Answer:
x = 2 + sqrt(5) or x = 2 - sqrt(5)
Step-by-step explanation using the quadratic formula:
Solve for x over the real numbers:
7 (x^2 - 4 x - 1) = 0
Divide both sides by 7:
x^2 - 4 x - 1 = 0
Add 1 to both sides:
x^2 - 4 x = 1
Add 4 to both sides:
x^2 - 4 x + 4 = 5
Write the left hand side as a square:
(x - 2)^2 = 5
Take the square root of both sides:
x - 2 = sqrt(5) or x - 2 = -sqrt(5)
Add 2 to both sides:
x = 2 + sqrt(5) or x - 2 = -sqrt(5)
Add 2 to both sides:
Answer: x = 2 + sqrt(5) or x = 2 - sqrt(5)
Answer:
Jeremy Will have more than just $200 to spend on Christmas presents.
Explanation :
He has a total of $1200.
He spends a $120 for car insurance. (1)
He needs to spend $25 a week for lunch. He has to do this for 16 weeks so 25*16 = $400. (2)
He needs to spend $20 a week for entertainment. For 16 weeks that'll be 20*16 = $320 (3)
adding (1) (2) and (3)
We get Jeremy's total spending will be $840. Jeremy has $1200.
1200-840 = $360
So Jeremy will have $360 to spend on Christmas present.
3r+n2−r+5−2n+2<span />=3r+n2+−r+5+−2n+2=3r+n2+−r+5+−2n+2<span />=(n2)+(−2n)+(3r+−r)+(5+2)<span />=n2+−2n+2r+7<span /><span />
=n2−2n+2r+7
Answer:
Q(t) = Q_o*e^(-0.000120968*t)
Step-by-step explanation:
Given:
- The ODE of the life of Carbon-14:
Q' = -r*Q
- The initial conditions Q(0) = Q_o
- Carbon isotope reaches its half life in t = 5730 yrs
Find:
The expression for Q(t).
Solution:
- Assuming Q(t) satisfies:
Q' = -r*Q
- Separate variables:
dQ / Q = -r .dt
- Integrate both sides:
Ln(Q) = -r*t + C
- Make the relation for Q:
Q = C*e^(-r*t)
- Using initial conditions given:
Q(0) = Q_o
Q_o = C*e^(-r*0)
C = Q_o
- The relation is:
Q(t) = Q_o*e^(-r*t)
- We are also given that the half life of carbon is t = 5730 years:
Q_o / 2 = Q_o*e^(-5730*r)
-Ln(0.5) = 5730*r
r = -Ln(0.5)/5730
r = 0.000120968
- Hence, our expression for Q(t) would be:
Q(t) = Q_o*e^(-0.000120968*t)
Answer:
11 pencils
Step-by-step explanation:
Subrtact $2.10 from $6 which equals 3.9 then divide 3.9 by $.35 which equalls 11.14 then round which gets you 11 pencils.