All Answers 358150 Answers

2880 / 2 =1440 km - 1/2 the distance of their trip.

1440 / 240 =6 days spent driving and stopping on their way to Montreal.

1440 / 480 =3 days spent driving and stopping on their way back to Halifax.

6 +3 + [6 days spent in Montreal] = 15 days or ~2 weeks - duration of their vacation. 

Dunno if this is correct:

We know the perimeter of a circle (or circumference) is \(2\pi R\). So that means if we want to find the area of a semi-circle, we have to divide the perimeter by 2:

Radius (R) = 5.

So it's 2 * 3.142 * 5 = 31.42. 

We have to divide this by 2 so we can get our final answer:

31.42 / 2 = 15.71.

Ahh I noticed why mine was incorrect, I only did the curvy side and forgot about the bottom:

15.71 + 10 = 25.71

Well, if we know the the total trip is 2880 km, and they drive 240km per day, 2880/240 = 12. So that means (i think) they drove 12 days in total. And they stayed in Montreal for 6 days. 12 + 6 = 18 days. So 18 days in total? That doesn't seem right. I'm assuming that the driving distance from Halifax to Montreal was 1440 km, and from Montreal and back to Halifax was also 1440km.

You can do it; it's easy.

1. From the recursion, a_2 = 24, and a_3 = 571.

2. From the recursion, a_2 = 1/2, a_3 = 2/3, a_4 = 3/4, and so on.  The tenth term a_{10} is 9/10.

Why did you repost?

please work out perimeter

Hi newsier!

\(P=(d\cdot \pi)/2 +d=(10\cdot 3.142)/2+10\)

\(P=25.71\)

  !

Thanks guest,

Yes it is a relatively common roadside, in the country anyway. :)

I actually took a photo to use here but I cannot remember if this is my photo or a different one from the internet.

There are 360^o around a point.

The formula to find the number of degrees in each interior angle of a regular polygon is:  (n - 2)·180^o/n

Therefore each interior angle of a regular octagon is:  (8 - 2)·180^o/8  =  135^o

Each interior angle of a regular triangle is  60^o

Subtracting:  360^o - 135^o - 60^o  =  165^o

This means that each interior angle of the regular n-gon is 165^o

Using the above formula:  (n - 2)·180^o/n  =  165^o

                           --->            (n - 2)·180^o  =  165^o·n

If you solve this equation, you will get the number of sides of the unknown regular polygon.

1. Thanks, 181 is right!

(a) Let P be the intersection of AD and MN, and let Q be the intersection of AL and MN.  Then by Menelaus's Theorem, Q is the midpoint of PK.  Since AD and LK are parallel, triangles ADL and LKQ are similar.  And since Q is the midpoint of PK, QK = PK/2 = DL/2.  Therefore, from the similar triangles, AD/LK = 2.

(b) Since QK = DL/2 and QG = LG/2, triangles GDL and GKQ are similar.  Then KG = DG/2, so by part (a), triangles ADG and LKG are similar.

(c) In part (b), we found that triangle GDL and GKQ were similar.  Then angle QKG = angle LDG, so D, G, and K are collinear.  And by the similarity in part (b), DG/GK = 2.  Easy!

The outer arc is  50/360 ^ths of the outer circle:  (50/360)(2·pi·8)

The inner arc is  50/360 ^ths of the inner circle:  (50/360)(2·pi·3.5)    [8 - 4.5  =  3.5]

The line segments are each 4.5 cm in length.

Add all four values to get your answer.

Using the formulas 1 + 2 + ... + n = n(n + 1)/2 and 1^2 + 2^2 + ... + n^2 = n(n + 1)(2n + 1)/6, the sum in the problem works out to 2n^4 + 9n^3 + 13n^2 + 6n = n(n + 1)(n + 2)(2n + 3), so an + b = 2n + 3.

Jennifer's age  =  J

Laurel's age     =  L

Nana's age      =  N

Jennifer is twice as old as Laurel:              J  =  2·L

Laurel is four years younger than Nana:    L  =  N - 4

Nana is two years younger than Jennifer:  N  =  J - 2

Combining  J  =  2·L  and  L  =  N - 4     --->     J  =  2·(N - 4)

Combining  J  =  2·(N - 4)  and  N  =  J - 2     --->     N  =  2·(N - 4) - 2

                                                                       --->     N  =  2N - 8 - 2

                                                                       --->     N  =  2N - 10

                                                                       --->    10  =  N

Let w = a + bi and z = c + di.  Then

\(\dfrac{w + z}{1 + wz} = \dfrac{a + c + bi + di}{1 + (a + bi)(c + di)}\)

To express this in rectangular form, we can multiply the numerator and denominator by the conjugate:

\(\dfrac{a + c + bi + di}{1 + (a + bi)(c + di)} = \dfrac{(a + c + bi + di)((1 - (a + bi)(c + di))}{(1 + (a + bi)(c + di))(1 - (a + bi)(c + di))}\)

The denominator simplifies to (1 - (a^2 + b^2)(c^2 + d^2)), which is real.  The numerator simplifies to a^2 - b^2 + c^2 - d^2, which is also real.  Therefore, the complex number (w + z)/(1 + wz) is real.

S = 0.15025711289495
T=1.051799790264645
S/T =0.15025711289495 / 1.051799790264645
S/T = 1 / 7

   sin(A)  =  opposite / hypotenuse

sin(58°)  =  x/14

           x  =  14·sin(58^o)

cos(Y)  =  adjacent / hypotenuse  =  6/15

cos(Y)  =  0.4000

        Y  =  cos^-1(0.4000)

        Y  =  66.4^o

2 + ì and   -2 - i  are different complex numbers, as are plus and minus 2 as the square roots of 4.

Let the number of minutes when they will be at the same altitude =M

520 + 40M =3800 - 120M, solve for M

M =41/2 =20.5 minutes - when both planes will be at 1340 feet.

1 cup of pineapple juice = P
1 cup of orange juice      =4P - 4

P + 4P - 4 =121, solve for P
P = 25 mg of vitamin C in 1 cup of pineapple juice
[25 x 4] - 4 = 96 mg of vitamin C in 1 cup of orange juice.

Thank you, Melody.  I love the new avatar.    I looked it up; it's an actual road sign in Australia.

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Grid cannot be seen.

the diagram Shows a sector of a circle radius 10cm and angle 135 degrees find out area     

The area of a circle is π • radius² 

The radius of the circle is 10 so the area of the entire circle would be 3.14 • 100 = 314 

There are 360^o in an entire circle so the segment would contain 135 / 360 of the circle  

(135/360) • 100 = 37.5 

Since the radius was given in cm, the area of the 135^o sector of the circle is 37.5 sq cm 

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