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zlopas [31]
3 years ago
14

Match each root with its meaning.

Mathematics
1 answer:
IRISSAK [1]3 years ago
7 0
Port is to carry
Voc is to voice or call
Tract is to pull
Vac is to empty
Struct is to build or form
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Evaluate using integration by parts ​
PolarNik [594]

Rather than carrying out IBP several times, let's establish a more general result. Let

I(n)=\displaystyle\int x^ne^x\,\mathrm dx

One round of IBP, setting

u=x^n\implies\mathrm du=nx^{n-1}\,\mathrm dx

\mathrm dv=e^x\,\mathrm dx\implies v=e^x

gives

\displaystyle I(n)=x^ne^x-n\int x^{n-1}e^x\,\mathrm dx

I(n)=x^ne^x-nI(n-1)

This is called a power-reduction formula. We could try solving for I(n) explicitly, but no need. n=5 is small enough to just expand I(5) as much as we need to.

I(5)=x^5e^x-5I(4)

I(5)=x^5e^x-5(x^4e^x-4I(3))=(x-5)x^4e^x+20I(3)

I(5)=(x-5)x^4e^x+20(x^3e^x-3I(2))=(x^2-5x+20)x^3e^x-60I(2)

I(5)=(x^2-5x+20)x^3e^x-60(x^2e^x-2I(1))=(x^3-5x^2+20x-60)x^2e^x+120I(1)

I(5)=(x^3-5x^2+20x-60)x^2e^x+120(xe^x-I(0))

Finally,

I(0)=\displaystyle\int e^x\,\mathrm dx=e^x+C

so we end up with

I(5)=(x^4-5x^3+20x^2-60x+120)xe^x-120e^x+C

I(5)=(x^5-5x^4+20x^3-60x^2+120x-120)e^x+C

and the antiderivative is

\displaystyle\int2x^5e^x\,\mathrm dx=(2x^5-10x^4+40x^3-120x^2+240x-240)e^x+C

8 0
2 years ago
Need help on this one question please
Elan Coil [88]
P(x, y) Q(x,y)
P(-2, -1) start at 0. Go to the left two squares, then go down 1 square. mark a point there
Q(2, 4) start at 0. Go to the right two squares, go up 4 squares. mark a point there.
connect two points
make a right triangle
Then use the pythereom 
4^{2} + 5^{2} = (PQ)^{2}
41 = (PQ)^{2}
\sqrt{41}  = PQ

6 0
2 years ago
If f(x)=-9x-3, find f(-5)
Andrews [41]

Answer:

42

Step-by-step explanation:

f(-5) = -9 × (-5) - 3 = 45 - 3 = 42

If you have any questions about the way I solved it, don't hesitate to ask me in the comments below =)

5 0
3 years ago
Which binomial is a factor of 49x2 + 84 xy + 36y2?
bezimeni [28]

Answer:

(7x+6y) is a binomial factor of the given expression  49x^2+84xy+36y^2

Therefore  49x^2+84xy+36y^2=(7x+6y)(7x+6y)

Step-by-step explanation:

Given expression is 49x^2+84xy+36y^2

To find the binomial factor :

49x^2+84xy+36y^2

Rewritting the above expression as

=7^2x^2+2(7)(6)xy+6^2y^2

=(7x)^2+2(7x)(6y)+(6y)^2

=(7x+6y)^2 ( using the formula =(a+b)^2=a^2+2ab+b^2 here a=7x and y=6y )

=(7x+6y)(7x+6y) ( using the formula =(a+b)^2=(a+b)(a+b) )

Therefore  49x^2+84xy+36y^2=(7x+6y)(7x+6y)

(7x+6y) is a binomial factor of the given expression  49x^2+84xy+36y^2

7 0
3 years ago
Can u help me with number 4 ?
Sati [7]

Answer: um how can l help you with 4

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
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