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square the numerator and the denominator

21/2)^2 = 441/4

There are 9 "sections" from exit 41 to exit 50.

If 8 of these exits are 6 km each, this would account for 8 x 6  =  48 km.

Since the total distance from exit 41 to exit 50 is 100 km, the maximum distance from exit 47 to exit 48

is  100 km - 48 km  =  52 km.

6km each minumum for 41-50   covers 9 exits     9 x 6 = 54 km to meet minumum   leaving 100-54= 46 km that can be added to the 6km

between 47 and 48    46 + 6 = 52 km

Let  A  =  adult ticket price

       C  =  child ticket price

First day:         6A +   7C  =  162.00   (multiply by -2)   --->   -12A - 14C  =  -324.00

Second day:  11A + 14C  =  311.00                                        11A + 14C  =   311.00

                          add down the columns:                                   -A             =   -13.00

                                                                                                               A  =  13.00

Since  A = 13.00  --->  6A + 7C  =  162.00   --->   6(13.00) + 7C  =  162.00

                                                                                   78.00 + 7C  =  162.00

                                                                                                7C  =  84.00

                                                                                                 C  =  12.00

Construction:

Let M be the point of tangency on the AB circle, draw the line between A and C and the part diameter from M through the centre O of the AB circle, meeting the 'A' tangent at N.

There's a well known theorem concerning the tangents to a circle from an outside point, in this instance we can say that AC.BC =  CM.CM.

That gets you the length of CM and  so you know everything about the triangle CMO.

The triangle  ANO is similar to the triangle CMO so we can deduce the length of ON, etc.. 

There are 7 choices for the first digit (2, 3, 4, 5, 6, 7, 8).

There are 4 choices for the second digit (4, 5, 6, 7)

There are 9 choices for the third digit (0, 1, 2, 3, 4, 6, 7, 8, 9).

Since these choices are independent, we need to multiply the three numbers:  7 x 4 x 9  to get the correct answer.

no thats not right but thank you <3!

Solve:  f² - 4f  =  8

            f² - 4f - 8  =  0

Using the quadratic formula:  a = 1  b = -4  c = -8

f  =  [ 4 + sqrt(16 +32) ] / 2   --->   [ 4 + 4sqrt(3) ] / 2  =  2 + 2sqrt(3)

f  =  [ 4 - sqrt(16 +32) ] / 2   --->   [ 4 - 4sqrt(3) ] / 2  =  2 - 2sqrt(3)

An equation for a parabola is  y  =  a(x - r)(x -s)  where r and s are x-intercepts.

Placing the two intercepts into this formula, we get:  y  =  a( x - (5 + sqrt(3) )( x - (5 - sqrt(3) )

   --->   y  =  a( x - 5 - sqrt(3) )( x - 5 + sqrt(3) )

           y  =  a(x² - 10x + 22)

Since the point (0, 4) is on this parabola:

           4  =  a(0² -10·0 + 22)

           4  =  22a

           a  =  2/11

y  =  (2/11)(x² - 10x + 22)

For the first break, the probability that you get a piece that is 1 or longer is 4/5.  Then for the second break, the probability that you get a piece that is 1 or longer is 3/5.  Therefore, the probability is 4/5*3/5 = 12/25.

Let L be the center of circle S, and let F be the center of circle T.  Since LA = AF = 1 and LF = sqrt(2), triangle LAF is a 45-45-90 triangle.  This means angle ALF is 45 degrees.  By symmetry, angle BLF is also 45 degrees.

Then angle ALB = angle ALF + angle LBF = 45 + 45 = 90 degrees, so arc AB is 90 degrees.  Since angle APB subtends arc AB, angle APB is 90/2 = 45 degrees.  Then by Poncelet's Theorem, triangle PCD is a 45-45-90 triangle, so angle PCD is 90 degrees.  Then angle ACD is 90 degrees, which implies that CD is a diameter of circle T.

First, we consider the triangles that have the vertices of the rectangle  as the right angle. We can get  right triangles for each vertex. For example, for vertex , we can get right triangles  and . Since there are four vertices, we can get  right triangles.

Next, we consider triangles that have  or  as the vertices. We can set  as a leg of the right triangles and get  right triangles with the third vertex , and .

