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Yes. Definitely there is some trick.

Remember that \(i^2=-1\),

so \(i^4=i^2\cdot i^2=-1\cdot -1=1\)

Therefore \(i^{4n}=(i^4)^n=1^n=1\), for any integer n.

\(i^8=(i^4)^2=1^2=1\)

\(i^{25}=i^{24}\times i=(i^4)^6\times i=1\times i = i\)

\(\cos^{-1}\) this one?

it is same as "acos".

\(v=\dfrac{1}{4}\pi d^2z\\ 4v= \pi d^2z\\ d^2=\dfrac{4v}{\pi z}\)

\(\because x^3=20x+7y\text{ and }y^3=7x+20y\\ \therefore x^3-y^3=(x-y)(x^2+xy+y^2)=13x-13y\\ x^2+xy+y^2 = 13\\ x^3+y^3 =(x+y)(x^2-xy+y^2)=27(x+y)\\ x^2-xy+y^2=27\\ (x^2+xy+y^2)-(x^2-xy+y^2)=-14\\ xy = -7\)

Pretty cool, Max

Love the "wiggle"  thing.....!!!!

Thank you for the explanation!

Since the apex angle = 2x, the side opposite it will have the same measure as the side opposite the other angle measuring 2x  = 27 cm

 

Why is it like that though?

https://www.desmos.com/calculator/kx7nzzw1bj --- sector

https://www.desmos.com/calculator/pk1qw7oc44 --- spiral

https://www.desmos.com/calculator/m6khfpqpq9 --- wiggle wiggle wiggle XD

https://www.desmos.com/calculator/qnbd93wkqu --- infinity sign

I created them all :D

Since the apex angle = 2x, the side opposite it will have the same measure as the side opposite the other angle measuring 2x  = 27 cm

So

a + b  =  27   (1)

And since the apex angle is bisected  we have that

a/b  =  11/27

27 a = 11b

a =  (11/27)b   (2)

Subbing (2)  into (1)  we have that

(11/27)b + b  = 27

(38/27)b  = 27      multipyl both sides by (27/38)

b  = 27^2/38  =  729/38 cm

And a  = (11/27)b  = (11/27) (729/38)  =  27 * 11 / 38  = 297/38 cm

We can use something called Heron's Formula to find the area

Area  = sqrt [ s (s -a) (s - b) (s - c) ]

Where a, b, c are the sides and s is the semi-perimeter =  [ a + b + c] / 2  =

[ 11 + 27 + 27 ] / 2   =  65/2 =  32.5 cm

So...the area is

sqrt [ 32.5 (32.5 - 11) (32.5 - 27) (32.5 - 27) ]  =  145.39  cm^2

Notice that we didn't actually have to find out what "x" was, at all...but....you could certainly do that using the Law of Cosines

= 200304.24

https://www.desmos.com/calculator/wp747grseh

I feel stupid by creating this thing XD

Dividing by a number means multiplying the reciprocal of the number.

So 1/2 divided by 7 = 1/2 x 1/7 = 1/(2x7) = 1/14

I'm assuming that you want each interval to be 2.57 units in length??

If so, the fraction evaluates to 100/2.57  ≈ 38.91... you will have about 38 intervals 

Assuming that we start at 0, the first interval ends at 2.57, the second interval ends at 2*2.57 = 5.14, the third at  3 *2.57  = 7.71, etc......

The last interval ends at  38*2.57  = 97.66

Because △ABC is similar to △DEF, angle ABC should equal 60 deg as well. 

\(\boxed{ \text{The sum of all interior angles of a triangle is 180}^{\circ}}\)

So Angle C = 180 - 55 - 60 = 65 deg :D

The measure of an intercepted arc  =  2 * measure of the inscribed angle...so...

2 * 72°   =

144°

1. P(both are greater than 15)   =  (5/20) (15/20)  =  (1/4) (3/4)  =  3/16

2. The first tile is odd and the second tile is less than 25  =

(10/20) (14/20)  =  

(1/2) (7/10) =

7/20

 3. The first tile is a multiple of 6 and the second tile is a multiple of 4 =

(3/20) ( 5/20) =

(3/20) (1/4) =

3/80

 4.  The first tile is less than 15 and the second tile is even or greater than 25

Let's look at the second one...it's a little tricky

Number ( even or > 25)  =

Number(even) + Number (.>25) - Number (even and > 25)

             10             +          5              -          3

                                       =        12

So we have

(14/20) ( 12/20)  =

(7/10) (3/5) =

21 / 50

This site doesn’t need a Recaptcha test. It needs a Retodit test.

The best one is the “Sopha King Retodit” test.

There  are   C(25,10)  = 3268760  different  groups possible

Jenny and her three best friends  comprise a partial group....to fill out the remaining spots we can choose any 6 of the 21 remaining people = C(21,6) =  54,264 posiible groups containing Jenny and her three best friends

So......the probability of this happening  =

 54264  / 3268760  =   21/1265 ≈ 0.0166 ≈  1.66 %

(-3, 4)  rotated 90°  counter-clockwise about the origin →  (-4, -3)

[ 90°  counter-clockwise rotations follow the rule (x, y) → (-y, x)  ]

Arc length  AB  =

2 *pi *  radius  *  (95 / 360)  =

2 * pi * 9 * (95/360)  ≈

14.92 ft

But why did you even put it?

////-////

4

There are  C(30,5)   = 142,506 possible groups

Assume that the three best friends comprise part of a group.....to fill out the group, we can choose any one of 27 remaining people for the fourth member and any one of 26 remaining people for the fifth member...so  ....ther are   27 * 26  = 702 possible groups comprising the three friends and two other people

So  the probability that the thrre friends are chosen for the group  =

702 / 142,506  =

1 /203 ≈

0.4926%

The probabiltiy is 3/30.

I will assume for this problem that i is for the imaginary number. If I should assume otherwise, tell me. I will, of course, simplify the given expression:
 

750 / 35 =21 3/7 gallons per minute-rate of flow

1,000 / 21 3/7 = 46 2/3 minutes-or 46 minutes and 40 seconds.