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denis-greek [22]
2 years ago
15

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.
zzz [600]
1st 159.967 2nd 7.52711×10^-14 3rd 1.59078×10^13
8 0
4 years ago
Read 2 more answers
How can I divide larger dividends.
Sphinxa [80]
You can add a decimal point at the end of number then zero. Example....
2.40
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5| 12.00
-10
________
20
-20
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0


2.4
8 0
3 years ago
Read 2 more answers
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