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4P+2D=36 i.e. 4 times the number of pigs is the number of pig-feet, 2D = duck-feet
P+D=10 ten animals total.
Multiply second equation by 4:
4P+4D=40
4P+2D=36 (and subtract first equation.
2D=4
2 ducks, 8 pigs. 10 animals.
4 duck feet + 32 pig-feet, total 36 feet.

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Say the diameter is d and the radius is .
Let h= height of the cylinder.



circumference is the LENGTH of the rounded side. This circumference is , or
circumference is

The surface area then is
and you were given in the description:
.
Solving for d is uncomplicated.

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It's a circle.
Its center is at (-7,4) and it had a radius of 8

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This is a circle centered at C(-7,4) with radius r=8

:)

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(6p + 11)(6p - 11)
----
= 36p^2 - 121
======================
Cheers,
Stan H.
======================

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I don't know which method they want you to use, but
I can try completing the square
---------------------
First, divide both sides by

--------------------------
Take 1/2 of the coefficient of ,
square it, and add it to both sides




Take the square root of both sides


and, also

---------------------
Here's the plot:

Since it doesn't contact the x-axis, there are no real roots

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George and Stanley are building a stone fence. They can complete the fence together in 8 hours, and George can complete it is 24 hours working alone.
----
George & Stan together rate::: 1/8 job/hr
George rate::::: 1/24 job/hr
----------
If they work together for 6 hours, then Stanley goes to the pub for a pint, how much longer must George work to finish the fence?
-----
6(1/8) + x/24 = 1 job
-----
3/4 + x/24 = 1
--------
18 + x = 24
x = 6 hrs. (Time George needs to finish)
===================
Cheers,
Stan H.

------

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zeros ,,

:)

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A man flies a small airplane from Fargo to Bismarck, North Dakota --- a
distance of 180 miles.
Because he is flying into a head wind, the trip takes him 2 hours.
On the way back, the wind is still blowing at the same speed, so the
return trip takes only 1 hour 12 minutes.
What is his speed in still air, and how fast is the wind blowing?
:
Change 1 hr 12 min: 1 + 12/60 = 1.2 hrs
:
Let s = his speed in still air
Let w = speed of the wind
then
(s-w) = effective speed against the wind
and
(s+w) = effective speed with the wind
:
Write a distance equation for each way; dist = time * speed
2(s - w) = 180
1.2(s+w) = 180
Simplify both equations, divide the 1st eq by 2, the 2nd eq by 1.2; results:
s - w = 90
s + w = 150
-------------addition eliminates w, find s
2s = 240
s = 240/2
s = 120 mph is the speed in still air
Find w
s + w = 150
120 + w = 150
w = 150 - 120
w = 30 mph is the speed of the wind
:
Check in 1st original equation
2(120-30) = 180
2(90) = 180

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Determine whether these equations are parallel, perpendicular, or neither.
8x=5y+3
-24x=15y+3
-----
y = (8/5)x - (3/5)
y = (-8/5)x - (1/5)
------
The slopes are (8/5) and (-8/5)
The lines are not parallel or perpendicular.
-------------------
Cheers,
Stan H.
==========================

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Tracey paid $190 for an item that was originally priced at $290. What percent of the original price did Tracey pay?
----------
x/100 = 190/290
x = 100(190/290)
x = 65.52%
------------------------
Cheers,
Stan H.

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$190 is 65.52% of $290

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Determine whether the lines x-5y=15 and -5x-y+2=0 are parallel, perpendicular, or neither.
I really need help with this one. Kim

x - 5y = 15 has a slope of , while - 5x - y + 2 = 0 has a slope of .

Since these two slopes are negative reciprocals of each other: and , then the slopes are perpendicular to each other.

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x-5y=15 has






and -5x-y+2=0 has





and so



they are perpendicular

:)

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it's 1 in 6^3 or 1 in 216.
Why not 1 in 6^4?
It would be that if you asked the chances of 4 rolls of a particular number, but here it's just the same, so the first roll is 'free.' only the next three rolls must match.

