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3 years ago

Where p and q are statements, p q is called the _____ of p and q.

Mathematics

2 answers:

dsp733 years ago

7 0

Answer with explanation:

It is given that , p and q are statements.

The Meaning of , p q is either,

1. p and q → Symbolic Representation→ p ∧ q

2. p or q → Symbolic Representation→ p ∨ q

"Statement" p q is a conditional statement which represents If p, then q, in which , p is a statement which is supposed as basis of reasoning and q is the conclusion drawn from it.

→→So, Where p and q are statements, p q is called the " Conditional Statement" of p and q.

enot [183]3 years ago

6 0

The answer is product.

When two or more numbers or variables are multiplied together, the final result after multiplication is called the product. So, since pq is the multiplication of p and q, then pq is the product.

Hope this helps :)

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Step-by-step explanation:

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3 years ago

What is the factorization of 729^15+1000?

igomit [66]

Answer:

The factorization of $729x^{15} +1000$ is $(9x^{5} +10)(81x^{10} -90x^{5} +100)$

Step-by-step explanation:

This is a case of factorization by sum and difference of cubes, this type of factorization applies only in binomials of the form $(a^{3} +b^{3} )$ or $(a^{3} -b^{3})$ . It is easy to recognize because the coefficients of the terms are perfect cube numbers (which means numbers that have exact cubic root, such as 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, etc.) and the exponents of the letters a and b are multiples of three (such as 3, 6, 9, 12, 15, 18, etc.).

Let's solve the factorization of $729x^{15} +1000$ by using the sum and difference of cubes factorization.

1.) We calculate the cubic root of each term in the equation $729x^{15} +1000$ , and the exponent of the letter x is divided by 3.

$\sqrt[3]{729x^{15}} =9x^{5}$

$1000=10^{3}$ then $\sqrt[3]{10^{3}} =10$

So, we got that

$729x^{15} +1000=(9x^{5})^{3} + (10)^{3}$ which has the form of $(a^{3} +b^{3} )$ which means is a sum of cubes.

Sum of cubes

$(a^{3} +b^{3} )=(a+b)(a^{2} -ab+b^{2})$

with $a= 9x^{5}$ y $b=10$

2.) Solving the sum of cubes.

$(9x^{5})^{3} + (10)^{3}=(9x^{5} +10)((9x^{5})^{2}-(9x^{5})(10)+10^{2} )$

$(9x^{5})^{3} + (10)^{3}=(9x^{5} +10)(81x^{10}-90x^{5}+100)$

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Answer:

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