Lastly, we can draw the diagonals , and . Since  and  are squares, each diagonal creates a  degree angle with the line segment . Therefore, we have two right triangles:  and .

Adding them together, we have a total of  8+4+2 = 14 right triangles

Think about it this way. 2x+1x as the ratio and it would equal the total, or 75. Your equation would be 3x=75. This would make the x value equal to 25. Since the ratio is 2:1, meaning there would be double the amount of boys than girls, you multiply the 2 in the ratio by what the "x" is to find the amount of boys.

50 boys 

25 girls 

How do I activate sin-1, cos-1 and tan-1 on the calculator   

Go to 2nd function, look for asin, acos, and atan 

but not asinh, acosh, atanh, those are hyperbolic functions, you don't need them... yet 

_.

\(log_b81=\frac{2}{3}\\ b^{log_b81}=b^{\frac{2}{3}}\\ 81=b^{\frac{2}{3}}\\ 9^2=b^{\frac{2}{3}}\\ \sqrt{9^2}=\sqrt{b^{\frac{2}{3}}}\\ 9=b^{\frac{1}{3}}\\ 9^3=b\\ b=729 \)

Which is exactly the same as Impasta got.    Thanks Impasta.

coding:

log_b81=\frac{2}{3}\\
b^{log_b81}=b^{\frac{2}{3}}\\
81=b^{\frac{2}{3}}\\
9^2=b^{\frac{2}{3}}\\
\sqrt{9^2}=\sqrt{b^{\frac{2}{3}}}\\
9=b^{\frac{1}{3}}\\
9^3=b\\

Hi Impasta,

That would give you the combined cost but it would not give you the cost of each one individually.

DO NOT DELETE QUESTIONS!

Google translation:

"as it approximates to full 0.5333
approximate a number"

I think it is asking for 0.5333 to the nearest integer.

The answer is 1

Se ho capito bene, allora la risposta è 1

8:12 = 8/12

A central angle of a circle whose radius is 8 centimeters subtends an arc whose length is  2π/9 centimeters.

What is the radian measure of the central angle?

A hamster runs in its wheel whose radius is 3 inches. The wheel completes 6.3 revolutions in 5 seconds.

What is the linear velocity of the hamster's wheel?

A bicycle is classified by the diameter of its tires. For example, a 20-inch bicycle has tires that are 20 inches in diameter.

The number of times a bicycle tire rotates in a given period of time is directly related to the distance traveled in that period of time.

Hello Guest!

 
1. Ein 26-Zoll-Fahrrad wird in die Pedale getreten, sodass sich die Reifen mit einer Geschwindigkeit von 200 Umdrehungen pro Minute drehen. Ein 20-Zoll-Fahrrad wird so in die Pedale getreten, dass sich seine Reifen ebenfalls mit einer Geschwindigkeit von 200 Umdrehungen pro Minute drehen. Was ist die Lineargeschwindigkeit jedes Fahrrads? Geben Sie Ihre Antworten in Zoll pro Minute an, gerundet auf das nächste Zehntel. 1.Antworten 16.328 und 12.560

2. Typischerweise wird die Geschwindigkeit, mit der sich ein Fahrrad bewegt, in Meilen pro Stunde ausgedrückt. Konvertieren Sie die Lineargeschwindigkeit des 26-Zoll-Fahrrads und des 20-Zoll-Fahrrads in Meilen pro Stunde. Runden Sie Ihre Antwort auf das nächste Zehntel.

1.

\(v=d\pi n\\ v_{26}=26in\cdot \pi\cdot 200/min\)

\(v_{26}=16336\ in/min\)

\(v_{20}=20in\cdot \pi\cdot 200/min\)

\(v_{20}=12566\ in/min\)

2.

\(v_{26}=16336\cdot \frac{in}{min}\cdot \frac{miles}{63360in}\cdot \frac{60min}{h}\)

\(v_{26}=15.5\ miles/h\)

\(v_{20}:v_{26}=20:26\\ v_{20}=\frac{15.5\cdot 20}{26}\ miles/h\\ \)

\(v_{20}=11.9\ miles/h\)

  !