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:)

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5 hens lay 6 eggs every 2 days.
Find the number of hen-days per egg
= hen-days per egg
:
How many eggs will 25 chickens lay in 40 days?
Invert the dividing fraction and multiply
(25*40) * = 600 eggs

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Perimeter of first triangle: 30 cm
second triangle: 15 cm
third triangle: 7.5 cm
...
nth triangle:
...
The sum of an infinite geometric series with first term and common ratio r is provided |r| < 1.
= = cm.

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Find the probability that less than 6 patients experienced dizziness.
X ~ Binomial(15, 0.45)
P(X < 6) = =

Find the probability that at least 7 patients experienced dizziness.
X ~ Binomial(15, 0.45)
P(X ≥ 7) = =

Find the probability that at most 4 patients did NOT experience dizziness.
X ~ Binomial(15, 0.55)
P(X ≤ 4) = =

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Find all solutions in the interval o and 2pi
1.) Cos^2x+ sinx +1= 0
1-sin^2(x)+sin(x)+1=0
sin^2(x)-sin(x)-2=0
(sin(x)-2)(sin(x)+1)=0
..
sin(x)=2 (reject, -1 ≤ sinx ≤ 1)
sin(x)=-1
x=3π/2

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Factoring the Sum of Two Cubes:
Step 1: Get the binomial factor
Cube root of the first term: y
Cube root of the second term: 5
The binomial factor is y + 5
Step 2: Get the trinomial factor
Square of the first term of the binomial factor:
Negative Product of the first and second term of the binomial factors = -5y
Square of the second term of the binomial factor: 25
The trinomial factor is
Step 3: The factored form of is .

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-6x +3x over 5 devided by 4x-8 over 25
GIVEN:



about as simple as you can make it but you can rewrite to bring the negative term in numerator away from the left:

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1-sin^2((pi/2)-x)
sin(π/2-x)=cos(x)
1-sin^2((pi/2)-x)=1-cos^2(x)=sin^2(x)

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First, get the length of the diameter by computing the
distance between the points (-6, 4) and (4, 8).
Using the distance formula:
d =
=
=
The length of the radius is half the length of the diameter.
r = = .
Next, we get the coordinates of the center of the circle by
computing the midpoint of the diameter with endpoints (-6,4) and (4,8).
Using the midpoint formula:
center = (, )
= (-1, 6)
The equation of the circle with center (h,k) and radius r is
, the center is (h,k) = (-1,6) and radius, r =
Equation:

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Division by a number means multiplication by its reciprocal. You then have







which can be finished multiplying whatever remains undone in the numerator and continuing simplifying, combining like-terms according to what's found.

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solve the equations for x, if 0is less than equal to x is less than equal to 2pi.
a) 8cos^2x=4
cos^2(x)=4/8=1/2
cos(x)=1/√2=√2/2
x=π/4, 3π/4 (in Q1 and Q2 where sin>0)

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Complete the identity.
1). cos θ - cos θ sin^2 θ = ?

2). (1 / cos^2 θ) - (1 / cot^2 θ) = ?

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I assume you mean to solve for d...

5(d+4)=7(d-2)

5d+20=7d-14


5d-5d+20+14=7d-5d-14+14


34=2d

d=17


:)

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how to find the value of sin 1380 cos 225 and tan 420
***
1380-3*360=1380-1080=300
sin(1380)=sin(300)=sin(60)=-√3/2 (in Q4 where sin<0)
..
cos(225)=cos(45)=-√2/2 (in Q3 where cos<0)
..
420-360=60
tan(420)=tan(60)=√3 (in Q1 where tan>0)

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please repost to include a question :)

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Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=80 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 8.47213595499958, -0.47213595499958. Here's your graph:

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Find the exact value of csc
sin(5π/4)=-√2/2 (in Q3 where sin<0)
csc(5π/4)=1/sin(5π/4)=-2/√2=-√2

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You are building a rectangular deck. The area of the deck should be 250 ft squared. You want the length of the deck to be 5 ft longer than twice its width.
let w be the width and 2w+5 is the length, then
w(2w+5) = 250
2w^2+5w-250=0
(2w+25) * (w-10) = 0 and
w=10 and l = 25

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Find the exact value of cot .
tan(2π/3)=-√3 (in Q2 where tan<0)
cot 2π/3=1/tan 2π/3=-1/√3=-√3/3