Answer:
n = -7,6
Step-by-step explanation:
n(n+1)+3=45
distributive property: a(b+c) = ab+ac
n²+n+3 = 45
n²+n -42 = 0
factor now
(n+7)(n-6) = 0
n = -7,6
So it tells us that g(3) = -5 and g'(x) = x^2 + 7.
So g(3) = -5 is the point (3, -5)
Using linear approximation
g(2.99) is the point (2.99, g(3) + g'(3)*(2.99-3))
now we just need to simplify that
(2.99, -5 + (16)*(-.01)) which is (2.99, -5 + -.16) which is (2.99, -5.16)
So g(2.99) = -5.16
Doing the same thing for the other g(3.01)
(3.01, g(3) + g'(3)*(3.01-3))
(3.01, -5 + 16*.01) which is (3.01, -4.84)
So g(3.01) = -4.84
So we have our linear approximation for the two.
If you wanted to, you could check your answer by finding g(x). Since you know g'(x), take the antiderivative and we will get
g(x) = 1/3x^3 + 7x + C
Since we know g(3) = -5, we can use that to solve for C
1/3(3)^3 + 7(3) + C = -5 and we find that C = -35
so that means g(x) = (x^3)/3 + 7x - 35
So just to check our linear approximations use that to find g(2.99) and g(3.01)
g(2.99) = -5.1597
g(3.01) = -4.8397
So as you can see, using the linear approximation we got our answers as
g(2.99) = -5.16
g(3.01) = -4.84
which are both really close to the actual answer. Not a bad method if you ever need to use it.
Answer:
The amount of Kroner that can be bought from 1/5 of one dollar.
Step-by-step explanation:
We have been given that goods that cost 1/5 of one dollar in the U.S. cost one kroner in Denmark. We are asked to find the the real exchange rate that would be computed as how many Danish goods per U.S. goods.
The real exchange rate tells us how much foreign currency can be exchanged for a unit of domestic currency.
It also tells us that how much the goods and services in the domestic country can be exchanged for the goods and services in a foreign country.
Therefore, the real exchange rate would be the amount of Kroner that can be bought from 1/5 of one dollar.
Rewrite the expression on the left using the distributive property
Hey there!
Your answer is 6n.
"Product of" represents multiplication. So, we can do a number times 6, or "6n".
Have a terrificly amazing day! :D
