Answer:
Step-by-step explanation:
Eight
590 = 1800 e^(-0.4t) Divide by 1800
0.32778 = e^(-0.4t) Put the value for e in the denominator.
0.32778 = 1 / e^(0.4t) Notice the sign's gone. Multiply both sides by e^(0.4t)
0.32778 *e^(0.4t) = 1 Divide by 0.32778
e^(0.4t) = 3.0508 Take the natural log of both sides.
0.4t = 1.11542 Divide both sides by 0.4
t = 2.78855
You should put this in the original equation to see if it checks. It does.
=============================
Nine
3^(3 - 3x) + 6 = 42 Subtract 6 from both sides
3^(3 - 3x) = 36 Take the log of both sides.
(3 - 3x) ln(3) = ln 36
(3 - 3x) *1.098612 = 3.58352 Divide by 1.098612
3 - 3x = 3.26186 Subtract 3 from both sides
- 3x = 0.26186 Divide by - 3
x = - 0.087287
The intervals refer to the x values where the function (graph) is increasing which means the y values are getting larger from left to right. Parantheses are used not brackets (parantheses means it doesn't include the value and brackets mean it does) so here the intervals would be
( negative infinity , -3)U( -3, 0 )
Answer: If the point of the circle P has coordinates: P=(x,y)
sine (Angle) = y/r
cosine (Angle) = x/r
tangent (Angle) = y/xw
where r=sqrt(x^2+y^2) is the radius of the circle
Example:
P=(3,4)=(x,y); x=3 and y=4
Radius of the circle: r
r=sqrt(x^2+y^2)
r=sqrt(3^2+4^2)
r=sqrt(9+16)
r=sqrt(25)
r=5
sin(Angle)=y/r
sin(Angle)=4/5
cosine(Angle)=x/r
cosine(Angle)=3/5
tangent(Angle)=y/x
tangle(Angle)=4/3
1 pie is cut into eighths or 1/8 a slice. 3 are taken out.
8/8-3/8=5/8 is left.
