Explanation

Let's evaluate the expressions using the given definition of a * b:

3 * 4 = 3 + 4 + (3)(4) = 3 + 4 + 12 = 19

2 * 3 = 2 + 3 + (2)(3) = 2 + 3 + 6 = 11

Now, let's subtract:

3 * 4 - 2 * 3 = 19 - 11 = 8

Explanation

(a + b) – (a – b)  

= a + b – a + b  

= 2b

Explanation

 (Using identity a² - b² = (a - b)(a + b)):  

(100 - 99)(100 + 99) = 1 × 199 = 199

Explanation

2x + 5 = 3 

2x= 3 - 5 

2x = -2 

x = -1

Explanation

4x + 12 = 36

4(x+3) = 36

x+3 = 36/4

x+3 = 9

Explanation

Normal Line to a Circle

Given circle equation: x² + y² = 25

This is a circle with center (0,0) and radius 5.

Given point: (2,3)

The normal line at a point on the circle is the line passing through the center and the point.

The slope of the line joining (0,0) and (2,3) is 3/2.

The equation of the line passing through (0,0) and (2,3) can be found using point-slope form y = mx, where m is the slope.

So, y = (3/2)x

Multiplying both sides by 2 to get rid of the fraction: 2y = 3x

Rearranging: 3x - 2y = 0

Explanation

The limit lim x→∞ 2/x is equal to 0.

As x approaches infinity, the denominator x becomes very large, and the numerator 2 remains constant.

Therefore, the ratio 2/x approaches 0.

Explanation

The value of the log can be either with base 10 or with base e.

The log10 10 value is 1

while the value of loge 10 or ln(10) is 2.302585.

ND18-9-2023

Explanation

• X does not have any sons or brothers but Y’s father is X’s father-son. Daughter is Y to X
• ***
  
  
• Y term is used here as female.
• X is a boy and Y is a girl.
• X does not have a son or brother.
• Y’s father and X are the same people.
• Therefore, Y is the daughter of X.

Explanation

∫³-1 dx = [x]³-1 = 3 - (-1) = 4