Answer:
Consider points (-1, 0) and (0, 1) :
![{ \tt{slope = \frac{y _{2} - y _{1} }{x _{2} - x _{1} } }} \\ { \tt{slope = \frac{1 - 0}{0 - ( - 1)} }} \\ { \boxed{ \bf{slope = 1}}}](https://tex.z-dn.net/?f=%7B%20%5Ctt%7Bslope%20%3D%20%20%5Cfrac%7By%20_%7B2%7D%20%20-%20y%20_%7B1%7D%20%7D%7Bx%20_%7B2%7D%20-%20x%20_%7B1%7D%20%7D%20%7D%7D%20%5C%5C%20%7B%20%5Ctt%7Bslope%20%3D%20%20%5Cfrac%7B1%20-%200%7D%7B0%20-%20%28%20-%201%29%7D%20%7D%7D%20%5C%5C%20%7B%20%5Cboxed%7B%20%5Cbf%7Bslope%20%3D%201%7D%7D%7D)
Prove we are to prove 4(coshx)^3 - 3(coshx) we are asked to prove 4(coshx)^3 - 3(coshx) to be equal to cosh 3x
= 4(e^x+e^(-x))^3/8 - 3(e^x+e^(-x))/2 = e^3x /2 +3e^x /2 + 3e^(-x) /2 + e^(-3x) /2 - 3(e^x+e^(-x))/2 = e^(3x) /2 + e^(-3x) /2 = cosh(3x) = LHS Since y = cosh x satisfies the equation if we replace the "2" with cosh3x, we require cosh 3x = 2 for the solution to work.
i.e. e^(3x)/2 + e^(-3x)/2 = 2
Setting e^(3x) = u, we have u^2 + 1 - 4u = 0
u = (4 + sqrt(12)) / 2 = 2 + sqrt(3), so x = ln((2+sqrt(3))/2) /3, Or u = (4 - sqrt(12)) / 2 = 2 - sqrt(3), so x = ln((2-sqrt(3))/2) /3,
Therefore, y = cosh x = e^(ln((2+sqrt(3))/2) /3) /2 + e^(-ln((2+sqrt(3))/2) /3) /2 = (2+sqrt(3))^(1/3) / 2 + (-2-sqrt(3))^(1/3) to be equ
= 4(e^x+e^(-x))^3/8 - 3(e^x+e^(-x))/2
= e^3x /2 +3e^x /2 + 3e^(-x) /2 + e^(-3x) /2 - 3(e^x+e^(-x))/2
= e^(3x) /2 + e^(-3x) /2
= cosh(3x)
= LHS
<span>Therefore, because y = cosh x satisfies the equation IF we replace the "2" with cosh3x, we require cosh 3x = 2 for the solution to work. </span>
i.e. e^(3x)/2 + e^(-3x)/2 = 2
Setting e^(3x) = u, we have u^2 + 1 - 4u = 0
u = (4 + sqrt(12)) / 2 = 2 + sqrt(3), so x = ln((2+sqrt(3))/2) /3,
Or u = (4 - sqrt(12)) / 2 = 2 - sqrt(3), so x = ln((2-sqrt(3))/2) /3,
Therefore, y = cosh x = e^(ln((2+sqrt(3))/2) /3) /2 + e^(-ln((2+sqrt(3))/2) /3) /2
= (2+sqrt(3))^(1/3) / 2 + (-2-sqrt(3))^(1/3)
Answer:
cite,evidence,cite,evidence, summary it basically means answer the question give evidence from the story explain do it again and then sum up your writing, i hope this is right.
Step-by-step explanation:
Answer:
10.68
Step-by-step explanation:
8.9*1.2
Answer:
gradient is 5
Step-by-step explanation:
x intercept, replace y with 0
y +5x= 13
0+ 5x =13
0 - 13= -5x
-13= -5x
-13/-5 = -5x/-5
x = 13/5
y intercept, replace x with 0
y+5x=13
y+5(0)=13
y+0=13
y =13