Atotal of $2,000 is invested at an annual interest rate of 2%. find the balance in the account after
10 years if it is compounded continuously (round to the nearest dollar).

The balance in the account after 10 years is US$ 2,442.81

Step-by-step explanation:

1. Let's review the data given to us for answering the question:

Investment amount = US$ 2,000

Duration of the investment = 10 years

Annual interest rate = 2% compounded continuously

2. Let's find the future value of this investment after 10 years, using the following formula:

FV = PV * eˣ ⁿ

PV = Investment = US$ 2,000

number of periods (n) = 10 (10 years compounded continuously)

rate (x) = 2% = 0.02

e = 2.71828 (Euler's number)

Replacing with the real values, we have:

FV = 2,000 * (2.71828)^0.02*10

FV = 2,000 * 2.71828^0.2

FV = 2,000 * 1.2214027

FV = US$ 2,442.81

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).