Answer:
To earn $10 in 1st month, the principal must be $4,000.
No, the poster cannot claim that "Open an account of $2 comma 500 and earn at least $10 interest in 1 month!".
Step-by-step explanation:
We have been given that a bank manager wants to encourage new customers to open accounts with principals of at least $2,500. He decides to make a poster advertising a simple interest rate of 3%. We are asked to find the principal to advertise that one can earn $10 the first month.
We will use simple interest formula to solve our given problem.
, where,
I = Amount of interest,
P = Principal amount,
r = Annual interest rate in decimal form,
t = Time in years.
1 month will be equal to 
.
Therefore, to earn $10 in 1st month, the principal must be $4,000.
Now, we will check if an account of $2,500 can earn at least $10 interest in 1 month.
Since the account earns an amount of $6.25 in one month, therefore, the poster is not true.
The area of a circle is A=πr².
Since π is about 3.14 we can substitute that into the equation.
So A=3.14×r²
We can substitute the given radius for r.
A= 3.14 × 5²
When a number is squared, or has the two over it, we multiply it by itself.
5 × 5= 25
A= 3.14 × 25
Simplify this and the area of the circle is about 78.5
A≈78.5
<u>Answer-</u>
<em>$23377</em><em> must be deposited to get $68000 at the end of 30 years.</em>
<u>Solution-</u>
We know that for compound interest,
Where,
A = Future amount = $68,000
P = ??
r = 3.575% annual = 0.03575
n = 4 as interest is compounded quarterly
t = time in year = 30 years
Putting the values,
Therefore, $23377 must be deposited to get $68000 at the end of 30 years.
8.1 Function of Two Variables
Many functions have several variables.
Ex. There are 3 types of football tickets. Type A costs $50, type B costs $30, and type C costs
$20. If in a match, x tickets of type A, y tickets of type B, and z tickets of type C are sold,
the total income of ticket sale is f(x, y, z) = 50x + 30y + 20z.
Def. A real-valued function of two variables f consists of
1. A domain A consisting of ordered pairs of some real numbers (x, y).
2. A rule that associates with each ordered pair in A with one real number, denoted by
z = f(x, y).
Ex. (Ex 1, p.532) f(x, y) = x + xy + y
w + 2. Compute f(0, 0), f(1, 2), and f(2, 1).
Ex. Find the domain of a. f(x, y) = x
2+y
2
, b. g(x, y) = 2
x−y
, c. h(x, y) = p
1 − x
2 − y
2.
Ex. Find the domain of g(r, s) = √
rs.
The graph of a function z = f(x, y) is the collection of all points {(x, y, f(x, y)) : x, y ∈ A}
in R
3
(Fig 5, p.534; Fig 6, p.535).
The graph of z = f(x, y) is 3 dimensional and it is difficult to draw. So we use level curves.
A level curve is the graph of
c = f(x, y)
on xy-plane for a constant c. By drawing the level curves corresponding to several admissible
values of c, we obtain a contour map. (Fig 7, p.535; Fig 8, p.536)
Ex. Ex 5, p.536.
HW. C8.1: SC1, 2, 3, Ex 31, 33
