# Posts by Mgraph

Total # Posts: 309

Calculus
a)f(x)=(x+2)(x-1)(x-2) c)From the graph a>=2, b>=0. The equation of the tangent y=b+(3a^2-2a-4)(x-a) and if x=0 y=b-(3a^3-2a^2-4a) or y=a^3-a^2-4a+4-(3a^3-2a^2-4a) y=-2a^3+a^2+4=(2-a)(6+3a+2a^2)-8 If a>2 then y<-8 (a,b)=(2,0)

Calc
The equation of a circle with the center at origin and passing through (1,sqrt3)is x^2+y^2=2^2 The distance between the point and semicircle is the difference R1-R2=4-2=2

CALCULUS
4sin^2(x)cos^2(x)=(sin2x)^2 (sin2x/cos2x)dx=(-1/2)d(cos2x)/cos2x

calculus
B)CLOCKWISE In 1st quadrant (for ex.)dx/dt>0, so x increases; C)dx/dt=d(cos(theta))/dt= d(cos(theta))/d(theta)*d(theta)/dt= -sin(theta)*d(theta)/dx, so dx/dt=-y*d(theta)/dt =>d(theta)/dt=-1

calculus
F(x) = f(xf(xf(x))) F'(x) = f'(xf(xf(x))) d/dx xf(xf(x)) F'(x) = f'(xf(xf(x))) [ f(xf(x)) + xf'(xf(x)) d/dx xf(x) ] F'(x) = f'(xf(xf(x))) [ f(xf(x)) + xf'(xf(x)) [f(x) + xf'(x)] ] F'(1) = f'(1*f(1*f(1))) [ f(1*f(1)) + 1*f'(1*f(1...

Math
-52 mod 13 = 0 -45-(-52)=7

calculus
3,4,5,6 2,3,6,7 2,4,5,7 1,4,5,8 1,2,7,8 1,3,6,8 1,4,5,8 (4,4,5,5)?

Calculus
We integrate by parts twice: 1)u=x^2, du=2xdx, dv=cos(x/4)dx, v=4sin(x/4) 2)u=8x, du=8dx, dv=sin(x/4)dx, v=-4cos(x/4) The answer I have already sent.

Math: Factoring
sqrt-2/3 ?

Math: Factoring
sqrt=square root?

HELP!!!!!!!!!GEOMETRY!!!!
You're welcome.

HELP!!!!!!!!!GEOMETRY!!!!
AB=sqrt(((-5)-(-4))^2+(1-(-3))^2)= sqrt((-1)^2+4^2)=sqrt(17) The perimeter=4*AB

math
3x^2-15x=6x^2-16x 3x^2-x=0 x(3x-1)=0 x=0 or x=1/3

College Algebra
Let it takes Todd X hours; Tom Y hours. X=Y+3 For one hour, Todd paints 1/X part of the bedroom, Tom - 1/Y; together - 1/X+1/Y 1/(1/X+1/Y)=2 2(X+Y)=XY 2(2Y+3)=(Y+3)Y 4Y+6=Y^2+3Y Y^2-Y-6=0 => Y=3, X=6

Maths
B3=20 The sum=B1/(1-q)=3*B1 =>q=2/3 B3=B1*q^2 20=B1*4/9 =>B1=45

trig
3sin^2(x)+sin(x)cos(x)=2sin^2(x)+2cos^2(x) sin^2(x)+sin(x)cos(x)-2cos^2(x)=0 Divide by cos^2(x) tan^2(x)+tan(x)-2=0 (tan(x)+2)(tan(x)-1)=0 tan(x)=-2 => x=-Arctan(2)+pi*n tan(x)=1 => x=pi/4+pi*n

applied maths
The average velocity=distance/time, time=60s distance=2*10^2/2+20*45+4*5^2/2=1050m

calculus
We want to "guess" that limh(x)=1/3 if x->0 h(1)=(tan(1)-1)/1^3=0.557408 h(0.1)=0.334672 h(0.005)=(tan(0.005)-0.005)/0.005^3=0.333342

calculus
f'(x)=11x^10*h(x)+x^11*h'(x) f'(-1)=11(-1)^10*h(-1)+(-1)^11*h'(-1)

Calculus
Antiderivative (one of) of y is 4sin(x/4)(x^2-32)+32x*cos(x/4)

Calculus II
Lengths of the sides of these squares are equal to y. The volume=Int(from -4 to 4)y^2dx= 2*Int(from 0 to 4)(16-x^2)dx= 2*(16x-x^3/3)(from 0 to 4)= 2(64-64/3)

math
124-6*(0+15)=34

trig

calculus
I agree with bobpursley if 0<x<=4 or 4<=x

calculus
What is f(4)?

f(0)=(0-1/2)^2(0+1)

math
There were 3 eggs.

