Problem 5. Suppose that the only paper money consists of 3-dollar bills and 10-dollar bills. Use mathematical induction to prove that any dollar amount greater than 17 dollars could be made from a combination of these bills.

Q: Write an equation of a circle with diameter AB. А(7,7), В(13,13) Choose the correct answer below. O…

A: using  formula for mid point & equation of circle

Q: near Methods

A: Given, x1x2˙=14-4510x1x2+4t3e12t2 cos4t-4 sin4t5 cos4t+8t7e12t4 cos4t+2 sin4t5 sin4t The eigen…

Q: Conditions

A:

Q: 1. Let S = 3 -6 (a) Is S a spanning set of R3? (b) Are the vectors in S linearly independent? 2. Let…

A: The following questions has been solved below.

Q: IV. (a) Write using summation notation: 1 +1 + 1 + 32 3 + 1 3" (b) Transform the summation by making…

A:

Q: Problem #15: Fill in the blanks below to show how you would find the zeros of the equation: J(x)=x +…

A: topic - quadratic equations

Q: A political scientist surveys 74 of the current 205 representatives in a state's congress. Of them,…

A: A Population is the entire group that you want to draw conclusions about. A sample is the specific…

Q: 2. Find the general solution of the system of differen- tial equations d X = dt + 4t³e4 / sin(3t)…

A:

Q: reason. This one is actually just an algebraic manipulation. Proposition 94: Proportion Lemma AD AE…

A: We prove it by  using the fact that AB=AD+DB and AC= AE+EC

Q: Compute the following. (1345) (234)

A: Given:      (1345)(234)

Q: Find the order of (3, 4) in Z4 × Z6

A: Z4={ 0,1,2,3 } mod 4Z6={ 0,1,2,3,4,5 } mod 6Order (a,b) in Zm*Zn = LCM { order( a), order (b)}

Q: Prove the following statement, using either the contrapositive statement or a proof by…

A: Proof by contradiction is done bellow

Q: Find the state transition matrix of the following system: = [] C = [0_1] 2 where A = [¹4²] -4 O a. O…

A:

Q: 5. Which of the following formulas are in CNF? a. (q^r) ⇒ (p ^ (q Vr)) b. p^((q^r)) ⇒ (q^r) c. d. ¬q…

A: To find: which of the following are in CNF.

Q: Write a plan for a coordinate proof of the following statement. The length of a diameter of a circle…

A: Given statement is " The length of a diameter of a circle is twice that of its radius".

Q: 3. Find the general solution of the system of differential equations * - ()* d 8 -5 10 + 4°c (…

A: given ,system of differential equations…

Q: Problem 1. Consider the matrices [1 1 0] A = |0 2 2 0 0 3 1 3 2 A? = |0 4 10 0 0 9 1/3 1/2 -1/3 1/3…

A: Given matrices are, A=110022003, A2=1320410009, A-1=1-1213012-130013 Now, λ ia an eigen value of…

Q: Recall question 3a from Tutorial 3 (Countable vs. Uncountable), where our proof had a problem when…

A:

Q: For any integer k, prove that gcd( 5k+3, 7k+4 ) = 1

A: Answer

Q: Discrete

A:

Q: Prove that v5 is irrational.

A: To prove 5 is irrational. Use the method of proof by contradiction.

Q: Question 03: Using "Proof by Contradiction" to show that, if 2n3 – 5n is odd then n is an even…

A: Question 03:  Proof by contradiction: Suppose that 2n3-5n is odd then n is not even. Because n is…

Q: Question (4): calculate eigenvectors, modal matrix (Q) and block diagonal matrix (denoting by Ã) of…

A:

Q: In how many ways can the letters of the word 'LEADER' be arranged? (A) 5! / 2! (B C(6,2) x 4! P(6,5)…

A:

Q: Solve the recurrence relation an = 7an-1 – 10am-2; ao = 2, a1 = 3 %3D O 4, = }5" – 2" 2" – 5" An = -…

A:

Q: . Let a and b be integers. If 7 | (17a + 256), prove that 7 | (10a + 11b).

A:

Q: Give an example of a function f(x) that is continuous for all values of x except x=2, where it has a…

A: We have to solve question with concept of removable discontinuity

Q: Trace O P and point A. Construct a tangent to O P that passes through A.

A:

Q: Determine whether the point (2,6) lies on the circle with radius 3 and center (- 2,4). The point…

A: