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3 years ago

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Mathematics

1 answer:

Elis [28]3 years ago

3 0

Answer: I believe the answer to that question is no

Step-by-step explanation: So you see, when there are not symbols that represent addition or subtraction, or any other operation, it's not considered a question.

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Find the integral of √(x² +4) W.R.T x

Allushta [10]

Answer:

$\frac{x}{2} *\sqrt{x^{2} +4}$ + $\frac{1}{2}$ *LN(| $\frac{x+\sqrt{x^{2} +4} }{2}$ |) +C

Step-by-step explanation:

we will have to do a trig sub for this

use x=a*tanθ for sqrt(x^2 +a^2) where a=2

x=2tanθ, dx= 2 sec^2 (θ) dθ

this turns $\int\limits {\sqrt{x^{2}+4 } } \, dx$ into integral(sqrt( [2tanθ]^2 +4) * 2sec^2 (θ) )dθ

the sqrt( [2tanθ]^2 +4) will condense into 2sec^2 (θ) after converting tan^2(θ) into sec^2(θ) -1

then it simplifies into integral(4*sec^3 (θ)) dθ

you will need to do integration by parts to work out the integral of sec^3(θ) but it will turn into (1/2)sec(θ)tan(θ) + (1/2) LN(|sec(θ)+tan(θ)|) +C

then you will need to rework your functions of θ back into functions of x

tanθ will resolve back into $\frac{x}{2}$ (see substitutions) while secθ will resolve into $\frac{\sqrt{x^{2} +4} }{2}$

sec(θ)= $\frac{\sqrt{x^{2} +4} }{2}$ is from its ratio identity of hyp/adj where the hyp. is $\sqrt{x^{2} +4}$ and adj is 2 (see tan(θ) ratio)

after resolving back into functions of x, substitute ratios for trig functions:

= $\frac{x}{2} *\sqrt{x^{2} +4}$ + $\frac{1}{2}$ *LN(| $\frac{x+\sqrt{x^{2} +4} }{2}$ |) +C

3 0

3 years ago

Choose the product. (3x^2 + 2x - 3)(x - 1)

PIT_PIT [208]

Step by step is like....:

(3x2+2x−3)(x−1)
=(3x2+2x+−3)(x+−1)
=(3x2)(x)+(3x2)(−1)+(2x)(x)+(2x)(−1)+(−3)(x)+(−3)(−1)
=3x3−3x2+2x2−2x−3x+3
=3x3−x2−5x+3

Hoped I helped!

4 0

4 years ago

The function f(x) is graphed below. Determine whether the degree of the function is

pychu [463]

It’s is even bc it doesn’t go through the origin

5 0

3 years ago

Read 2 more answers

What two integers have a product of -20 and a sum of -8

Rufina [12.5K]

-10 and 2
-10 x 2 = -20
-10 + 2 = -8

7 0

3 years ago

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PLEASE ANSWER: 3 1/2 + (-7) x (2 2/3 + 1 1/2) = ?

Novay_Z [31]

Answer:

$-\frac{77}{3}$

Step-by-step explanation:

So we have the equation: $3\frac{1}{2} + (-7) * (2\frac{2}{3} + 1\frac{1}{2})$ . and I'm assuming you meant to do mixed fractions and not actually multiplying. 2 * 2/3. So the first thing to do is follow PEMDAS which essentially says Parenthesis first, Exponents next, Multiplication or Division, and then Addition or Subtract. So let's start by evaluating the 2 2/3 and 1 1/2. The first step is to combine 2 into the 2/3 and the 1 into 1/2. This is done by multiplying the 2 by the denominator of 3, and adding it to the numerator so: $2\frac{2}{3} = > \frac{(2*3)+2}{3} = > \frac{8}{3}$ . And you do this for the 1/2 as well: $1\frac{1}{2} = > \frac{(2*1)+1}{2}= > \frac{3}{2}$ .

Now when adding fractions, you can only add them when they have the same denominator, so we have the get 3/2 and 8/3 to have the same denominator. You can list the multiplies of 2 and 3 to try to find a LCM, but in this case, I'll just multiply 2 and 3, since they're really small numbers, also because 6 is the LCM. $\frac{8}{3} * \frac{2}{2} = \frac{16}{6}$ . And now do this to the 3/2 you get: $\frac{3}{2} * \frac{3}{3} = \frac{9}{6}$ . Now the inside of the parenthesis is: $\frac{9}{6} + \frac{16}{6} = \frac{25}{6}$ . So now we have the equation: $3\frac{1}{2} -7 * \frac{25}{6}$ . Also notice how I got ride of the plus sign and made it negative? Think of it as having a 1 in front and simply distributing that to the -7, 1*(-7) becomes -7.

Now to multiply the fraction by a whole number you simply multiply the denominator and numerator, and you can think of the denominator of a whole number as a 1. So this gives you: $\frac{-7}{1} * \frac{25}{6} = \frac{-7 * 25}{1 * 6} = -\frac{175}{6}$ . Now we have the equation: $3\frac{1}{2} - \frac{175}{6}$ . And to subtract these two numbers I'll make the 3 1/2 a fraction by multiplying the 3 by the denominator and adding it to the 1 which should become 7/2. And after that multiply both sides by 3/3 to get 21/6 so they have the same denominator. This gives you the equation: $\frac{21}{6} - \frac{175}{6} = \frac{21-175}{6} = -\frac{154}{6}$ . Which can simplify by dividing both sides by 2 to get: $-\frac{77}{3}$

6 0

2 years ago

Read 2 more answers