MATH help
Straight line is a special case of the curve just like the natural numbers are a special case of integers

MATH help
cos^2(t)=(1-x)/3 sin^2(t)=(y+2)/4 Add two equations 1=(1-x)/3+(y+2)/4 12=4-4x+3y+6 y=(4/3)x+2/3

calculus 2
y-2=4x-x^2 The volume=pi*Int.[0,4](4x-x^2)^2dx= pi*Int.[0,4](16x^2-8x^3+x^4)dx= pi*(16/3x^3-2x^4+1/5x^5)[0,4]= pi*(1024/3-512+1024/5)=pi*1024/30

geometry
Let R(x1,y1), S(x2,y2), then x1=(2*2+8)/3=4, y1=(2*3+(-9))/3=-1 x2=(2+2*8)/3=6, y2=(3+2*(-9))/3=-5

calculus
For all x: 0<=x<=pi/2 4sin(x)<e^(7x) We begin to integrate with respect to y: Int.[from 4sin(x) to e^(7x)]...dy

Math
(x-4)^2+y^2=16 x^2-8x+16+y^2=16 x^2+y^2=8x r^2=8r*cos(theta) r=8cos(theta)

Math
x=7cos(30), y=7sin(30)

First find (x-3i)(x+3i)=x^2+9 and then (x-3)(x^2+9)=x^3-3x^2+9x-27

Geometry
AC=BD...

Geometry
34=2x-10

algebra
Let we invest \$X in 1st fund, then 0.115X+0.14(15000-X)=1950 0.115X+2100-0.14X=1950 150=0.025X X=6000

statistics
p=.001, n=2000 a)Expected number of errors=np=2 b)P(k)=2000Ck*.001^k*.999^(2000-k) c)P(0)=.999^2000 d)P(1)=2000*.001*.999^1999 e)P(k>=1)=1-P(0)

Calculus (typo)
Int=1/5(sin(t)-t*COS(t))+C

Calculus
t=x^5, dt=5x^4dx x^9*sin(x^5)dx=x^5*sin(x^5)*x^4*dx= t*sin(t)*(1/5)dt Int=1/5(sin(t)-t*sin(t))+C, t=x^5

Calculus
If z=cos(2q) then dz=-2sin(2q)dq. Integral=-1/2*Integral z^4dz= -1/10*z^5+C

statistics
66-5*3-5*9

calculus
Reiny found a positive root but there is a negative root x=-0.55 (approximately) We can started with x=-1

Mathematics optimization
f'(c)=(b^2-a^2)/(b-a)=b+a=2c=>c=(a+b)/2

calculus
a^2-b^2=(a-b)(a+b) 4-x^2=2^2-x^2

calculus
1)x^2(x^2-9)=x^2(x-3)(x+3)>0 x>3 or x<-3 2)x*2^x(4-x^2)=x*2^x(2-x)(2+x)<=0 -2<=x<=0 or x>=2

Math
232,441

Algebra 2
2011/0 is not real number

math
The length is x and 70-x. The area is 7x=210

MATHS
Let segments AB and CD have common point E. Then AC<AE+EC and BD<BE+ED. AE+EC+BE+ED=AB+CD

Math OPTIMIZATION
y(12-x-y)=4(12-4-4)=16

Math OPTIMIZATION
The total area A=A(x,y). A=x(12-x)+y(12-x-y)=12x-x^2+12y-xy-y^2 Partial derivatives A'x=12-2x-y A'y=12-x-2y Solve the equations A'x=A'y=0 => a. x=y=4 b. Amax=32+16=48 c. 24+16=40

Math
2(4)=8

College Precalculus
14x/(x^2-121)>=0 14x/((x-11)(x+11))>=0 x>11 or -11<x<=0

College Precalculus
7x+17>0

Math
59+95=154

Math
n+(n+1)=x 2n+1=x 2n=x-1 n is the lesser of two numbers

Math
x^2-y^2=(x-y)(x+y)=(2b/a)(2a/b)=4

statistics
1.2=(score on the test - 100)/15

math
Let f (n) - the number of options that a cat can pass through n steps. On the n - th step can proceed or (n - 1) - th, or (n - 2) - th. Number of options to pass n is the number of steps to pass the options n - 1 steps plus the number of options to pass n - 2 steps, that is f...

