Perimeter = 2 ( width + length)
294 = 2 (56 + length)
294/2 = 56 + length
147 = 56 + length
147 - 56 = length
91 = length
so the length is 91 feet
Answer:
3x−4y=9 −3x+2y=9
Add these equations to eliminate x: −2y=18
Then solve−2y=18
for y: −2y=18 −2y −2 = 18 −2 (Divide both sides by -2)
y=−9
Now that we've found y let's plug it back in to solve for x.
Write down an original equation: 3x−4y=9
Substitute−9for y in 3x−4y=9: 3x−(4)(−9)=9
3x+36=9(Simplify both sides of the equation)
3x+36+−36=9+−36(Add -36 to both sides)
3x=−27 3x 3 = −27 3 (Divide both sides by 3) x=−9
Answer: x=−9 and y=−9
Hope This Helps!!!
Not quite sure about #1 but x=58°
Answer:
81x+2
Step-by-step explanation:
2x+x=3x
3×3×3×3=81x
(a) Assuming that Q satisfies the differential equation Q' = -rQ, determine the decay constant r for carbon-14. (b) Find an expression for Q(t) at any time t, if Q(0) = Qo. (c) Suppose that certain remains are discovered in which the current residual amount of carbon-14 is 20% of the original amount. Determine the age of these remains.
Answer:
a) r = (In 2)/(t1/2) = (In 2)/5730 = 0.000121/year
b) Q(t) = Q₀ (e^-rt)
c) Are of the 20% remnant of Carbon-14 = 13301.14 years.
Step-by-step explanation:
Q' = -rQ
Q' = dQ/dt
dQ/dt = -rQ
dQ/Q = -rdt
Integrating the left hand side from Q₀ to Q₀/2 and the right hand side from 0 to t1/2 (half life, t1/2 = 5730 years)
In ((Q₀/2)/Q₀) = -r(t1/2)
In (1/2) = -r(t1/2)
In 2 = r(t1/2)
r = (In 2)/(t1/2) = (In 2)/5730 = 0.000121 /year
b) Q' = -rQ
Q' = dQ/dt
dQ/dt = -rQ
dQ/Q = -rdt
Integrating the left hand side from Q₀ to Q(t) and the right hand side from 0 to t.
In (Q(t)/Q₀) = -rt
Q(t)/Q₀ = e^(-rt)
Q(t) = Q₀ (e^-rt)
c) Q(t) = Q₀ (e^-rt)
Q(t) = 0.2Q₀, t = ? and r = 0.000121/year
0.2Q₀ = Q₀ (e^-rt)
0.2 = e^-rt
In 0.2 = -rt
-1.6094 = - 0.000121 × t
t = 1.6094/0.000121 = 13301.14 years.
Hope this Helps!
