In which area of the diagram does the number −11 belong?

2 answers:

8 0

Integers and Rational Numbers, it is because if -11 is a Integer, it also has to be a Rational number. But your actual answer is Integers.

Dahasolnce [82]3 years ago

3 0

I can't see where the diagram is, but I've taken this test before so here is my answer; the correct answer choice is B) Integers. An Integer is any whole number on the negative side. If you look at the question, it's asking where -11 belongs. This number is a negative whole number, so it belongs in Integers.

Hope this helps!!

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Write the algebraic expression for the difference between the squares of two numbers.

V125BC [204]

The algebraic expression for the difference between the squares of the two numbers, supposing the two numbers to be a and b, is

a² - b² = (a + b)(a - b).

An algebraic expression is a combination of terms, where the terms are separated using mathematical operators like plus (+), minus (-), multiply (*), and divide (/).

The terms are combinations of numerals and variables.

Variables are represented alphanumerically, which can hold any value as per the expression they are used in.

In the question, we are asked to write the algebraic expression for the difference between the squares of two numbers.

We assume the two numbers to be a and b respectively.

Thus, we are asked to write an expression for the difference between the square of a and square of b, that is, we are asked to write an expression for a² - b².

We know that a² - b² is an identity, which can be shown as (a + b)(a - b).

Thus, the algebraic expression for the difference between the squares of the two numbers, supposing the two numbers to be a and b, is a² - b² = (a + b)(a - b).

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6 0

1 year ago

4. Using the geometric sum formulas, evaluate each of the following sums and express your answer in Cartesian form.

nikitadnepr [17]

Answer:

$\sum_{n=0}^9cos(\frac{\pi n}{2})=1$

$\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=0$

$\sum_{n=0}^\infty (\frac{1}{2})^n cos(\frac{\pi n}{2})=\frac{1}{2}$

Step-by-step explanation:

$\sum_{n=0}^9cos(\frac{\pi n}{2})=\frac{1}{2}(\sum_{n=0}^9 (e^{\frac{i\pi n}{2}}+ e^{\frac{i\pi n}{2}}))$

$=\frac{1}{2}(\frac{1-e^{\frac{10i\pi}{2}}}{1-e^{\frac{i\pi}{2}}}+\frac{1-e^{-\frac{10i\pi}{2}}}{1-e^{-\frac{i\pi}{2}}})$

$=\frac{1}{2}(\frac{1+1}{1-i}+\frac{1+1}{1+i})=1$

2nd

$\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=\frac{1-e^{\frac{i2\pi N}{N}}}{1-e^{\frac{i2\pi}{N}}}$

$=\frac{1-1}{1-e^{\frac{i2\pi}{N}}}=0$

3th

$\sum_{n=0}^\infty (\frac{1}{2})^n cos(\frac{\pi n}{2})==\frac{1}{2}(\sum_{n=0}^\infty ((\frac{e^{\frac{i\pi n}{2}}}{2})^n+ (\frac{e^{-\frac{i\pi n}{2}}}{2})^n))$