To calculate the value of the half life we proceed as follows;
a/2=ae^(-2.360t)
the a(s) will cancel and we shall remain with:
1/2=e^-2.360t
introducing the natural logs we get:
ln (1/2)=ln e^(-2.360t)
ln(1/2)=-2.360t
hence;
t=(ln 0.5)/(-2.360)
t=0.294
the answer is t=0.294
Simplifying
10 = 2r + -8
Reorder the terms:
10 = -8 + 2r
Solving
10 = -8 + 2r
Solving for variable 'r'.
Move all terms containing r to the left, all other terms to the right.
Add '-2r' to each side of the equation.
10 + -2r = -8 + 2r + -2r
Combine like terms: 2r + -2r = 0
10 + -2r = -8 + 0
10 + -2r = -8
Add '-10' to each side of the equation.
10 + -10 + -2r = -8 + -10
Combine like terms: 10 + -10 = 0
0 + -2r = -8 + -10
-2r = -8 + -10
Combine like terms: -8 + -10 = -18
-2r = -18
Divide each side by '-2'.
r = 9
Simplifying
r = 9
Answer:
y=447.3 pounds
x= 297.3 pounds
Step-by-step explanation:
Step one:
given data
Tea A costs $9 per pound and
Tea B cost $6 per pound.
let the number of pounds of Tea A be x
and for Tea B be y pounds
The total cost of the mixture = $8 per pound
hence
9x+6y=8---------1
The total weight of the mixture
150 pounds
x+y=150-----------2
Step two:
9x+6y=8---------1
x+y=150---------2
from eqn 2 x=150-y
put x= 150-y in eqn 1
9(150-y)+6y=8---------1
1350-9y+6y=8
1350-8=9y-6y
1342=3y
divide both sides by 3
y= 1342/3
y=447.3 pounds
put y= 447.3 in eqn 2
x+447.3= 150
x= 150-446=7.3
x= -297.3
x= 297.3 pounds
Make 3 2/9 improper fraction
3 2/9 = 29/9
29/9 * 3/5 = 87/45 = 29/15
The answer is 29/15
x - y = 14
given the ratio x : y = 5 : 3
then let x = 5x and y = 3x, hence equation can be expressed as
5x + 3x = 56
8x = 56 ( divide both sides by 8 )
x = 7
Hence x = 5 × 7 = 35 and y = 3 × 7 = 21
Thus x - y = 35 - 21 = 14
