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2 years ago

Integral formula! and example!

Mathematics

1 answer:

telo118 [61]2 years ago

7 0

Answer:

Formula for Integration:

Formula for Integration:\int {1\over x} \;dx= \ln x+C. \int \sin x\;dx=-\cos x+C. \int \cos x\;dx= \sin x + C. \int \sec^2 x\;dx=\tan x+C.

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Show work and Factor 4x^2+xy-18y^2

grigory [225]

Answer:

$4x^2+xy-18y^2=(4x+9y)\,(x-2y)$

Step-by-step explanation:

Let's examine the following general product of two binomials with variables x and y in different terms:

$(ax+by)\,(cx+dy)= ac\,x^2+adxy+bcxy+bdy^2$

so we want the following to happen:

$a\,c = 4\\ad+bc=1\\bd--18$

Notice as well that $ad+bc =1$ means that those two products must differ in just one unit so, one of them has to be negative, or three of them negative. Given that the product $bd=-18$ , then we can consider the case in which one of this (b or d) is the negative factor. So let's then assume that $a\,\,and \,\,c$ are positive.

We can then try combinations for $a\,\,and \,\,c$ such as:

$a = 4;\,\,c=1\\a=2;\,\,c=2\\a=1;\,\,c=4$

Just by selecting the first one $(a=4;\,\,c=1)$

we get that $4d_b=1\\b=-4d-1$

and since

$bd=-18\\(-4d-1)\,d=-18\\-4d^2-d=-18\\4d^2+d-18=0$

This quadratic equation give as one of its solutions the integer: d = -2, and consequently,

$d=-18/(-2)\\d=9$

Now we have a good combination of parameters to render the factoring form of the original trinomial:

$a=4; \,\,b=9;\,\,c=1;\,\,d=-2$

which makes our factorization:

$(4x+9y)\,(x-2y)=4x^2+xy-18y^2$

6 0

3 years ago

Write and solve a proportion to answer the question. (Skills Review Handbook) 22. 30 is 15% of what number?

algol13

Answer:

The answer is 148.6666667

Step-by-step explanation:

1) Set a linear quation

$\frac{22.30}{x} = \frac{15}{100}$

2) Cross multiply

$15x = 22.30 \times 100$

3) Multiple the right side

$15x = 2230$

4) Divide both side by 15

$\frac{15x}{15} = \frac{2230}{15}$

5) Solve the linear equation

$x = 148.6666667$

3 0

2 years ago

What is the solution, if any, to the inequality |3x|≥0?

Murljashka [212]

The inequality is all real numbers.

<h3>What is inequality?</h3>

A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

Given:

|3x|≥0

3x = 0

Divide both sides of the equation by the coefficient of variable

x= 0/3

x=0 = RHS

Learn more about inequality here:

brainly.com/question/20383699

#SPJ1

4 0

2 years ago

What is 3.47 x 10^-6 times 4.61 x 10^7 equals? And what is 3.47 x 10^-6 over 4.61 x 10^7 in scientific notation. Also what is 5.