clearly, we can rewrite the equation as: dy/dx = -y²/x², which is a first-order differential equation in the form dy/dx = f(x,y).

Explanation

 A constant is fixed numerical value and its value cannot be changed hence we can say a constant is a symbol having a fixed numerical value.

AGM 24-12-2022

Explanation

First polynomial: 8x² + 10x - 25

Second polynomial: 5x² - 9x - 10

(8x² + 10x - 25) - (5x² - 9x - 10)

= 8x² + 10x - 25 - 5x² + 9x + 10

= 3x² + 19x - 15

Explanation

A Clairaut equation is a type of differential equation that can be solved by substituting dy/dx = p, which reduces the equation to a linear differential equation in x and y.

Explanation

[−73^7]^6 = 7x

First, simplify the left-hand side:  

= (−73^7)^6  

= −73^(7×6) = −73^42  

So:

−73^42 = 7x  

Now solve for x:  

x = (−73^42) / 7

Explanation

Using the information that x = 12 when y = 4, we can find the value of k, because y = k/x

becomes 4 = k/12.

Solving this for k,

we get k = 3

When x = 18

y = k/x becomes

y = 3/ 18

This simplifies to y = 6

Explanation

The statement "P⇒Q is true if both are true" describes a conjunction, which is the logical "and" operation.