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Artyom0805 [142]
3 years ago
6

PICTURE INCLUDED. WILL GIVE YOU BRAINLIEST

Mathematics
1 answer:
AfilCa [17]3 years ago
3 0
Purple line: axis of symmetry
Orange curve: parabola
Black dots: zero, x intercept, asymptote
Red dot: minimum, maximum, dilation
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Whats the intrgral of <img src="https://tex.z-dn.net/?f=%20%5Cint%20%20%5Cfrac%7Bx%5E2%2Bx-3%7D%7B%28x%5E3%2Bx%5E2-4x-4%29%5E2%7
rosijanka [135]
\displaystyle\int\frac{x^2+x-3}{(x^3+x^2-4x-4)^2}\,\mathrm dx

Notice that x^3+x^2-4x-4=x^2(x+1)-4(x+1)=(x-2)(x+2)(x+1). Decompose the integrand into partial fractions:

\dfrac{x^2+x-3}{(x-2)^2(x+2)^2(x+1)^2}
=\dfrac1{3(x+1)}-\dfrac{11}{32(x+2)}-\dfrac1{3(x+1)^2}-\dfrac1{16(x+2)^2}+\dfrac1{96(x-2)}+\dfrac1{48(x-2)^2}

Integrating term-by-term, you get

\displaystyle\int\frac{x^2+x-3}{(x^3+x^2-4x-4)^2}\,\mathrm dx
=-\dfrac1{48(x-2)}+\dfrac1{3(x+1)}+\dfrac1{16(x+2)}+\dfrac1{96}\ln|x-2|+\dfrac13\ln|x+1|-\dfrac{11}{32}\ln|x+2|+C
5 0
4 years ago
HELP!!! First gets Top Answer!!!
Marta_Voda [28]
It is approximately -.4048

H=10^(-pH)

log H = -pH

pH=-logH => so it is affirmed that it is -.40

4 0
4 years ago
In an isosceles triangle the base angles are congruent. True False
kherson [118]
This statement is false<span>. Because the </span>base angles<span> of an </span>isosceles triangle<span> are</span>congruent<span>, if one </span>base angle<span> is a right </span>angle<span> then both </span>base angles<span> must be right</span>angles<span>. It is impossible to have a </span>triangle<span> with two right (90^\circ)</span>angles<span>.</span>
4 0
4 years ago
Read 2 more answers
2 questions here:
solmaris [256]
<span>1. Make y the subject 
a) 4y=12x+18
y = 3x + 4.5

b) 2x=7-3y
3y = -2x + 7
y = -2/3x + 7/3

2.
a) what is the equation of the line which passes through both (-2,-4) and (6,16)

slope = (16 + 4)/(6 +2) = 20/8 = 2.5
y = mx + b
-4 =2.5(-2) +b
-4 = -5 +b
b = 1

equation
y = 2.5x + 1


b) what is the equation of the line perpendicular to y= 1/2X + 7 passing through point (3,9)

</span>y= 1/2X + 7
slope = 1/2

slope of line perpendicular = -2

passing through point (3,9)

y = mx + b
9 = -2 (3) + b
b = 15

equation

y = -2x + 15

6 0
3 years ago
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When is a quadrilateral a parallelogram?
brilliants [131]
C. when opposite sides are congruent and parallel
6 0
3 years ago
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