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What is the 32nd term of the arithmetic sequence where a1 equals 15 and a13 equals -57?
Suppose the sequence is defined by an = a0 + n*d Then a1 = a0 + d = 15 and a13 = a0 + 13d = -57 Subtracting the first from the second: 12d = -72 so that d = -6 and then a0 - 6 = 15 gives a0 = 21 So a32 = 21 - 32*6 = -171
Equations that have the same solution?
It is not clear what the question requires. Yes, there are plenty of equations that have the same solution. For example, each and every equation of direct proportionality has the solution (0, 0). So what? every polynomial of the form y = anxn + an-1xn-1 + ... + a1x + a0 has the solution (0, a0). Again, so what?
Prove if a number is divisible by 3 then the sum of its digits must also be divisible by 3?
Suppose an (n+1)-digit number, X, is divisible by 3. Let X = a0*100 + a1*101 + a2*102 + ... + an*10n = a0 + a1*(1+9) + a2*(1+99) + ... + an*(1+999..9) = [a0 + a1 + a2 + ... + an] + [a1*9 + a2*99 + ... + an*999..9] 3 divides 9, 99, 999, etc so 3 divides each term in the second brackets (parentheses). Therefore 3 must divide the sum in the first brackets. That is, 3 must divide the sum of digits.
What is 7a to the 0 power?
Anything (except zero) to the power of zero is 1. If written as 7a0, this is operated as 7 x (a0) = 7 x 1 = 7. If written as (7a)0, it is simply 1 by the first statement.
Why can you never divide by zero?
Dividing by zero would mean multiplying by the reciprocal of 0, but 0 has no reciprocal because 0 times any number is 0, not 1. Multiplicative property of 0 Prove: If a is any real number, then a0 = 0 and 0a = 0 Proof: Statement _____________ Reason 1. 0 = 0 + 0 ____________ 1. Identity property of addition 2. a0 = a(0 + 0) _________ 2. Multiplication property of equality 3. a0 = a0 + a0 _________ 3. Distributive property of mult. with respect to add. 4. But a0 = a0 + 0 _______ 4. Identity property of addition 5. a0 + a0 = a0 + 0 ______ 5. Substitution principle 6. a0 = 0 ______________ 6. Subtraction property of equality 7. 0a = 0 ______________ 7. Commutative property of multiplication Therefore, division by zero has no meaning in the set of real numbers. (Source: Algebra: Structure and Method Book 1) In my opinion, the answer to this question depends upon which definition of division you are using ie. the Algebraic definition of division as the multiplication by a reciprocal or the Arithmetic definition of division as a/b = c because a = bc. Any discussion about division by zero must however centre around the above proof which is based on the properties of the real numbers. The two cases are: 1. Dividing a nonzero number by zero, which does violate the multiplicative property of zero and therefore the properties of the real numbers upon which it is proven, as shown above. 2. Dividing zero by zero, which does not violate the multiplicative property of zero, but multiplication by zero is an operation that can not be "undone." a/b = c is defined by a = b*c. If a/0 = c, then a = 0*c. But 0*c = 0. Hence, if a is not equal to 0, no value of c can make the statment a = 0*c true, while if a = 0, every value of c will make the statement true. Thus, a/0 either has no value or is indefinite in value. Division is not always possible in the system of numbers consisting of the integers (6 is divisible by 2 and 3 but not by 5), but in those cases where it is, the result is always uniquely determined. In the system of all rational numbers (that is, the integers and fractions) division is not only unique but is always realizable with one exception-division by zero. On the basis of the definition of division given above, it is apparent that it is not possible to divide a number different from zero by zero. The result of dividing zero by zero, according to the definition, can be any number since c*0 = 0 in all cases. It is usually preferable in algebra (in order not to violate the uniqueness of division) to consider division by zero to be impossible for ALL cases. In mathematics the art of asking questions is more valuable than solving problems.
What is the definition of a zero exponent?
For any number (a) not equal to 0, a0=1
How do you prove a0 equals 1?
a0=(a-1\a-1)=a\a=1
How old is a sample of wood with 75 percent of 14 Carbon how old is the sample t125730 years?
t is equal to = (1/2)ln(A/A0))
How do you find D?
A= A0e^-kt A0= A/ e^kt = Ae^kt A0= A+ D* D*= A0- A D*= Ae^kt - A D*= A(e^kt - 1)
What is the size of an A-Sheet?
A0 is 1 meter square.
A0⋅a6?
A0
Design a combinational circuit that accepts a 3 bit number and generates a 6 bit binary number equal to the square of the input number?
Let the inputs be A2 A1 A0 & outputs be S5 S4 S3 S2 S1 S0. Now, make a truth table as follows A2 A1 A0 S5 S4 S3 S2 S1 S0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 and so on....... Finally we'll get S0 = A0 S1 = 0 S2 = A1 A2(bar) S3 = A0 [ A1 XOR A2] S4 = A2 [A1(bar) + A0 ] S5 = A1 A2
What maths sequences can you start with 4 and 8?
one rule would be an+1 = an + 4 ; a0= 4. This gives 4,8,12,16,20,..... This is called an arithmetic sequence. A geometric rule would be an+1 = 2an; a0= 4. This gives 4,8,16,32,64,... Another rule is an+1 = an/2 + 6 ; a0= 4. This gives 4, 8, 10, 11, 11.5,11.75, ....
Write a C program to generate following sequence eg when 5 is pressed the sequence should be 0 1 1 2 3 5 and if 3 is pressed 0 1 1 2 the sequence should be according to the number pressed?
/* the sequence printed is Fibonacci's sequence, each element is calculated as a sum of two previous elements */#includeint main(){int i;int n;int a0=0;int a1=1;printf("How many elements do you want to print? ");scanf("%d",&n);printf("0 ");if (n > 0)printf("1 ");for (i = 2; i
How many inches is A0?
A0 paper is 46.8 x 33.1 in.
What is the area of a A4 sheet of paper?
The A series of paper is such that each numbered size of paper has exactly half the area of the previous size. ie A1 is 1/2 the area of A0, A2 is half the area of A1, and so on. Also, A0 has an area of exactly 1 sq m. Thus A1 has an area of 1/2 that of A0, A2 has an area of (1/2)^2 = 1/4 of A0, An has an area of (1/2)^n of that of A0 = (1/2)^n sq m 1 m = 100 cm 1 sq m = 1 m x 1 m = 100 cm x 100 cm = 10000 sq cm → A4 has an area of (1/2)^4 sq m = 1/16 sq m = 0.0625 sq m = 0.0625 x 10000 sq cm = 625 sq cm.
What size is A4 paper?
210 × 297 mm. A4 is the standard size for most countries, excluding the US, Canada and a few others.A4 is one of a series of paper sizes, starting with A0. A0 has an area of 1 m². If you fold A0 into two you get A1, and so on.All sizes in the A-series have the same ratio of length/width, which is the square root of 2.
