15. A sequence of two different digits is randomly chosen from the digits 0–4; the digit is larger than the second. ANSWER I S= {01, 02, 03, 04, 10, 12, 13, 14, 20, 21, 23, 24, 30, 31, 32, 34, 40, 41, 42, ; Е 3 {10, 20, 21, 30, 31, 32, 40, 41, 42, 43}

Q: 1. Find the distance between P and Q. P(−4, 12); Q(−12, 4)

A: Explained below

Q: Let C(-6,3) and D(3,0). Determine which is larger: ||CE|| or ||DE|, if E(-2,1)

A:

Q: Use DeMoirve's Theorem to find: (1– iv3)2

A: We first try to express 1-i3 using polar form.r=12+(-3)2=1+3=4=2θ=tan-1yx=tan-1-31=tan-1-3=-π3So,…

Q: 769° 45° C. a) What is the measure of <ADB?

A: We can find the measure of angle ADB as below

Q: The distance between a and b is lb -al.

A: Here, a=-0.5 &amp; b=3

Q: 6. Describe the reflection(s) that will carry the trapezoid onto itself. Write the equation of a…

A:

Q: 6.1 Calculate the order of the element a) (4,9) in Z18XZ18- b) (7,5) in Z12×Zg. c) (8,6,4) in Z18×…

A:

Q: In r dx 7.)

A:

Q: 3. Prove the pythagorean Theorem

A:

Q: flx). a/2)=6x+6.and hlx) -alA 88

A:

Q: find u ·v.

A:

Q: 11. Prove (AUB) × C = (A x C) U (B × C)

A: 11 prove (A U B)*C = (A X C) U (B X C) here this is the property of distributive  so this is direct…

Q: What is Rolles Theorem and how do you find "c"?

A: What is Rolle’s Theorem and how do you find c

Q: 3) Let x = (-1,3,2,-4), and y = (1,0,2,3). Find the following distances || x = || = ? []x - || =?

A:

Q: Let f(x) =Ex-12. Find Ihe fallewing fla)=) +f72)3=

A: Function value

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.