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You have the rght idea, HiylinLink...but the ladder length is actually the hypotenuse of a right triangle

So....it reaches

√ [ 12^2 - 3^2 ]  =

√ 144 - 9 ]   =

√135 ≈  

11.6 ft

3. This system has one solution

y= 8x-14

Y=x^2+4x-10 

what is the Y coordinate of the solution? 

x^2 + 4x - 10 =  8x - 14

x^2 - 4x + 4 = 0

(x - 2) ^2 = 0

x = 2

And y =  8(2) - 14  =   2

2. What are the real solutions to the system of equations? 

Y= X^2 - 5x+ 6 

Y= -4x+6

Set the y's qual and we have

x^2 - 5x + 6 = -4x + 6      simplify

x^2 - x = 0  factor

x ( x - 1 ) = 0

Setting both factors to 0 and solving for x produces

x = 0     or   x  = 1

So....the solutions are  ( 0, 6)  and ( 1, 2)

Using quadratic formula, you get these 2 roots for your equation:

x = 1/14 (1 + sqrt(85))    and       x = 1/14 (1 - sqrt(85))

But evaluating them as 2 sequences, both of them DIVERGE, because of 1 added at the beginning!. If you remove it, then they CONVERGE to -1

The circumference of the whole circle =  2pi * 3 = 6 pi cm

So

2/3 pi / 6pi =     measure of angle RHT / 360

2/18 = 1/9 =  measure of angle RHT /360

360 (1/9) =  measure of angle RHT

40° =   measure of angle RHT

And angle RST is an inscribed angle = 1/2 RHT  =  20°

pi / 6  rads = 30°

So...this sector is 1/12 the total area of the circle =  3 in ^2

This distance will be the diagonal of a square with a side of 27.5 m

The diagonal =   √2 * side length  = √2 * 27.5 = 38.89 m

42 x 15%/100% = $6.30

Nice, bigbrotheprodude.....!!!!

The circumference of the circle will be     2pi (5) = 10 pi cm

So the measure of arc RST can be found as

(25/3) pi /  [10 pi  ]  = arc RST / 360

25/30 = arc RST / 360

5/6  = arc RST /360

(5/6)360 = arc RST

300° = arc RST

Then minor arc RT = 60°

And since angle RST is an inscribed angle intercepting minor arc RT, its measure is (1/2) 60° = 30°

Just as bigbrotheprodude  found....!!!!

Given the major arc and the minor arc share the same chord, the angle RST will be:
∠RST=1/2∠RHT
∠RHT=1/3π=1/3×180=60
hence
∠RST=1/2×60=30°

 Answer: 30°
 

This is  a geometric series with a  common ratio of x

So we have that....using the sum of an infinite geometric series.....

4 / ( 1 - x) > 8

4 > 8 ( 1 - x)

4 > 8 - 8x

8x > 4

x > 1/2

However    x must also be < 1

So the solution is

(1/2 , 1 )

The circumference is also tripled.

Third time this has been posted in the last few minutes...

https://web2.0calc.com/questions/help_3472

This was the formal weapon of a Jedi Knight. Not as clumsy or random as a blaster. More skill than simple sight was required for its use. An elegant weapon. It was a symbol as well. Anyone can use a blaster or a fusion cutter — but to use a lightsaber well was a mark of someone a cut above the ordinary

Forms a right angle = 90°

(3 + 2i) ( 4 + i)  =

4(3 + 2i) + i  ( 3 + 2i)  =

12 + 8i + 3i + 2i^2   =

12 + 11i + 2(-1) 

10 + 11i

(5 -  2i)^3  =

(5 - 2i) ( 5 - 2i) ( 5 - 2i) =

(25 - 5*2i - 5*2i + 4i^2) ( 5 - 2i) =

(25 - 20i + 4(-1) ) ( 5 - 2i) =

(21 - 20i) ( 5 - 2i) =

(105  - 100i - 42i + 40i^2 ) =

(105 - 142 i + 40(-1) ) =

 65 - 142 i 

(a + bi) ( a - bi)  =

a^2  + abi - abi - b^2i^2 =

a^2 - b^2(-1) =

a^2 + b^2

The radius at the point of tangency is perpendicular to the tangent line. Secant – a line that intersects a circle at two points. Inscribed Angle - an angle made from points sitting on the circle's edge.

We want to know   when t  produces a min height

Note that a t = 0, the height = 100 ft

So....the t that produces a min height is given by   - (-60) / (2 * 10)  =  60 / 20  =   3 seconds