Algebra
??? 4y-2y=34-26

Math
3x+3+5x-7=180 or =Pi

calculus
Z'x=12x^3+12x^2=0=>x=0 or x=-1 Z'y=24y^3-48y^2+24y=0=>y=0 or y=1 Z(0,0)=0 Z(0,1)=2 Z(-1,0)=-1 <---Lowest Z(-1,1)=1

{-7,-6,-5}

math
y=(3/2)(x^2+x)

trig
sin^2(theta)=1-(-3/4)^2=7/16 => sin(theta)=+ or -sqrt(7)/4 sin(2theta)=2*sin(theta)*cos(theta)

algebra
y=195-15*x

Trig
sin(-315)=sin(-315+360)=sin(45)=sqrt(2)/2

maths
volume=3.14159*(150cm)^2*(72-70)cm

calculus
If f(x)=x^3+5x then f(3)=27+15=42, f(6)=216+36=252 and slope=(252-42)/(6-3)

math
nonlinear, f(3)=2*3^2-3*3+4=18-9+4 f(-3)=2*(-3)^2-3*(-3)+4=18+9+4

y=-x^4+6

Applied Calculus
C(x)=ax+b a*10000+b=5380 a*15000+b=7690

math
Let the distance to school S, my speed=S/30 the speed of my brother=S/40 and I catch up with him after t min. Then S/40*(t+8)=S/30*t 30t+240=40t

calculus
1/(x^2-90^2)

ALGEBRA II ( inaccuracy
... add the two last eq. 3S1+S2=28 ... 4S1=28

Trigonometry
8sin^2+2cos^2=8sin^2+2(1-sin^2)=> a=6 & b=2

Math
1,7,7,13

statistics
range=max-min=99-78=21 sample mean=(78+91+93+93+99)/5=90.8 (78-90.8)^2=163.84 (91-90.8)^2=0.04 (93-90.8)^2=4.84 (99-90.8)^2=67.24 sample variance=(163.84+0.04+4.84+4.84+67.24)/4=60.2

calculus
The equation of this plane is -3(x-7)+1(y-1)+2(z-5)=0 or -3x+y+2z+10=0

math
Let Y=1/(X+1) then y:1, 1/2, 1/3, 1/4 P(Y=y):1/6, 1/2, 1/5, 2/15 E(Y)=1*1/6+1/2*1/2+1/3*1/5+1/4*2/15

calculus
PQ^2=1+9+4=14 PR^2=25+1+9=35 QR^2=16+4+1=21

math
3*5+6^2+54-5

math
From the terms of problem => r=1 doesn't satisfy (S13=21, S21=13). From my proof => such G.P. doesn't exist.

math
I'll try to show that the equation of Reiny 21r^21-13r^13=8 has only one real solution r=1. Let F(r)=21r^21-13r^13-8, F(1)=0. F'(r)=441r^20-169r^12= =169r^12(441/169r^8-1)=169r^2(21/13r^4+1)* (21/13r^4-1)=169r^2(21/13r^4+1)* (sqrt(21/13)r^2+1)(sqrt(21/13)r^2-1) F'...

calc 1
f'(c)=(f(4)-f(1))/(4-1) f(4)=4/6=2/3 f(1)=1/3 f'(c)=1/9 f'(x)=(x+2-x)/(x+2)^2 2/(c+2)^2=1/9 (c+2)^2=18 c+2=3*sqrt(2)

1/2 cup fraction word problem
1/2=(1*7)/(2*7)=7/14

math
=(16*x^2*y*4*x^5*y^2*z)^1/3= =(64*x^7*y^6*z)^1/3= =64^1/3*(x^7)^1/3*(y^6)^1/3*z^1/3= 4*x^(7/3)*y^2*z^1/3

HELPPP!! rate of change
(y-2)/(4-(-1))=-4/5

calculus2
You can change 1 and 0. The simplest example of non-integrable function are: 1/x in the interval [0, b]

calculus2
An example of this is the function that is 1 on any rational number and 0 elsewhere.

f(y)=1 when y not 0 f(y)=0 when y=0 g(x)=0 when x-is irrational number g(x)=1/p when x=q/p, p&q-coprime numbers f(g(x))=0 when x-is irrational f(g(x))=1 when x=q/p

Trigonometry
cos(76pi)=cos(74pi)=...=cos(2pi)=cos0=1 sec(23pi)=sec(21pi)=...=sec(3pi)=sec(pi)= -1 because the period T=2pi (If pi=n)

Math
log(20/9)=log20-log9=log10+log2-log9= =1+0.30-0.95

Math
The accumulation value at the end of nth period A=P(1+i)^n A=1000*1.09^8=1,992.56

Math
5000=2500*1.03^t 1.03^t=2 t=ln2/ln1.03=23.4

Algebra
An=12Cn*x^(12-n)*y^n, n=0,1,2,3,...,12 A6=12C6*x^6*y^6 12C6=924 BTW, mCn=m!/(n!(m-n)!)

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