The vendor sells the jugs containing 13 , 15, 16, 21 and 22 gallons
This totals 87 gallons
1/3 of this = 29 gallons which means that he sells the jugs containing 13 and 16 gallons to Randy
The remaining 2/3 = 58 gallons which means that he sells the jugs containing 15, 21 and 22 gallons to Lisa
He keeps the remaining jug which contains 21 gallons of blue punch
Hold on... I got 2sqrt(2). I did a different method.
solution without calculus
\(\color{BrickRed}m=x^2+x+4x+4-3x\\ x^2+2x+4-m=0\\ x=-\frac{p}{2}\pm \sqrt{(\frac{p}{2})^2-q}\\ x=-1\pm\sqrt{1^2-4+m}\)
\(\color{blue}1^2-4+m=0\\ m=4-1\)
\(m=3\\ x=-1\)
!
Thanks CPHill! I already solved this problem lol but anyone is welcome to try it!
x^2 + y^2/4 = 1 using implicit differentiation we have that
2x + (1/2)yy' = 0
y' = -2x / (1/2 y)
y' = -4x/ y
Yhe slope of the line = 2
So....we want to find where
-4x / y = 2
-4x = 2y
-2x = y
Sub this back into the equation of the ellipse for y
x^2 + (-2x)^2/4 = 1
x^2 + 4x^2/4 = 1
2x^2 = 1
x^2 = ±√(1/2)
When x = √(1/2), y = -2√(1/2)
When x = -√(1/2) , y = 2√(1/2)
Subbing into the equation of the line
-2√(1/2) = 2√(1/2) + b → b = - 4√(1/2)
And
2√(1/2) = -2√(1/2) + b → b = 4√(1/2)
See the graph here : https://www.desmos.com/calculator/7ifp0ajbri
Hello Guest!
\(x²-4x+13=0 \)
p q
\(\color{blue}x=-\frac{p}{2}\pm \sqrt{(\frac{p}{2})^2-q}\\ x=2\pm\sqrt{2^2-13}\\ x=2\pm\sqrt{9\cdot(-1)}\\ x=2\pm3 \sqrt{-1}\\ x=2\pm3i\)
\(x_1=2+3i\\ x_2=2-3i\)
Sorry, misread the question:
12 x 14 should be: 12 x 15 =180= (1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180) >>Total = 18 divisors
m mod 14 = 4,
(m - n) mod 14 =10, solve for m, n
m = 14 c + 4 and n = 14 d + 8, So:
m =4 and n = 8
[4 + 8] mod 14 ==12
10 x 12 = 120 has 16 divisors: (1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120) >>Total = 16 divisors
Also:
12 x 14 =168 has 16 divisors: (1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168) >>Total = 16 divisors
2^i*3^j ==2^3 * 3^4 =648
648 =(1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648) >>Total = 1815
1 - Sum up the first infinite series using the "Infinite Series formula"
2 - Whatever sum you get from (1) above, multiply it by 3 and that is the sum of the 2nd infinite series.
3 - Again, use the "infinite Sum Formula" to find n, bearing in mind that the "common ratio" of the 2nd series is:(4 + n) / 12. You should get n = 16 / 3
Please show us what you have attempted for yourself.
Think of the planes as being at the vertices of a right-angled triangle, where the right-angle is where they intersect.
The initial distances of the two planes from the intersection point are x1 and x2 respectively, They have velocities v1 and v2.
Then the following four equations apply:
v1 = x1/2
v2 = x2/2
v2 = v1 + 100
x12 + x22 = 10002
Solve these simultaneous equations to find the velocities.
How about you give your thoughts parpar1?
What do YOU think parpar1?
Here is how:
\((x+1)^3+x^2\cdot q(x)\\ =x^3+3x^2+3x+1+x^2\cdot q(x)\\ =x^2(x+3)+3x+1+x^2\cdot q(x)\\ =x^2(x+3+q(x))+3x+1\\ if\;\;q(x)=-3-x\\ \text{Then the degree of the resuling polynomial will be 1} \)
let diagonal be d = 2
square, area As = 2 u2
rectangle, area Ar = √3
ratio R = Ar / As = √3 / 2 = 0.866025403
R2 = 0.75 ==> 3/4
For what value of m does the equation (x + 4)(x + 1) = m + 3x have exactly one real solution?
\((x + 4)(x + 1) = m + 3x\\ m=(x + 4)(x + 1) -3x\\ m=x^2+x+4x+4-3x\)
\(m(x)=x^2+2x+4\)
\(\frac{dm(x)}{dx}=2x+2=0 \)
\(x=-1\\ m=3\)
\(\color{BrickRed}(x + 4)(x + 1) = m + 3x\\ x^2+x+4x+4=3+3x\\ x^2+2x+1=0\\ x=-1\pm\sqrt{(-1)^2-1}\\ \color{blue}x=-1\)
Which of the following equations correctly represents the distance between points (1, -1) and (-2, 2)?
\({\color{blue}D=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}}=\sqrt{(2-(-1))^2+(-2-1)^2}\)
\(D=4.2426\)
1000-943 разве будет =56 А?
Нет... 1000 – 943 = 57
.
Here is the same question posted Apr. 29, 2018 and is markedly different from this post and it appears solvable:
On my ping-pong team there are four times as many right-handed boys as left-handed boys. Of the students on the team who are left-handed, there are twice as many girls as there are boys. Half of the girls who are on the team are left-handed. If there are 36 people on the team, how many are right-handed boys?
wiskdls Apr 29, 2018
LG RG LB RB Total
2 2 1 4 9
4 4 2 8 18
6 6 3 12 27
8 8 4 16 36
∠BAO = sin-1(3.5 / 5) = 44.427 deg.
BO = 2.5 / cos(∠BAO) = 3.50070021
OM = sqrt(BO2 - BM2) = 0.070014 ( M is the midpoint on BC)
Area OBC = BM * OM = 0.245049744 units squared
In triangle ABC, AB= AC=5 and BC=7. Let O be the circumcenter of triangle ABC. Find the area of triangle OBC.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Let M be a midpoint on AB.
Angle BAO ==> β = arcsin(3.5 / 5) ==> 44.427004º
Area of triangle ABC ==> A1 [sqrt(52 - 3.52) * 3.5 ==> A1 = 12.49749975 u2
Area of polygon ABOC ==> A2 = 2[(tanβ * 2.5) * 2.5] A2 = 12.25245073 u2
Δ OBC area ==> A = A1 - A2 = 0.24504902 u2
Let the diagonal length of both = D
In the rectangle... the side opp the 30° angle = D/2 and .the side opp the 60° angle = D√3/2 and
The area of the rectangle = D^2 [√3/4]
In the square......the side length = D/√2
Area of square = (D / √2)^2 = D^2/2
R = D^2 [ √3/4] / [D^2 / 2 ] = (√3/2)
R^2 = 3/4
EDIT TO CORRECT A PRIOR MISTAKE
The slope of this segment is [ 9 - 3 ] / [ 7 - 1 ] = 6/6 = 1
The perpendicular line to this segment will have a negative reciprocal slope = -1
Since this line is a perpendicular bisector, we need to find the mdpoint of the segment.....this is given by
( [ 1+ 7] / 2 , [ 3 + 9] / 2 ) = (8/2 , 12/2 ) = (4, 6)
The equation of the perpendicular line is
y = -1 ( x -4) + 6
y = -x + 4 + 6 add x to both sides and simplify
x + y = 10
So...b = 10