Answer:
2x+1
Step-by-step explanation:
x = 1st integer
x+1 = next consecutive integer
The sum is
x+ (x+1)
Combine like terms
2x+1
Follow pemdas. Evaluate operations in parentheses first.
2*(-7)+14-4
Then multiply
-14+14-4
Then add and subtract from left to right
-14+14=0
0-4=-4
Final answer: -4
If f(x) has an inverse on [a, b], then integrating by parts (take u = f(x) and dv = dx), we can show

Let
. Compute the inverse:
![f\left(f^{-1}(x)\right) = \sqrt{1 + f^{-1}(x)^3} = x \implies f^{-1}(x) = \sqrt[3]{x^2-1}](https://tex.z-dn.net/?f=f%5Cleft%28f%5E%7B-1%7D%28x%29%5Cright%29%20%3D%20%5Csqrt%7B1%20%2B%20f%5E%7B-1%7D%28x%29%5E3%7D%20%3D%20x%20%5Cimplies%20f%5E%7B-1%7D%28x%29%20%3D%20%5Csqrt%5B3%5D%7Bx%5E2-1%7D)
and we immediately notice that
.
So, we can write the given integral as

Splitting up terms and replacing
in the first integral, we get

For this case we have a function of the form:

Where,
A: initial amount
b: decrease rate
x: time in years
Substituting values we have:

For 2010 we have:
Answer:
an exponential decay function to model this situation is:
y = 1300 * (0.97) ^ x
The population in 2010 is:
y = 1083
Answer:
Vector equation:

Parametric equations:



Step-by-step explanation:
The line is parallel to the vector 3i + 2j − k.
So the vector of this line is a multiple of this vector, so i will use 6i + 4j - 2k.
The line goes through the point (4, 2.1, 3.1).
So the parametric equations are:



The vector equation is:
