# Posts by Mgraph

Total # Posts: 309

Math
The present value An of the annuity=10,000 An=p*(1-(1+i)^-n)/i 10000=750*(1-1.05^-n)/0.05 500=750*(1-1.05^-n) 2/3=1-1.05^-n 1.05^-n=1/3 1.05^n=3 n=ln3/ln1.05=22.51708531

Math
(1+ nominal rate)= =(1+ inflation rate)(1+ risk free rate)

Math-Calc
I mean cos(-0.000000001)/sin(-0.000000001)= =-999999999

Math-Calc
sin(-0.000000001)=-0.000000001 cos(-0.000000001)=0.999999999 sin/cos=-999999999

pre calc
Consider the geometric method. b(b>0)- is the leg in a isosceles rectangular triangle with height=6 6^2+6^2=b^2

pre calc
Draw two tangents to the circle x^2+y^2=6^2 parallel to the line y=x in the second and fourth quadrants. b is y-intercept of these tangents. Сonsider the algebraic method. Find the coordinates of common points of the line and circle: x^2+(x+b)^2=36 2x^2+2bx+b^2-36=0 ...

PRE CALC
x=1, y=-4, z=-5

Math
Yes

Math
If you say a system is consistent, it means that it can be solved. If you say a system is inconsistent, it means that the system has no solution. If a system is dependent, it has infinite solutions and if it is independent, it has a unique solution. Both dependent and ...

Math
Domain {1,2,3,4} Range {3} Yes

math
Мultiply both sides by 3x if 1/(3x) or by 3 if (1/3)x

Calculus ll
f'x=e^2y (e^2y-const) f'y=2xe^2y (x-const)

COLLEGE ALGEBRA ..HELP!
Don't worry sometimes it happens that 2*2=5

COLLEGE ALGEBRA ..HELP!
x^2+11/12x=5/12 x^2+2*(11/24)*x+(11/24)^2=5/12+(11/24)^2 (x+11/24)^2=(19/24)^2 x+11/24=19/24 or x+11/24=-19/24

pre calc
Solve the system: a*0^3+b*0^2+c*0+d=-4 a*1^3+b*1^2+c*1+d=-8 a*(-1)^3+b+(-1)^2+c*(-1)+d=-8 a*2^3+b*2^2+c*2+d=-2 d=-4 a+b+c+d=-8 -a+b-c+d=-8 8a+4b+2c+d=-2 Add the 2nd and the 3rd: 2b+2d=-16 d=-4 b=-4 a+c=0 8a+2c=18 Subtract from the 4th 2*3rd: 6a=18 a=3, b=-4, c=-3, d=-4

maths (trigonometry)
Q2)Because sina, cosa, tana - g.p. cos^2(a)=sina*tana=sin^2(a)/cosa cos^2(a)=(1-cos^2(a))/cosa cos^3(a)=1-cos^2(a)

Math quick check thx
Math failed: 1,2,3,4,5,6,7,8,9,10,11,12,13 Ela failed: 10,11,12,13,14,...,33,34,35 Neither: 36,37,38,39,40,41,42

(62-mean)/st.dev.=-3.75 (83-mean)/st.dev.=1.5 Solve this system.

M+2M-4+7=42 M=13 failed Math

math
x^2+2xy+y^2+x+y-2=(x+y+2)(x+y-1) y=-x-2 y=-x+1

maths (trigonometry)
45&15

Calculus AB
(x^2+1)/(x^2-x)=(x^2-x+x+1)/(x^2-x)= =1+(x+1)/(x^2-x)=1+2/(x-1)-1/x

Calculus AB
x^3-x^2+x+3=(x+1)(x^2-2x+3) (x^2+5)/(x^3-x^2+x+3)= =A/(x+1)+(Bx+C)/(x^2-2x+3) A(x^2-2x+3)+(Bx+C)(x+1)=x^2+5 A+B=1 -2A+B+C=0 3A+C=5 Find A,B,C

Maths
Let f(x)=x^3-x^2-8x=x(x^2-x-8). f(x) has 3 real roots. f'(x)=3x^2-2x-8=(3x+4)(x-2) maxf(x)=f(-4/3)=-64/27-16/9+32/3=176/27 minf(x)=f(2)=8-4-16=-12 -176/27<k<12

college algebra
(7h+j)(6h-5j)

arithmetic
If a:b:c=2:1:3 then a=2b, c=3b If 2a-3b+c=8 then 4b-3b+3b=8, b=2

TRIGO
Let z=tan^2(x), z>0 F(z)=9z+4/z, F'(z)=9-4/z^2, F'(z)=0 if z=2/3 minF(z)=F(2/3)=12 (corresponding value of x exists)

Pre calc
Do you know how to solve equation a*sinx+b*cosx=c ?

Pre calc
cosx/1+sinx or cosx/(1+sinx) 1+six/cosx or (1+sinx)/cosx ?

Trig
Multiply both sides by sin^2(x). sin^2(x)=cos^2(x)+sin(x) sin^2(x)=1-sin^2(x)+sin(x) 2sin^2(x)-sin(x)-1=0 (2sin(x)+1)(sin(x)-1)=0 sin(x)=-1/2, x=7pi/6, x=11pi/6 or sin(x)=1, x=pi/2

math
342

math 12
I think that nobody knows how to solve it algebraically. If x=16 left side=0, right side=2.3*10^(-10) Ask your teacher again.

math
Multiply both sides by log16. log16/log2=4 log16/log4=2 log16/log8=4/3 log16/log16=1 logx(4+2+4/3+1)=25*log16 logx=3*log16 logx=log(16^3) x=16^3=4096 (check the answer at the back)

algebra
(-2)^5

Math - Possible or Potential rational zeros
Potential rational zeros are: +-1,+-2,+-7,+-14 f(-1)=1+7-3-19+14=0 f(x)=(x+1)g(x), g(x)=x^3-8x^2+5x+14 g(-1)=-1-8-5+14=0 g(x)=(x+1)h(x), f(x)=(x+1)^2*h(x), h(x)=x^2-9x+14 h(2)=4-18+14=0 h(x)=(x-2)(x-7) f(x)=(x-2)(x-7)(x+1)^2

Math - Real number system
Let f(x)=x^4+6x^3+x^2-24x-20 Real roots are looking for among +-1,+-2,+-4,+-5,+-10,+-20 f(-1)=1-6+1+24-20=0 Divide f(x) by (x+1): f(x)=(x+1)(x^3+5x^2-4x-20) Let g(x)=x^3+5x^2-4x-20 g(-5)=-125+125+20-20=0 Divide g(x) by (x+5): g(x)=(x+5)(x^2-4) f(x)=(x+1)(x+5)(x+2)(x-2)

Math
If the function f(x) is continuous on [a,b] and f(a)*f(b)<0 then on (a,b) there are at least one zero. Polynomial is continuous on R. Compute f(-2.8) and f(-2.7)

Math
i^3=-i s^2i ???

Math
Substitute: x^2=z => x^4=z^2 z^2-91z-900=0 (z-100)(z+9)=0 If z=100, x^2=100 then x=10 or x=-10 If z=-9, x^2=-9=9i^2 then x=3i or x=-3i

algebra
1)+-1 2),3)+-1,+-5

geometry help
115=height*(4+19)/2

Math
y=x^4-10x^2+7x+30 or y=7x+21 or ...

Statistics
a)k=1-(0.07+0.20+0.38+0.13)=0.22 b)M(X)=0*0.07+1*0.20+2*0.38+3*0.22+4*0.13= =2.14 c)M(X^2)=0*0.07+1*0.20+4*0.38+9*0.22+ +16*0.13=5.78 The standard deviation= =sqrt(M(X^2)-M(X)^2)=1.10

Algebra
Solve the equation: 11200=10000(1+0.048*(how long))

Math
Surface Area=Base Area+Lateral Area SA=BA+LA The side of the octagon a=2*apothem*tan(45/2) BA=0.5*8a*apothem=8*apothem^2*tan(45/2) LA=4a*(slant height) slant height=sqrt(height^2+apothem^2) tan(45/2)=0.4142

Calculus
The vertices of the rectangle are points: (-x,0),(x,0),(x,12-x^2),(-x,12-x^2). The area A(x)=2x(12-x^2) A(x)=24x-2x^3 A'(x)=24-6x^2=0 => x=+-2 max A(x)=A(2)=48-16=32

Geometry
The surface area SA=Pi*r^2+Pi*r*s, s=sqrt(r^2+h^2) 500*Pi=Pi*r^2+Pi*r*sqrt(r^2+225) 500=r^2+r*sqrt(r^2+225) 500-r^2=r*sqrt(r^2+225) (500-r^2)^2=(r*sqrt(r^2+225))^2 250000-1000r^2+r^4=r^2(r^2+225) 250000=1225r^2 r^2=250000/1225

Geometry
RECTANGULAR prism with bases of a RADIUS??

Math
Let A is the length of a side of the larger square, a - of the smaller square. The length of the smaller side of a rectangle is (A-a)/2, the length of the bigger side is (A-a)/2+a. 4a=2((A-a)/2+(A-a)/2+a) 4a=2A A/a=2/1

find real and complex 0
f(x)=x^3+4x^2-2x^2-8x+2x+8=(x^3+4x^2)- (2x^2+8x)+(2x+8)=x^2(x+4)-2x(x+4)+2(x+4)= (x+4)(x^2-2x+2) x+4=0 => x=-4 or x^2-2x+2=0 => x=1+i or x=1-i

Math
L*W*H=7500 2(L*W+L*H+W*H)=2600 This system has an infinite number of solutions and one of them is: L=30, W=25, H=10

Form a polynomial f(x) from coefficient and it's 0
Because the coefficients of f(x) are REAL, f(x) has zeros: 6i and -6i, 7i and -7i. For example, f(x)=(x-6i)(x+6i)(x-7i)(x+7i)= (x^2+36)(x^2+49)

Statistics
The formula of the conditional probability P(X\Y)=P(XY)/P(Y) a)Y="at least one is a boy" Y=BB+BG+GB, P(Y)=3/4 X=BB If X then Y => XY=X P(XY)=P(X)=1/4 P(X\Y)=(1/4)/(3/4)=1/3 b)Y="the older child is a boy" Y=BB+BG, P(Y)=1/2 X=BB, XY=X, P(XY)=1/4 P(X/Y)=(1/...

Math

math
Differentiating the equation: x*f(x)=-(x^2+1)*f(x)+1 f(x)=1/(x^2+x+1)

statistics
X=2=1+1 (1st face + 2nd face)P=1/36 X=3=1+2=2+1 P=2/36 X=4=1+3=3+1=2+2 P=3/36 X=5=1+4=4+1=2+3=3+2 P=4/36 X=6=1+5=5+1=2+4=4+2=3+3 P=5/36 X=7=1+6=6+1=2+5=5+2=3+4=4+3 P=6/36 X=8=2+6=6+2=3+5=5+3=4+4 P=5/36 X=9=3+6=6+3=4+5=5+4 P=4/36 X=10=4+6=6+4=5+5 P=3/36 X=11=5+6=6+5 P=2/36 X=12...

calculus
1)f'(x)=(1/2)*3(x^2-6x+23)^2*(2x-6)= (1/2)*2(x-3)*3(x^2-6x+23)^2= (x-3)*3(x^2-6x+26)=3(x-3)(x^2-6x+23) In the differential equation we separate variables: 27*sqrt(y)dy=2*(x-3)*sqrt(x^2-6x+23)dx Let z=x^2-6x+23 then dz=(x^2-6x+23)'dx dz=(2x-6)dx=2*(x-3)dx 27sqrt(y)dy=...

(1x) ?

Math
DE=BC/2

geometry
12*12cm

math
y^2+2y=2x-5 y^2+2y+1=2x-5+1 (y+1)^2=2x-4 (y+1)^2=4*(1/2)(x-2) vertex (2,-1) focus (2.5,-1) directrix x=1.5

math
1000-31^2=39 (n=31) 39=1*25+14*1 15 coins 39=3*10+9*1 12 coins 39=7*5+4*1 11 coins

math
=w^18-7w^9y^5-2w^9y^5+14y^10= (w^18-7w^9y^5)-(2w^9y^5-14y^10)= w^9(w^9-7y^5)-2y^5(w^9-7y^5)= (w^9-7y^5)(w^9-2y^5)

Trig
Because -pi/2<tan^-1(v)<pi/2 cos(tan^-1(v))=+1/sqrt(v^2+1) (only +)

Trig
1)From definition -->tan(tan^-1(v))=v 2)cos^2(a)=1/(tan^2(a)+1) cos(a)=+-1/sqrt(tan^2(a)+1) cos(tan^-1(v))=+-1/sqrt(v^2+1)

math
Let x- is the side of the barn. The area of the yard A(x)=x*(120-x)/2=60x-x^2/2 A'(x)=60-x=0 => x=60,(120-x)/2=30 max A=1800m^2

Math
30+x=3(6+x)

Algebra
1)y=(+ or -)sqrt(4-(x-2)^2) not a function 2)y=4-x^2-4x function 3)y=4-x function 4)y=4/x function

Algebra
2)... 4y+y...?

Algebra
sqrt(y^2)=absolute value of y ( IyI )

Math
z=(x-m)/б x=zб+m x=1*2+72=74

math
... and one unit to the left

Trig
1.With each point (x,y) we also have point (-x,y)-->the graph is symmetric y-axis 2.With each point (x,y) we have points (-x,y), (x,-y), (-x,-y) --> y-axis, x-axis, origin

algebra
L = T + 42 2L = 5T - 24

algebra
Let y= ax+b then 592=10a+b 968=18a+b and we find a and b.

Calculus
Area=2Pi(int from 0 to 1) y*sqrt(1+(y')^2)dx

Statistics
P=30C10(0.3)^10(0.7)^20

statistics
P=P(5)+P(6)+P(7)+P(8)+P(9)+P(10)+P(11)+ P(12) P(k)=12Ck(0.7)^k(0.3)^(12-k), k=5,6,...,12 You can also find the probability of the opposite event.

maths
Is it an answer on my question? 2cos^2(x)=1+cos(2x) ydy=(2+cos(2x))dx integrating y^2/2=2x+sin(2x)/2+C Find C 1/2=C y=sqrt(4x+sin(2x)+1)

math
a)(x-6)/2=(y-5)/(-3)=(z-1)/7 b)The normal equation of the plane (2/sqrt(62))x-(3/sqrt(62))y+(7/sqrt(62))z- -4/sqrt(62)=0 62=2^2+(-3)^2+7^2 The distance=(2*4-3*(-2)+7*3-4)/sqrt(62)= sqrt(31/2)

Algebra 2
9(x^2-10x+25-25)-4y^2+189=0 9(x-5)^2-225-4y^2+189=0 9(x-5)^2-4y^2=36 (x-5)^2/2^2 - y^2/3^2=1 hyperbola

Calculus
Let C(x,y)-centroid. Obviously, x=pi/2 The area of the region=2 y=(1/2)(1/2)(integral from 0 to pi) sin^2(x)dx=pi/8

trigonometry
cos(2x)-1=-2sin^2(x) sin(2x)=2sin(x)cos(x) The equation is -2sin(x)(sin(x)+cos(x))=0 sin(x)=0 or sin(x)+cos(x)=0 sin(x)=0==>x=pi,2pi,3pi,4pi sin(x)+cos(x)=0, sin(x)=-c0s(x) tan(x)=-1==>x=3pi/4,7pi/4,11pi/4,15pi/4, 19pi/4 (E)

maths
dx/dy or dy/dx ?

maths
f!(x)-? maybe f'(x)

Algebra 2
1. Let sqrt3=m/n where m,n-relatively primes. 3n^2=m^2 ==>m multiple of 3, m=3k 3n^2=9k^2 n^2=3k^2 ==>n multiple of 3.

Algebra 2
1. P(x)=(x-2)(x+2)^3 3 times 2. P(x)=(x-1)(x+1)^4 4 times 3. x^3-5x^2+4x+5=(x^2-3x-2)(x-c)+1=>5=2c+1 c=2

Algebra 2
1. P(-sqrt2)=-4sqrt2+4-4sqrt2+4 No 2. P(i)=-i-1+i+1-i-1+i+1=0 Yes 3. P(-2i)=8i-4-8i+4=0 Yes

Math
Pascal triangle: 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1<- (2x+5y)^6=(2x)^6+6(2x)^5(5y)+15(2x)^4(5y)^2+20(2x)^3(5y)^3+15(2x)^2(5y)^4+6(2x)(5y)^5+ (5y)^6

Calculus
This is right

The answer is wrong because function x^(-2)>0 on [-2,2] except x=0 =>integral>0 This is Improper integral which is divergent. x^(-1)-->infinity if x-->0

Calculus 3
The airplane velocity should be (20,-a) where a=sqrt(400^2-20^2)

maths
f'(x)=e^3x(3cos(2x)-2sin(2x))=0 3cos(2x)=2sin(2x) divide by 2cos(2x) tan(2x)=1.5 x=0.4914(rad) f(0.2618)=1.90 f(0.4914)=2.42 <--- f(0.7854)=0

maths
B in form: -1/8(cos(4x)+2x^2)^2+C

calculus
Find C from equality 18*(2^3/2)=(2(1^2-6*1+23)^3/2)/3 +C and substitute in the general solution. C is not 0. Can you write this differential equation?

calculus
Where is constant C ?

Math
Еhe ratio of areas of similar figures is equal to the ratio of the squares of linear dimensions x=10.99(15/12)^2

calculus
h(h^-1(x))=3(cx/m-1)+c=x (from definition h^-1) (3c/m)x-3+c=x c=3 m=9

trig
The answer would be 3/8, but the angles are (approximately) 22,68,90

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