Let p(x)=x^3+2x^2+kx+3
On dividing p(x) by x-3, the remainder is 21. Therefore,
P(3)=21
Substituting x=3 in p(x)
P(3)=3^3 +2*(3)^2+k*3+3
=27+18+3k+3
=48+3k
We know that, p(3)=21.
So, 48+3k=21
3k=21-48
3k=-27
k=-27/3 =-9
now, p(x) =x^3+2x^2-9x-18
-2 is a factor of p(x) on inspection. Therefore, divide p(x) by x+2 to find the
zeroes of the polynomial.
On dividing, we get the factors to be, (x^2-9)(x+2)
(x^2-3^2)(x+2)
Factorizing using the identity a^2-b^2=(a+b)(a-b) we get,
(x+3)(x-3)(x+2)
Therefore, the zeroes of the polynomials are -3,+3 and -2.
1/5 using the slope formula
The formula used for this is the same one used to find interest accrued in a bank account that compounds continuously. The only difference is that our r here, the rate, is a negative number because the carbon is deteriorating over time, whereas money grows over time. That formula is this one:
where A is what's left in the end, P is the initial amount of carbon, r is the rate at which it deteriorates (sometimes a k in other formulas, but same thing!) and t is the time in years. For us, that formula, filled in, looks like this:
First thing to do is to simplify that multiplication involving the exponents. Doing that gives us:
On your calculator, you have a 2nd button and an LN button. If you push 2nd and then LN you get this in your display:
and it's up to you to add the exponent on the e. Our exponent is the -.516. So do that and then multiply that result by 32 to get that your answer is 19.1 g of carbon remaining.
6 and 1/6 because 37 divided by 6 equals 6 R 1
The answer should be 21 hope it helps