All Answers 358150 Answers

Always happy to save a life.......or even bail somebody out on Trig homework..LOL!!!

The word slope (gradient, incline, pitch) is used to describe the measurement of the steepness of a straight line.  The higher the slope, the steeper the line.  The slope of a line is a rate of change.

Thank you so much Chris! You saved my life!

Sorry, but

-5^2  = -1(5)^2 = -1*25 = -25

The exponent only applies to the 5, not to the "understood" -1 out front.

Note however.......

(-5)^2  = (-1*5)^2  = (-1)^2*(5)^2 = 1 * 25  = 25

The exponent applies to both the 5 and the "understood" -1 in front.

1. cos² x(1 + tan² x) = 1
2. sec x tan x(1 – sin² x) = sin x
3. csc x(2sin x - √2) = 0
4. cos²(2x) – sin²(2x) = 0
5. sin² θ csc² θ = sin² θ + cos² θ

-----------------------------------------------------------------------------------------------

1.  cos^2x (1 +tan^2x)  = 1  ???

     cos^2x (sec^2x)  = 1

     cos^2x(1/cos^2x) = 1   identity

2.  secx tanx (cos^2x)  = sinx ??? 

(1/cosx)(sinx/cosx)(cos^2x)  = sinx

[(sinx)/(cos^2x)]cos^2x  = sinx

sinx = sinx     identity

3 and 4 aren't indentites...these are equations....some values of x may make them true, but not all values 

5. sin^2x csc^2x  = sin^2x + cos^2x  ???

sin^2x(1/sin^2x)  = 1

1 = 1   identity

$$\small{\text{
$
\begin{array}{|c|c|c|c|c|c|c|c|}
\hline
\mathrm{child} & #1 & #2 & #3 & #4 & #5 & #6 & #7 \\
\hline
#1 & x & \textcolor[rgb]{1,0,0}{(1,2)} & \textcolor[rgb]{1,0,0}{(1,3)} & \textcolor[rgb]{1,0,0}{(1,4)} & \textcolor[rgb]{1,0,0}{(1,5)} & \textcolor[rgb]{1,0,0}{(1,6)} & \textcolor[rgb]{1,0,0}{(1,7)} \\
\hline
#2 & & x & \textcolor[rgb]{1,0,0}{(2,3)} & \textcolor[rgb]{1,0,0}{(2,4)} & \textcolor[rgb]{1,0,0}{(2,5)} & \textcolor[rgb]{1,0,0}{(2,6)} & \textcolor[rgb]{1,0,0}{(2,7)} \\
\hline
#3 & & & x & \textcolor[rgb]{1,0,0}{(3,4)} & \textcolor[rgb]{1,0,0}{(3,5)} & \textcolor[rgb]{1,0,0}{(3,6)} & \textcolor[rgb]{1,0,0}{(3,7)} \\
\hline
#4 & & & & x & \textcolor[rgb]{1,0,0}{(4,5)} & \textcolor[rgb]{1,0,0}{(4,6)} & \textcolor[rgb]{1,0,0}{(4,7)} \\
\hline
#5 & & & & & x & \textcolor[rgb]{1,0,0}{(5,6)} & \textcolor[rgb]{1,0,0}{(5,7)} \\
\hline
#6 & & & & & & x & \textcolor[rgb]{1,0,0}{(6,7)} \\
\hline
#7 & & & & & & & x \\
\hline
\end{array}=\textcolor[rgb]{1,0,0}{(21)} \ \mathrm{handshakes}
$}}$$

Well, MG1....I'll take the plunge, here.

Note that the first child shakes 6 other hands.

The second child shakes 5 other hands - he/she has already shaken the hand of the first child.

The third child shakes 4 other hands.....since he/she has already shaken the hand of the first two.

So, continuing likewise, we have.....

6 + 5 + 4 +.....+ 1   =   (6)(7)/2   = 21 handshakes in all

$${\mathtt{3}}{\mathtt{\,\small\textbf+\,}}{\mathtt{4}} = {\mathtt{7}}$$

We would have to know the y value associated with each x value to know which one(s) best approximated the root(s).

You just type it into the calculator. 

1/2

$${\frac{{\mathtt{1}}}{{\mathtt{2}}}} = {\mathtt{0.5}}$$

4*5=20

$${\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{5}} = {\mathtt{20}}$$

Thanks, MG1.....i might could have gotten "whole" numbers had I made some different assumptions, but.....like I said...it's pretty close....

The answer is 5.196

9+10=19, but for silly people it's 21

I love Math.I'm good at it for my  age and maths refers to everything/

$${\mathtt{29}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6}}{\mathtt{\,\small\textbf+\,}}{\mathtt{10}}{\mathtt{\,\small\textbf+\,}}{\mathtt{17}}{\mathtt{\,\small\textbf+\,}}{\mathtt{5}}{\mathtt{\,\small\textbf+\,}}{\mathtt{31}}{\mathtt{\,\small\textbf+\,}}{\mathtt{47}}{\mathtt{\,\small\textbf+\,}}{\mathtt{54}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6}}{\mathtt{\,\small\textbf+\,}}{\mathtt{42}}{\mathtt{\,\small\textbf+\,}}{\mathtt{24}}{\mathtt{\,\small\textbf+\,}}{\mathtt{53}} = {\mathtt{330}}$$

1 1/2 divided by 1/2

$$\dfrac{
1\frac{1}{2} }
{\frac{1}{2} }\\\\
=\dfrac{
1+\frac{1}{2} }
{\frac{1}{2} }\\\\
=\dfrac{ 1 } {\frac{1}{2} }
+\dfrac{ \frac{1}{2} } {\frac{1}{2} }\\\\
=\dfrac{ 1 } {\frac{1}{2} }
+1\\\\
=1\cdot \frac{2}{1} }
+1\\
= 2+1\\
=3$$

or

$$\dfrac{
1\frac{1}{2} }
{\frac{1}{2} }\\\\
=
\dfrac{
\frac{3}{2} }
{\frac{1}{2}
}\\\\
=
\frac{3}{2} \cdot
\frac{2}{1} \\
=3$$

For the title = 19.

For the question=1

9+10=19 , but if you want to be silly 21.

Thanks guys, your explanations were really helpful. I'm however still stuck on the third one :/

Nice workings CPhill!

19 because that vine is stupid

It is the eighth number 45

100%......you would search around the bag and find the one thing that wouldn't stick you......that thing would have to be the marble.....you would then draw it out of the bag...