hi! can someone please help me with these questions please? thanks! 4) The half-
ID: 2833797 • Letter: H
Question
hi! can someone please help me with these questions please? thanks!
4)
The half-life of Radium-226 is 1590 years. If a sample contains 100 mg, how many mg will remain after 3000 years? If 4000 dollars is invested in a bank account at an interest rate of 8 per cent per year, find the amount in the bank after 7 years if interest is compounded annually Find the amount in the bank after 7 years if interest is compounded quaterly Find the amount in the bank after 7 years if interest is compounded monthly Finally, find the amount in the bank after 7 years if interest is compounded continuously Given that f(x) = x10h(x) h(-1) = 3 h'(-1) = 6 Calculate The altitude of a triangle is increasing at a rate of 1.000 centimeters/minute while the area of the triangle is increasing at a rate of 2.500 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 8.000 centimeters and the area is 96.000 square centimeters? Draw yourself a general "representative" triangle and label the base one variable and the altitude (height) another variable. Note that to solve this problem you don't need to know how big nor what shape the triangle really is.Explanation / Answer
(1)
The first calculation is correct, but the second responder is correct that the half-life of radium 226 is 1620 years. We have
A = Ao*(1/2)^(t/T) Where Ao is the original amount, A is the amount left, t is the elapsed time, and T is the half-life.
Plugging the numbers into the equation we have:
A = 100(1/2)^(3000/1620)
=27.7 grams
(2)
A)
If 4000 dollars is invested in a bank account at an interest rate of 8 per cent per year,
find the amount in the bank after 7 years if interest is compounded annually = 400(1+8/1000)7
=$6855.3
B)
Find the amount in the bank after 7 years if interest is compounded quarterly = 4000(1+8/400)28
=$6964.097
C)
Find the amount in the bank after 7 years if interest is compounded monthly = 4000(1+8/1200)84
=$6989.69
(3)
df/dx=(10x^9)h(x)+h'(x)[x^10], plug in what we're given
df/dx(x=-1)=[10(-1)^9]*h(-1)+h'(-1)[(-...
df/dx(=-1)=-10(3)+6(1)
df/dx(x=-1)=-24
(4)
A = (1/2)bh
when A = 96
96 = (1/2)b(8)
b = 96/(4)
b = 24 cm
dA/dt = (1/2)b * (dh/dt) + (1/2)h * (db/dt)
2.5 = (1/2)(24)*(1) + (1/2)(8)*(db/dt)
2.5 = 12 + 4(db/dt)
db/dt = (2.5-12)/4
db/dt = -2.375 cm/s
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.