All Answers 358514 Answers

This looks difficult...but it's not.....

Notice  that  400! / 398!  =  (400 x 399 x 398 x 397.......) / (398 x 397 x 396 x 395...)

All all the terms on the "top" cancel with all the terms on the "bottom" except 400 x 399

Can you take it from here??

I could give you the answer....but it is more important that you understand this fully...here is an excellent ( and an easy-to-understand) resource.....

The area of the rectangle = 12mm X 18mm = 216mm^2

And the area os a square = side^2

Thus

side^2  = 216    take the sq root of both sides

side = sqrt 216  = sqrt (36 * 6) = 6*sqrt(6)   ......and that's in mm

Just put  "sqrt 53" into the calculator.....what is the "whole" number part of the answer???....what two integers does this whole number lie between???

Alternative "hint"

7^2  = 49

8^2 = 64

Does 53 lie between these two numbers??

Just put (3.54 x 3.68) into the calculator and hit '='......magic will occur and your answer will be in m^2

7x-15=3x-39     add 39  to both sides......subtract 7x from both sides

24 = -4x          divide both sides by -4

24 / -4  = x = -6

6 - 2x = 50       subtract 6 from both sides

-2x = 44        divide both sides by -2

x = 44 / -2  

x = -22

actually it is -6

the answer is 6 because you draw a line through the equal sign then you subtract the 15 over to the 39 which will give you 24. then subtract 3x to 7x which will give you 4x. then 4x=24, so you divide 4x to 24 and you will get you answer. x=6

Hit the"2nd" button on the calc...you will see  the asin, acos, atan which = sin-1, cos-1 and tan-1

Yep...we do some trig on here....post your question  !!!

3x+5y-8=0 that passes through the point (-8,1)

We have the form Ax + BY + C = 0  and the slope of this line is just -A/B = -3/5

And a perpendicular line will have negative reciprocal slope = 5/3

And using the point-slope form, we have

y = (5/3)(x + 8) - 1

y = (5/3)x + 40/3 - 1

y = (5/3)x + 37/3

In standard form, we have

5x - 3y + 37 = 0

Here's the graph of both lines

In this case, it's the number preceding the "x," i.e., "4"....

tan T = sin T / cos T = .5299/.8481 = 0.6248083952364108

And "T" is given by

tan^-1 (0.6248083952364108) = about 32° (± n360°)

{Verify for yourself using the inverse sine and cosine functions for the given values of sine and cosine that this is true.... !!!!}

An even three digit number will have a "2" or a '6" at the end.

So, if it has a "2"  at the end, we just want to find the number of permutes that can be formed by selecting 2 of any of the remaining 4 digits= nPr(4,2) =  12

And the same number can be made if the "6" is at the end, so that's 12 + 12 = 24

The number of even four digit numbers is similar. The  number will have a 2 or 6 at the end, and we just want to find the number of permutes that can be formed by selecting any 3 of the remaining 4 digits = nPr(4,3) = 24. And, as above, the same number can be formed if the 6 is at the end.

So, since "or" usually means "add," we have 12 + 12 + 24 + 24 = 72 total even 3 or 4 digit even numbers

It really depends on where you are going in life job wise. There are jobs out there where you  use math on a daily basis and are needed daily.

a + bi = -√2 - √2i   (the "i" isn't under the root)

The modulus is given by l z l  = √ (a^2 + b^2) = √[(-√2)^2 + (-√2)^2 ] = √(2 + 2) = √4 = 2

And the arg(z), Θ, is given by

tan^-1 (b/a) = tan ^-1 (-√2/-√2) = tan^-1(1) = 5pi/4 + n(2pi)  .... for n = 0,±1,±2, ±3, ±4...

{remember that we're in the 3rd quadrant}

12 less than y= y-12

Because y is your original number and the number you are looking for(x) is supposed to be 12 less than y.

Fo example, if y=5 then your answer would be -7 because that's 12 less than 5.

Easy solution: Look at the y first not twelve, if it say 12 less, you count off from y which goes don not up.

12-y is wrong because, you are using 12 as our original value, and you sum would be wrong.

Welcome.    

(7x3)+5=26

Steps: USE PEMDAS

Parenthesis first> (7x3)=21

Then Add> 21+5=26

112/12 = 28/3  = 9 + 1/3

Two ships leave a Port O. One ship travels on a bearing of 3400 to a point P which is 50 km from O. The other ship travels on a bearing of 0600 to a point Q, 85 km from O. (a) Draw a diagram to represent the position of the port and the two ships. On your diagram, carefully label North, the given angles and the distances travelled. (b) Calculate the distance PQ in km (c) Determine the bearing of P from Q.

I'm assuming that 3400 = 340.0    and that 0600 = 60.0

Then the angle between them is just 80°

We can use the Law of Cosines to find PQ =

PQ^2  = 85^2 + 50^2 - 2(85)(50)cos(80)

PQ^2 = 8248.9904898305

PQ = about 90.824 km

And the bearing from P to Q is given by [90 + sin-1(4.485/90.824)]° = [90 + 2.83]° = 92.83°

Here's a diagram.....("North" is at the "top' )

thank you for the help

 7

$${\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{7}} = {\mathtt{21}}$$